Pauling, Linus
1989-01-01
A doubly icosahedral complex involves roughly spherical clusters of atoms with icosahedral point-group symmetry, which are themselves, in parallel orientation, icosahedrally packed. These complexes may form cubic crystallites; three structures of this sort have been identified. Analysis of electron diffraction photographs of the decagonal quasicrystal Al6Pd has led to its description as involving pentagonal twinning of an orthorhombic crystal with a = 51.6 , b = 37.6 , and c = 33.24 , with about 4202 atoms in the unit, comprising two 1980-atom doubly icosahedral complexes, each involving icosahedral packing of 45 44-atom icosahedral complexes (at 0 0 0 and 1/2 1/2 1/2) and 242 interstitial atoms. The complexes and clusters are oriented with one of their fivefold axes in the c-axis direction. Images PMID:16594092
Ellzey, M L; Villagran, Dino
2003-01-01
Generating relations and irreducible representations are given for the icosahedral point group, I(h), that are suited to computerized projection of symmetry-adapted bases of arbitrary spaces invariant to the group. With 120 elements I(h ) is a good prototype for symmetry-adaptation to a large finite nonabelian group. The four- and five-dimensional irreducible representations are obtained by coupling direct products of the three-dimensional irreducible representations using the symmetry-adaptation algorithm. The method is applied to the Hckel treatment of icosahedral C(20) fullerene. PMID:14632422
Pauling, Linus
1988-01-01
A 780-atom primitive tetragonal unit with edges 27.3, 27.3, and 12.6 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. PMID:16593915
Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold
Parity-time symmetry broken by point-group symmetry
Fernndez, Francisco M., E-mail: fernande@quimica.unlp.edu.ar; Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), Divisin Qumica Terica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)] [INIFTA (UNLP, CCT La Plata-CONICET), Divisin Qumica Terica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrdinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrdinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Size-dependent fivefold and icosahedral symmetry in silver clusters
Xing Xiaopeng; Danell, Ryan M.; Burns, Michael M.; Parks, Joel H. [Rowland Institute at Harvard, 100 Edwin H. Land Boulevard, Cambridge, Massachusetts 02142 (United States); Garzon, Ignacio L.; Michaelian, Karo [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, A.P. 20-364, 01000 Mexico, DF (Mexico); Blom, Martine N. [Institut fuer Nanotechnologie, Forschungszentrum Karlsruhe, Postfach 3640, 76021 Karlsruhe (Germany)
2005-08-15
Trapped ion electron diffraction measurements on silver cluster cations, Ag{sub n}{sup +} for sizes n=36-46,55 at {approx}120 K describe an evolution in structural symmetry with increasing cluster size. Diffraction patterns characterize fivefold symmetry at smaller sizes which evolves to icosahedral symmetry at n=55. Low energy isomer structures were identified by statistical search methods and optimized by density-functional calculations. Comparison of diffraction data with these theoretical structures confirms the presence of local order having fivefold symmetry for sizes n=36-39,43 and global order having icosahedral symmetry at the closed shell size n=55.
Symmetry, stability, and diffraction properties of icosahedral crystals
Bak, P.
1985-01-01
In a remarkable experiment on an Mn-Al alloy, Shechtman et al. observed a diffraction spectrum with icosahedral symmetry. This is inconsistent with discrete translational invariance since the symmetry includes a five-fold axis. In this paper, it is shown that the crystallography and diffraction pattern can be described by a six-dimensional space group. The crystal structure in 3d is obtained as a cut along a 3d hyperplane in a regular 6d crystal. Displacements of the 6d crystal along 6 orthogonal directions define 6 continuous symmetries for the icosahedral crystal, three of which are phase symmetries describing internal rearrangements of the atoms.
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.
Cao, Wenwu
Allowed mesoscopic point group symmetries in domain average engineering of perovskite ferroelectric average engineering in proper ferroelectric systems arising from the cubic Pm3m symmetry perovskite4 Both solid solution systems have a perovskite structure. Poling along one of the pseudocubic axes
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
Katharyn E. K. Nottis; Margaret E. Kastner
2005-01-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four students in a sophomore-level inorganic chemistry class at a small private university were divided by
Perturbation theory by the moment method and point-group symmetry
Francisco M. Fernndez
2014-09-14
We analyze earlier applications of perturbation theory by the moment method (also called inner product method) to anharmonic oscillators. For concreteness we focus on two-dimensional models with symmetry $C_{4v}$ and $C_{2v}$ and reveal the reason why some of those earlier treatments proved unsuitable for the calculation of the perturbation corrections for some excited states. Point-group symmetry enables one to predict which states require special treatment.
Paris-Sud XI, Universit de
1835 Crystallography of quasicrystals ; application to icosahedral symmetry L. S. Levitov (1) and J dimension is 6. The case of icosahedral crystallography is worked out in detail. A complete classification.14D - 61.50E 1. Introduction. Quasicrystals are well known to have crystallographi- cally forbidden
Pentagonal and icosahedral order in rapidly cooled metals.
Nelson, D R; Halperin, B I
1985-07-19
The discovery of an alloy of aluminum and manganese with sharp Bragg diffraction spots and an icosahedral point group symmetry was announced last year. The icosahedral symmetry appears to be an intrinsic property of the material and not an artifact of twinning. There are remarkable similarities between the observed diffraction patterns and aperiodic tesselations of space called Penrose tiles. The relation between the experiments and Penrose tiles, as well as phenomenological descriptions of the icosahedral aluminum-manganese alloy as a superposition of incommensurate density waves, are reviewed. Other types of exotic crystallography are also discussed. PMID:17759134
Pentagonal and icosahedral order in rapidly cooled metals
NASA Astrophysics Data System (ADS)
Nelson, D. R.; Halperin, B. I.
1985-07-01
The discovery of an alloy of aluminum and manganese with sharp Bragg diffraction spots and an icosahedral point group symmetry was announced last year. The icosahedral symmetry appears to be an intrinsic property fo the material and not an artifact of twinning. There are remarkable similarities between the observed diffraction patterns and aperiodic tesselations of space called Penrose tiles. The relation between the experiments and Penrose tiles, as well as phenomenological descriptions of the icosahedral aluminum-manganese alloy as a superposition of incommensurate density waves, are reviewed. Other types of exotic crystallography are also discussed.
Superlattice ordering of cubic symmetry in an icosahedral Al-Pd-Mn phase
M. Audier; M. Duneau; M. De Boissieu; M. Boudard; A. Letoublon
1999-01-01
A new Al-Pd-Mn phase, called F2M, and its reversible transformation with an icosahedral structure at high temperature have been identified in a previous synchrotron X-ray diffraction study (de Boissieu et al. 1998, Phil. Mag. A, 78, 305). From the present results of a transmission electron microscopy study, it is shown that such a phase exhibits a cubic symmetry with local
Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Fuji, Yohei; Pollmann, Frank; Oshikawa, Masaki
2015-05-01
The ground state of the S =1 antiferromagnetic Heisenberg chain belongs to the Haldane phasea well-known example of the symmetry-protected topological phase. A staggered field applied to the S =1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a nonlocal order parameter are given in terms of a matrix-product state formulation.
Dislocations in icosahedral quasicrystals.
Feuerbacher, Michael
2012-10-21
Dislocations in quasicrystals, as a direct result of the lack of translational symmetry in these materials, possess various salient features. The Burgers vector of a dislocation in an icosahedral quasicrystal is a 6-dimensional vector, which reflects the fact that the dislocation, besides the phonon-type strain field analogous to dislocations in ordinary crystals, is associated inseparably with a further type of defect, the phasons. Phasons are critically involved in the formation and motion of dislocations in quasicrystals and govern the macroscopic plastic behaviour of these materials. In this article the properties of dislocations in icosahedral quasicrystals are comprehensively reviewed, starting from a continuum-mechanical description, via core-structure simulation, to their full experimental characterization. The experimental results presented address the icosahedral phases in the well explored systems Al-Pd-Mn and Zn-Mg-Dy. PMID:22760204
M. Deboissieu; M. Boudard; T. Ishimasa; E. Elkaim; J. P. Lauriat; A. Letoublon; M. Audierf; M. Duneau; A. Davroski
1998-01-01
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 .,
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
NASA Astrophysics Data System (ADS)
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-07-01
Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7- 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.
Computer Simulated Growth of Icosahedral Glass
Y. A. J. Leino; M. M. Salomaa
1990-01-01
One possible model for materials displaying classically forbidden symmetry properties (apart from perfect quasicrystals) is the icosahedral glass model. We simulate the random growth of two types of two-dimensional icosahedral glasses consisting of the Penrose tiles, First we restrict the growth with the arrow rules, then we let the structure develop totally freely. The diffraction patterns have a clear five-fold
Metallic phase with long-range orientational order and no translational symmetry
D. Shechtman; I. Blech; D. Gratias; J. W. Cahn
1984-01-01
A metallic solid (Al-14-at. pct.-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations, has been observed. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice. The solid is metastable and forms from the melt by a first-order transition.
Crystallography of icosahedral crystals
NASA Astrophysics Data System (ADS)
Bak, P.
The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal cannot in general be viewed as a space-filling arrangemment of a small number of different Penrose tiles. The intensities of Bragg spots are given directly as the intensities of Bragg spots of the six-dimensional crystal.
Crystallography of icosahedral crystals
Bak, P.
1986-01-01
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.
Icosahedral quasiperiodic ground states?
NASA Astrophysics Data System (ADS)
Narasimhan, Subha; Jaric, Marko V.
1989-01-01
An icosahedral quasiperiodic zero-temperature phase with lower enthalpy than in Bravais and close-packed crystal structures has been found for a system of particles interacting via a square-well potential. This remains true after small changes in the potential, pressure, and even after small changes within a class of icosahedral structures. Above a certain critical pressure, the icosahedral phase transforms into the bcc Bravais crystal structure.
Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis
L. Bendersky
1985-01-01
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
Crystal field theory and the Shubnikov point groups
Arthur P. Cracknell
1968-01-01
Two pieces of theory which have so far remained unconnected, crystal field theory and the theory of corepresentations of non-unitary groups, are brought together here for the study of the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups. The cases of the various possible relative strengths of the
Computer Simulated Growth of Icosahedral Glass
NASA Astrophysics Data System (ADS)
Leino, Y. A. J.; Salomaa, M. M.
1990-01-01
One possible model for materials displaying classically forbidden symmetry properties (apart from perfect quasicrystals) is the icosahedral glass model. We simulate the random growth of two types of two-dimensional icosahedral glasses consisting of the Penrose tiles, First we restrict the growth with the arrow rules, then we let the structure develop totally freely. The diffraction patterns have a clear five-fold symmetry in both cases. The diffraction peak intensities do not differ, but shapes of the central peaks vary depending on whether the arrow rules are imposed or not. Finally, we show that the half-width of the central peak decreases when the size of the simulation increases until a finite disorder-limited value is achieved. This phenomenon is in agreement with the behaviour of physical quasicrystallites and in contradiction with perfect mathematical quasicrystals which have Bragg peaks of zero width.
Bulk topological invariants in noninteracting point group symmetric insulators
NASA Astrophysics Data System (ADS)
Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
2012-09-01
We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number of a Cn-invariant insulator can be determined, up to a multiple of n, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a Cn-invariant insulator is also determined, up to a multiple of n, by the Cn eigenvalue of the Slater determinant of a noninteracting many-body system; and (iii) the Chern number vanishes in insulators with dihedral point groups Dn, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that (i) only insulators with point groups Cn, Cnh, and Sn PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization P3 in the term P3EB, the axion term in the electrodynamics of the insulator (medium).
Growth of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Socolar, Joshua; Hann, Connor; Steinhardt, Paul
2015-03-01
The discovery of an icosahedral quasicrystal that formed naturally in a rock sample originating from a meteorite highlights fundamental questions about quasicrystal formation. ?The growth of a well-ordered quasicrystal through kinetics dominated by local energetics is known to be possible in principle for 2D systems: a Penrose tiling, for example, can be grown from a particular type of small seed by adding tiles only to surface sites where the tile type and orientation are unambiguously determined by already placed tiles that share a vertex. We consider the generalization of this result to icosahedral quasicrystal tilings comprised of Ammann rhombohedra. Numerical simulations strongly suggest that infinite, well-ordered, icosahedral quasicrystals can be generated. Unlike the 2D case, defects are generated outside the original seed, but the number of such defects appears to grow only linearly with the cluster radius. Analysis of the lift of the tiling to a 6D hypercubic lattice provides key insights into the growth mechanism.
Hydrodynamics of icosahedral quasicrystals
T. C. Lubensky; Sriram Ramaswamy; John Toner
1985-01-01
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
Pauling, L
1990-01-01
An analysis of electron micrographs of Al5Mn quasicrystals obtained by rapidly cooling a molten alloy with composition Al17Mn and removing the Al matrix by electrosolution, revealing aggregates of 20 microcrystals at the corners of a pentagonal dodecahedron, supports the proposal that these microcrystals are cubic crystals twinned about an icosahedral seed, with each cubic microcrystal sharing a threefold axis and three symmetry planes with the seed. Images PMID:11607108
Topological Invariants in Point Group Symmetric Photonic Topological Insulators
Chen, Xiao-Dong; Chen, Wen-Jie; Wang, Jia-Rong; Dong, Jian-Wen
2014-01-01
We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {\\epsilon}/{\\mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.
Gilbert, Matthew
2012-01-01
symmetric insulators Chen Fang,1 Matthew J. Gilbert,2,3 and B. Andrei Bernevig1 1 Department of Physics in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number
NSDL National Science Digital Library
Dean Johnson
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.
So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal
Linus Pauling
1987-01-01
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
NASA Astrophysics Data System (ADS)
Blatov, V. A.; Ilyushin, G. D.
2012-12-01
A database of intermetallic compounds has been compiled using the TOPOS program package. This database includes 514 topological types, containing 12- and 13-atom icosahedral i clusters. An isolated group of 1649 i clusters is described by 14 point groups and their maximum symmetry D 3 d (bar 3 m) and T h ( m bar 3) is established, respectively, in 47 and 25 types of crystal structures. A structural analysis of the outer quasispherical shells showed that local 63-atom i configurations 1@12@50, which contain 50 atoms in the second layer, are implemented in 8 out of 19 cases. Examples of new topologically different types of 50-atom D50 deltahedra in the Samson phases ?-Mg23Al30 and ?-Mg2Al3 are presented. Four topologically different sites with coordination numbers of 5, 6, 6, or 7 are established in the ? shell and seven sites with coordination numbers of 5, 5, 6, 6, 6, 6, or 7 are found in the ? shell. The inner i clusters for the ?-Mg2Al3 structure (with the symmetry bar 3 m) and the ?-Mg23Al30 structure (with the symmetry bar 3) have a similar chemical composition, i.e., Mg7Al6 and Mg6Al7, and their 50-atom shells are chemically identical to 18Mg + 32Al. The configurations found supplement the series of known two-layer icosahedral Bergman and Mackay clusters in the form of deltahedra with 32- and 42-atom shells.
Mechanical properties of icosahedral virus capsids
NASA Astrophysics Data System (ADS)
Vliegenthart, G. A.; Gompper, G.
2007-12-01
Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the viral DNA. We employ computer simulations to study the mechanical properties of crystalline shells with icosahedral symmetry that serve as a model for virus capsids. The shells are positioned on a substrate and deformed by a uni-axial force excerted by a small bead. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number N of elementary building blocks (capsomers), and the Fppl-von Krmn number ? which characterizes the relative importance of shear and bending elasticity.
Nanosize icosahedral quasicrystal in Mg90Ca10 glass: an ab initio molecular dynamics study.
Durandurdu, Murat
2012-07-21
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
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and
NSDL National Science Digital Library
Dexter Perkins
This summary exercise involves crystal system and point group identification and stereo diagram construction. Students are presented with 5 blocks and for each block they must determine it's point group and crystal system, make stereo diagrams showing all symmetry and faces, and draw the blocks by hand or with SHAPE and label the Miller Indices.
Effects of scars on icosahedral crystalline shell stability under external pressure
NASA Astrophysics Data System (ADS)
Wan, Duanduan; Bowick, Mark J.; Sknepnek, Rastko
2015-03-01
We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically required defects to shells with extended defect arrays (grain boundary "scars" with nonvanishing net disclination charge). We perform both Monte Carlo and conjugate gradient simulations to compare how shells with and without scars deform quasistatically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally symmetric shell depend on the Fppl-von Krmn number.
Alternative approaches to onion-like icosahedral fullerenes.
Janner, A
2014-03-01
The fullerenes of the C60 series (C60, C240, C540, C960, C1500, C2160 etc.) form onion-like shells with icosahedral Ih symmetry. Up to C2160, their geometry has been optimized by Dunlap & Zope from computations according to the analytic density-functional theory and shown by Wardman to obey structural constraints derived from an affine-extended Ih group. In this paper, these approaches are compared with models based on crystallographic scaling transformations. To start with, it is shown that the 56 symmetry-inequivalent computed carbon positions, approximated by the corresponding ones in the models, are mutually related by crystallographic scalings. This result is consistent with Wardman's remark that the affine-extension approach simultaneously models different shells of a carbon onion. From the regularities observed in the fullerene models derived from scaling, an icosahedral infinite C60 onion molecule is defined, with shells consisting of all successive fullerenes of the C60 series. The structural relations between the C60 onion and graphite lead to a one-parameter model with the same Euclidean symmetry P63mc as graphite and having a c/a = ?(2) ratio, where ? = 1.618 is the golden number. This ratio approximates (up to a 4% discrepancy) the value observed in graphite. A number of tables and figures illustrate successive steps of the present investigation. PMID:24572318
So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal
NASA Astrophysics Data System (ADS)
Pauling, Linus
1987-01-01
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 of CuLi3Al6, the electron diffraction photographs, and the high-resolution electron micrographs.
Nam, H-S; Hwang, Nong M; Yu, B D; Yoon, J-K
2002-12-30
The freezing behavior of gold nanoclusters was studied by employing molecular dynamics simulations based on the semiempirical embedded-atom method. Investigations of the gold nanoclusters revealed that, just after freezing, ordered nanosurfaces with a fivefold symmetry were formed with interior atoms remaining in the disordered state. Further lowering of temperatures induced nanocrystallization of the interior atoms that proceeded from the surface towards the core region, finally leading to an icosahedral structure. These dynamic processes explain why the icosahedral cluster structure is dominantly formed in spite of its energetic metastability. PMID:12513216
NASA Astrophysics Data System (ADS)
Nam, H.-S.; Hwang, Nong M.; Yu, B. D.; Yoon, J.-K.
2002-12-01
The freezing behavior of gold nanoclusters was studied by employing molecular dynamics simulations based on the semiempirical embedded-atom method. Investigations of the gold nanoclusters revealed that, just after freezing, ordered nanosurfaces with a fivefold symmetry were formed with interior atoms remaining in the disordered state. Further lowering of temperatures induced nanocrystallization of the interior atoms that proceeded from the surface towards the core region, finally leading to an icosahedral structure. These dynamic processes explain why the icosahedral cluster structure is dominantly formed in spite of its energetic metastability.
Spinor representation of icosahedral g orbitals
B. R. Judd; Edwin Lo
1999-01-01
The four components of an icosahedral g orbital are represented by the irreducible spinor representation 0953-4075\\/32\\/5\\/003\\/img1 of 0953-4075\\/32\\/5\\/003\\/img2 (or, equivalently, SO(4)), where the two SO(3) groups are associated with the irreducible representations (IRs) 0953-4075\\/32\\/5\\/003\\/img3 and 0953-4075\\/32\\/5\\/003\\/img4 of the icosahedral group I. This enables the properties of the icosahedral configurations 0953-4075\\/32\\/5\\/003\\/img5 to be calculated by the familiar techniques of angular-momentum theory.
NSDL National Science Digital Library
Jo Edkins
2007-01-01
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.
NSDL National Science Digital Library
Dexter Perkins
This is an introduction to basic symmetry elements. Students make drawings that show good examples of rotation axes and mirror planes and inversion centers with and without a 2-fold axis. They describe real objects a mirror plane, an inversion center, and 2, 3, 4, and 6-fold axes in 3D. They think about symmetry in atomic structures and indicate which symmetry elements are present in ball and stick models of minerals. Then they count the different kinds of symmetry elements present in wooden blocks and real minerals.
Surface structures of Al-Pd-Mn and Al-Cu-Fe icosahedral quasicrystals
Shen, Z.
1999-02-12
In this dissertation, the author reports on the surface structure of i-Al-Pd-Mn twofold, threefold, fivefold and i-Al-Cu-Fe fivefold surfaces. The LEED studies indicate the existence of two distinct stages in the regrowth of all four surfaces after Ar{sup +} sputtering. In the first stage, upon annealing at relatively low temperature: 500K--800K (depending on different surfaces), a cubic phase appears. The cubic LEED patterns transform irreversibly to unreconstructed quasicrystalline patterns upon annealing to higher temperatures, indicating that the cubic overlayers are metastable. Based upon the data for three chemically-identical, but symmetrically-inequivalent surfaces, a model is developed for the relation between the cubic overlayers and the quasicrystalline substrate. The model is based upon the related symmetries of cubic close-packed and icosahedral-packed materials. These results may be general among Al-rich, icosahedral materials. STM study of Al-Pd-Mn fivefold surface shows that terrace-step-kink structures start to form on the surface after annealing above 700K. Large, atomic ally-flat terraces were formed after annealing at 900K. Fine structures with fivefold icosahedral symmetry were found on those terraces. Data analysis and comparison of the STM images and structure model of icosahedral Al-Pd-Mn suggest that the fine structures in the STM images may be the pseudo Mackay (PMI) clusters which are the structure units of the structure model. Based upon his results, he can conclude that quasicrystalline structures are the stable structures of quasicrystal surfaces. In other words, quasicrystalline structures extend from the bulk to the surface. As a result of the effort reported in this dissertation, he believes that he has increased his understanding of the surface structure of icosahedral quasicrystals to a new level.
Icosahedral Platinum Alloy Nanocrystals with Enhanced Electrocatalytic Activities
Chen, Sow-Hsin
Icosahedral Platinum Alloy Nanocrystals with Enhanced Electrocatalytic Activities Jianbo Wu,, Liang) icosahedral nanocrystals based on the gas reducing agent in liquid solution method. Both CO gas and organic the Pt-M alloy icosahedral nanocrystals generated, Pt3Ni had an impressive ORR specific activity of 1
Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials
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
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.}
Experimental Evidence of Icosahedral and Decahedral Packing in One-Dimensional Nanostructures
Velzquez-Salazar, J. Jess; Esparza, Rodrigo; Meja-Rosales, Sergio Javier; Estrada-Salas, Rubn; Ponce, Arturo; Deepak, Francis Leonard; Castro-Guerrero, Carlos; Jos-Yacamn, Miguel
2011-01-01
The packing of spheres is a subject that has drawn the attention of mathematicians and philosophers for centuries, and that currently attracts the interest of the scientific community in several fields. At the nanoscale, the packing of atoms affect the chemical and structural properties of the material, and hence, its potential applications. This report describes the experimental formation of five-fold nanostructures by the packing of interpenetrated icosahedral and decahedral units. These nanowires, formed by the reaction of a mixture of metal salts (Au and Ag) in the presence of oleylamine, are obtained when the chemical composition is specifically Ag/Au=3/1. The experimental images of the icosahedral nanowires have a high likelihood with simulated electron micrographs of structures formed by two or three Boerdijk-Coxeter-Bernal helices roped on a single structure, whereas for the decahedral wires, simulations using a model of adjacent decahedra match the experimental structures. To our knowledge, this is the first report of the synthesis of nanowires formed by the packing of structures with five-fold symmetry. These icosahedral nanowire structures remind those of quasicrystals that can only be formed if at least two atomic species are present and in which icosahedral and decahedral packing has been found for bulk crystals. PMID:21790155
Beta cell device using icosahedral boride compounds
Aselage, Terrence L. (62 Avenida Del Sol, Cedar Crest, NM 87008); Emin, David (1502 Harvard Ct., NE., Albuquerque, NM 87106-3712)
2002-01-01
A beta cell for converting beta-particle energies into electrical energy having a semiconductor junction that incorporates an icosahedral boride compound selected from B.sub.12 As.sub.2, B.sub.12 P.sub.2, elemental boron having an .alpha.-rhombohedral structure, elemental boron having a .beta.-rhombohedral structure, and boron carbides of the chemical formula B.sub.12-x C.sub.3-x, where 0.15
Hargittai, I.
1986-01-01
This book demonstrates the progress in the application of the symmetry concept. Highlights symmetry as a fundamental concept in science and as the best unifying idea crossing various branches of most human activities. In addition to its use in traditional symmetry-oriented fields, the concept has made headway in other areas such as reaction chemistry, musicology, nuclear physics, biology, cosmology, etc. This work, illustrated with over 400 drawings, brings together the most diverse fields from mathematics to psychology, the creative and performing arts and most branches of the sciences.
Stability of the X -Y phase of the two-dimensional C4 point group insulator
NASA Astrophysics Data System (ADS)
de Leeuw, Bart; Kppersbusch, Carolin; Juri?i?, Vladimir; Fritz, Lars
2015-06-01
Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this paper we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators but only if the Sz component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes, and the surface states localize, even if the crystalline symmetries are intact on average.
Crack Propagation in Icosahedral Model Quasicrystals
Roth, Johannes
Crack Propagation in Icosahedral Model Quasicrystals Christoph Rudhart, Frohmut R?osch, Franz G surfaces is observed. 1 Introduction Quasicrystals are intermetallic alloys whose di#raction patterns not apply to quasicrystals. Although it is possible to grow single quasicrystals of centimeter size, ex
Crack Propagation in Icosahedral Model Quasicrystals
Gähler, Franz
Crack Propagation in Icosahedral Model Quasicrystals Christoph Rudhart, Frohmut R¨osch, Franz G surfaces is observed. 1 Introduction Quasicrystals are intermetallic alloys whose diffraction patterns not apply to quasicrystals. Although it is possible to grow single quasicrystals of centimeter size, ex
Thermal stability of Al-Cu-Fe icosahedral alloys
NASA Astrophysics Data System (ADS)
Bessire, M.; Quivy, A.; Lefebvre, S.; Devaud-Rzepski, J.; Calvayrac, Y.
1991-12-01
A stable ideally quasiperiodic phase exists in a small range of concentration, close to the composition Al{62}Cu{25.5}Fe{12.5}. Reducing the iron content, or replacing small amounts of copper by aluminium, lead to icosahedral alloys which exhibit around 650 ^{circ}C structural transformations of unclear nature: in the X-ray powder diffraction pattern, the peak profiles become purely Lorentzian (Al{62.3}Cu{25.3}Fe{12.4}) or diffuse side-bands appear in the tails of the Bragg peaks (Al{63}Cu{24.5}Fe{12.5}). In the last case long annealing treatments eventually transform the Bragg peaks into diffuse peaks located at positions clearly off the ideal icosahedral symmetry. Small deviations from this composition range lead to Bragg peaks with shoulders whatever the heat-treatment may be; perfect icosahedral order is never obtained for these compositions (Al{63,25}Cu{24,5}Fe{12,25}, Al{64}Cu{24}Fe{12}, Al{63}Cu{25}Fe{12}). Une phase stable idalement quasipriodique existe dans un petit domaine de concentration, au voisinage de la composition Al{62}Cu{25,5}Fe{12,5}. La diminution de la teneur en fer, ou le remplacement de faibles quantits de cuivre par de l'aluminium, conduisent des alliages icosadriques qui subissent vers 650 ^{circ}C des transformations structurales dont la nature n'est pas clairement identifie: dans le diagramme de diffraction des rayons X sur poudre, les profils de raies deviennent purement Lorentziens (Al{62,3}Cu{25,3}Fe{12,4}) ou bien des raies diffuses apparaissent dans le pied des pics de Bragg (Al{63}Cu{24,5}Fe{12,5}). Dans ce dernier cas un long traitement de recuit transforme finalement les pics de Bragg en des pics diffus localiss des positions clairement en dehors de celles correspondant la symtrie icosadrique idale. De faibles carts ce domaine de compositions conduisent des diagrammes de rayons X o les pics de Bragg sont pauls quel que soit le traitement thermique ; l'ordre icosadrique parfait n'est jamais obtenu pour ces compositions (Al{63,25}Cu{24,5}Fe{12,25}, Al{64}Cu{24}Fe{12}, Al{63}Cu{25}Fe{12}).
Tsutomu Ishimasa; Yasushi Kaneko; Hiroshi Kaneko
2002-01-01
New icosahedral quasicrystals have been discovered in ZnMgSc and ZnMgTi alloy systems. The former forms at the alloy composition of Zn80Mg5Sc15, and belongs to P-type (aP=0.7111 nm) showing high degree of structural perfection. The icosahedral atomic cluster included in 1\\/1 approximant crystal, Zn17Sc3, suggests that the ZnMgSc icosahedral quasicrystal has structural similarity to the Cd-based icosahedral quasicrystals recently reported. Preliminary
Castell, Martin
Growth of Ag icosahedral nanocrystals on a SrTiO3,,001... support Fabien Silly and Martin R the structure and morphology of self-assembled silver nanocrystals supported on a SrTiO3 001 - 2 1 substrate using scanning tunneling microscopy. Ag forms nanocrystals with five-fold symmetry which have
Simulation of dislocations in icosahedral quasicrystals with IMD
Gähler, Franz
Simulation of dislocations in icosahedral quasicrystals with IMD Gunther Schaaf, Franz G and massively parallel supercomputers. Especially the simulations of dislocations in icosahedral quasicrystals are given by central pair potentials. Such twobody potentials have mainly been used for quasicrystals
Icosahedral short-range order in deeply undercooled metallic melts.
Schenk, T; Holland-Moritz, D; Simonet, V; Bellissent, R; Herlach, D M
2002-08-12
Experimental evidence of icosahedral short-range order in stable and deeply undercooled melts of pure metallic elements is obtained using the combination of electromagnetic levitation with neutron scattering. This icosahedral short-range order is shown to occur in the bulk metallic melt independently of the system investigated. It strongly increases with the degree of undercooling. PMID:12190531
Topological Quantum Hashing with the Icosahedral Group
Burrello, Michele [International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (Italy); Xu Haitan [Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China); Mussardo, Giuseppe [International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste (Italy); International Centre for Theoretical Physics (ICTP), I-34014 Trieste (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Trieste (Italy); Wan Xin [Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Gyeongbuk 790-784 (Korea, Republic of); Department of Physics, Pohang University of Science and Technology, Pohang, Gyeongbuk 790-784 (Korea, Republic of); Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China)
2010-04-23
We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log{sup 2}(1/{epsilon})), we can approximate all SU(2) matrices to an average error {epsilon} with a cost of O(log(1/{epsilon})) in time. The algorithm is applicable to generic quantum compiling.
Topological quantum hashing with the icosahedral group.
Burrello, Michele; Xu, Haitan; Mussardo, Giuseppe; Wan, Xin
2010-04-23
We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/epsilon)), we can approximate all SU(2) matrices to an average error epsilon with a cost of O(log(1/epsilon)) in time. The algorithm is applicable to generic quantum compiling. PMID:20482034
Density waves theory of the capsid structure of small icosahedral viruses
V. L. Lorman; S. B. Rochal
2006-11-24
We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for the proteins constituting viral capsid shell. Corresponding density distribution function which generates the positions has universal form without any fitting parameter. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug geometrical model for capsid construction and those violating it. The quasiequivalence of protein environments in viral capsid and peculiarities of the assembly thermodynamics are also discussed.
Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal.
Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fourne, V; Tsai, A P; McGrath, R; Sharma, H R
2014-01-01
The structure of the twofold surface of the icosahedral (i-)Ag-In-Yb quasicrystal has been investigated using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). The LEED confirms that the surface exhibits quasicrystalline long range order with the twofold rotational symmetry expected from the bulk. STM images reveal a step-terrace structure with terrace size comparable to that of the other high symmetry surfaces of the same quasicrystal. The distribution of step heights and high resolution STM images of terraces suggest that the surface terminates at bulk planes that intersect the center of rhombic triacontahedral clusters, the building blocks of the system, as in the case of the threefold and fivefold surfaces of the system. These planes are rich in Yb and In. No facets are observed on the surface, suggesting that the twofold surface is as stable as the other high symmetry surfaces. PMID:24263167
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching
Magnetic property of a ZnMgSc icosahedral quasicrystal
Shiro Kashimoto; Senni Motomura; Hiroshi Nakano; Yasushi Kaneko; Tsutomu Ishimasa; Susumu Matsuo
2002-01-01
We have investigated the magnetism of a new Zn80Mg5Sc15 P-type icosahedral quasicrystal and a Zn85.5Sc14.5 cubic phase, which is interpreted to be a 1\\/1 approximant of the new icosahedral quasicrystal, in the temperature region between 2 and 700 K. The magnetic susceptibility of the Zn80Mg5Sc15 icosahedral quasicrystal shows an increase from ?1.310?7 to ?0.810?7 cgsemu\\/g with a rise in temperature
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
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.
NASA Astrophysics Data System (ADS)
Vail, Benjamin; Aris, Damian; Scarlete, Mihai
The present study proposes an algorithm for point-group analysis (PGA) of the vibrational activity of molecules, adapted for the efficient utilization of the linear packages incorporated into currently available symbolic computation engines (SCE), such as Maple, Mathcad, or Mathematica. By the creation of this algorithm, we have addressed the need for a numerically friendly environment, outside the "locked" procedures within molecular modeling packages, which will preserve its flexibility, transparency, and maneuverability, regardless of the complexity of the calculation. The format of the character tables of the point groups significant to chemical species has been adapted to ensure automatic numerization, and consistent input of the alphanumeric data from the existent character tables into the SCE templates designed to perform the PGA. The two proposed templates address two complementary objectives: (i) a totally transparent and interactive file has been designed to allow access to all intermediate results at all levels of the procedure for easy implementation of potential additional modules of special interest 1-5, and (ii) for fast output and routine calculations of the IR/Raman vibrational activity of molecules based on their point groups, a totally automatic file with a highly simplified input interface has been designed. The numerical interface conveniently replaces the usual graphic user interface that is common to most commercial molecular modeling software packages, requiring minimum input determination. The structure for both templates is based on the use of the digitized forms for the character tables, for the symmetry operations, and for symmetry elements, all saved in dedicated libraries uploaded to the numerical database of the SCE.
The algebraic theory of quasicrystals with five-fold symmetries
S. Berman; R. V. Moody
1994-01-01
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
Molecular symmetry with quaternions.
Fritzer, H P
2001-09-01
A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry. PMID:11666072
Analysis of phases in the structure determination of an icosahedral virus
Plevka, Pavel; Kaufmann, Brbel; Rossmann, Michael G.
2011-01-01
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 ?. 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. PMID:21636897
Analysis of phases in the structure determination of an icosahedral virus
Plevka, Pavel; Kaufmann, Brbel; Rossmann, Michael G. (Purdue)
2012-03-15
The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or {pi}. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.
Monitoring structural transitions in icosahedral virus protein cages by site-directed spin labeling.
Usselman, Robert J; Walter, Eric D; Willits, Debbie; Douglas, Trevor; Young, Mark; Singel, David J
2011-03-30
This work describes an approach for calculating and measuring dipolar interactions in multispin systems to monitor conformational changes in icosahedral protein cages using site-directed spin labeling. Cowpea chlorotic mottle virus (CCMV) is used as a template that undergoes a pH-dependent reversible capsid expansion wherein the protein cage swells by 10%. The sequence-position-dependent geometric presentation of attached spin-label groups provides a strategy for targeting amino acid residues most probative of structural change. The labeled protein cage residues and structural transition were found to affect the local mobility and dipolar interactions of the spin label, respectively. Line-shape changes provided a spectral signature that could be used to follow the conformational change in CCMV coat dynamics. The results provide evidence for a concerted swelling process in which the cages exist in only two structural forms, with essentially no intermediates. This methodology can be generalized for all symmetry types of icosahedral protein architectures to monitor protein cage dynamics. PMID:21388197
F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system
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
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.
Dynamical x-ray diffraction from an icosahedral quasicrystal
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
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.
The homological functor of a Bieberbach group with a cyclic point group of order two
NASA Astrophysics Data System (ADS)
Hassim, Hazzirah Izzati Mat; Sarmin, Nor Haniza; Ali, Nor Muhainiah Mohd; Masri, Rohaidah; Idrus, Nor'ashiqin Mohd
2014-07-01
The generalized presentation of a Bieberbach group with cyclic point group of order two can be obtained from the fact that any Bieberbach group of dimension n is a direct product of the group of the smallest dimension with a free abelian group. In this paper, by using the group presentation, the homological functor of a Bieberbach group a with cyclic point group of order two of dimension n is found.
Structure and reactivity of Bi allotropes on the fivefold icosahedral Al-Pd-Mn quasicrystal surface.
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
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
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya., E-mail: shevchenko@isc.nw.ru; Madison, Alexey E. [Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, nab. Makarova 2, Saint Petersburg 199034 (Russian Federation); Mackay, Alan L. [School of Crystallography, Birkbeck College, University of London, Malet Street, London WC1E 7HX (United Kingdom); Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, nab. Makarova 2, Saint Petersburg 199034 (Russian Federation)
2007-03-01
In icosahedral carbon nanoparticles, the diamond-like core can undergo a reversible topological transition into and coexist coherently with the onion shells. The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive smoothing (puckering) of atomic networks without disturbance of their topological integrity. The possibility of coherent coexistence of icosahedral diamond-like core with onion shells is shown.
Microindentation of Al-Cu-Fe icosahedral quasicrystal
Giacometti, E.; Baluc, N.; Bonneville, J.; Rabier, J.
1999-10-08
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.
Solvothermal synthesis of NiCo alloy icosahedral nanocrystals.
Cheng, Mingzhu; Wen, Ming; Zhou, Shiqing; Wu, Qingsheng; Sun, Baolei
2012-02-01
New dimensional NiCo alloy icosahedral nanocrystals with controllable size have been first reported and synthesized through an Ostwald ripening process in a template-absent solvothermal reaction system. The proposed synthesis is corroborated by scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction analysis (XRD), energy-dispersive X-ray spectroscopy (EDX), and X-ray photoelectron spectroscopy (XPS). The as-obtained NiCo icosahedral nanocrystals exhibit the size- and component-dependent magnetic behaviors. The coercivity (H(c)) depends on both the magnetocrystalline and structure anisotropy, and the saturation magnetizations (M(s)) decided by the content of Co. H(c) decreases from 189.02 to 147.95 Oe with the increase of the icosahedral NCs size from 200 to 850 nm. Especially, the H(c) of the icosahedral NCs at 157.38 Oe is higher than that of nanospheres at 104.02 Oe. In addition, M(s) and H(c) increased with the increasing Co content. It can be an ideal building block for applications in magnetic media, sensors, and other devices. PMID:22256904
Epifano, Carolina; Krijnse-Locker, Jacomine; Salas, Mara L.; Salas, Jos; Rodrguez, Javier M.
2006-01-01
The mechanisms involved in the construction of the icosahedral capsid of the African swine fever virus (ASFV) particle are not well understood at present. Capsid formation requires protein p72, the major capsid component, but other viral proteins are likely to play also a role in this process. We have examined the function of the ASFV structural protein pB438L, encoded by gene B438L, in virus morphogenesis. We show that protein pB438L associates with membranes during the infection, behaving as an integral membrane protein. Using a recombinant ASFV that inducibly expresses protein pB438L, we have determined that this structural protein is essential for the formation of infectious virus particles. In the absence of the protein, the virus assembly sites contain, instead of icosahedral particles, large aberrant tubular structures of viral origin as well as bilobulate forms that present morphological similarities with the tubules. The filamentous particles, which possess an aberrant core shell domain and an inner envelope, are covered by a capsid-like layer that, although containing the major capsid protein p72, does not acquire icosahedral morphology. This capsid, however, is to some extent functional, as the filamentous particles can move from the virus assembly sites to the plasma membrane and exit the cell by budding. The finding that, in the absence of protein pB438L, the viral particles formed have a tubular structure in which the icosahedral symmetry is lost supports a role for this protein in the construction or stabilization of the icosahedral vertices of the virus particle. PMID:17005638
NASA Astrophysics Data System (ADS)
Ting, Tan Yee; Idrus, Nor'ashiqin Mohd.; Masri, Rohaidah; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2014-06-01
Torsion free crystallographic groups, called Bieberbach groups, appear as fundamental groups of compact, connected, flat Riemannian manifolds and have many interesting properties. New properties of the group can be obtained by, not limited to, exploring the groups and by computing their homological functors such as nonabelian tensor squares, the central subgroup of nonabelian tensor squares, the kernel of the mapping of nonabelian tensor squares of a group to the group and many more. In this paper, the homological functor, J(G) of a centerless torsion free crystallographic group of dimension five with a nonabelian point group which is a dihedral point group is computed using commutator calculus.
Reconstructing an Icosahedral Virus from Single-Particle Diffraction Experiments
Saldin, Dilano; Schwander, Peter; Uddin, Miraj; Schmidt, Marius
2011-01-01
The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called "diffract-and-destroy" experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK.
Reconstructing an icosahedral virus from single-particle diffraction experiments.
Saldin, D K; Poon, H-C; Schwander, P; Uddin, M; Schmidt, M
2011-08-29
The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called "diffract-and-destroy" experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK. PMID:21935096
Photoemission study of an Al-Cu-Fe icosahedral phase
M. Mori; S. Matsuo; T. Ishimasa; T. Matsuura; K. Kamiya; H. Inokuchi; T. Matsukawa
1991-01-01
Photoemission spectra of the Al-Cu-Fe quasicrystal with the icosahedral phase were studied at room temperature. The line shape of the overall observed spectrum is like a large peak on a plateau cut-off at EF. The large peak observed at about 4 eV below EF seems to originate mainly from the 3d state of Cu atoms. The bump was observed at
New superlattice ordering in AlPdMn and AlPdMnSi icosahedral quasicrystals
T. Ishimasa; M. Mori
1992-01-01
AlPdMnSi alloys with nominal compositions (AlPdMn) Si and 0 ? x ?; 0.03 were annealed at various temperatures between 1075 and 779 K. The existence of the following five structures has been recognized in these alloys by electron microscopy observations: traditional Ftype icosahedral phase, an Ftype icosahedral phase with a new superlattice ordering, a third Ftype icosahedral phase with a
Formation of F- and P-Type Icosahedral Quasicrystals in the Zn Mg Ho Alloy System
Takayuki Shimizu; Tsutomu Ishimasa
1998-01-01
Two types of icosahedral quasicrystals, F- and P-types, formed at 563C in the Zn60Mg40-xHox alloy depending on Ho content. In the composition range of 6≦x≦10, F-type icosahedral quasicrystal formed as a major phase in these alloys. The intensity of superlattice reflections which occurred due to F-type ordering became weaker in the alloys with lower Ho content. At x=5, P-type icosahedral
Stability of an icosahedral incommensurate phase formed in an immiscible alloy system
Huang, L.J.; Liu, B.X. (Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China (CN) Chinese Center of Advanced Science and Technology (World Laboratory), P.O. Box 8730, Beijing 100080 (China)); Li, H. (Department of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China))
1990-05-01
A stability study of the icosahedral incommensurate Fe{sub 60}Cu{sub 40} phase formed directly by ion mixing at room temperature indicates that this metastable phase is unstable against thermal annealing to 300{plus minus}25 {degree}C, but annealing to the higher temperature (800{plus minus}25 {degree}C) reestablished the icosahedral order. The changes of the magnetic properties associated with the icosahedral phase formation are also presented.
Hyun, Jae-Kyung; Radjainia, Mazdak; Kingston, Richard L; Mitra, Alok K
2010-05-14
In a mature and infectious retroviral particle, the capsid protein (CA) forms a shell surrounding the genomic RNA and the replicative machinery of the virus. The irregular nature of this capsid shell precludes direct atomic resolution structural analysis. CA hexamers and pentamers are the fundamental building blocks of the capsid, however the pentameric state, in particular, remains poorly characterized. We have developed an efficient in vitro protocol for studying the assembly of Rous sarcoma virus (RSV) CA that involves mild acidification and produces structures modeling the authentic viral capsid. These structures include regular spherical particles with T = 1 icosahedral symmetry, built from CA pentamers alone. These particles were subject to cryoelectron microscopy (cryo-EM) and image processing, and a pseudo-atomic model of the icosahedron was created by docking atomic structures of the constituent CA domains into the cryo-EM-derived three-dimensional density map. The N-terminal domain (NTD) of CA forms pentameric turrets, which decorate the surface of the icosahedron, while the C-terminal domain (CTD) of CA is positioned underneath, linking the pentamers. Biophysical analysis of the icosahedral particle preparation reveals that CA monomers and icosahedra are the only detectable species and that these exist in reversible equilibrium at pH 5. These same acidic conditions are known to promote formation of a RSV CA CTD dimer, present within the icosahedral particle, which facilitates capsid assembly. The results are consistent with a model in which RSV CA assembly is a nucleation-limited process driven by very weak protein-protein interactions. PMID:20228062
Hyun, Jae-Kyung; Radjainia, Mazdak; Kingston, Richard L.; Mitra, Alok K.
2010-01-01
In a mature and infectious retroviral particle, the capsid protein (CA) forms a shell surrounding the genomic RNA and the replicative machinery of the virus. The irregular nature of this capsid shell precludes direct atomic resolution structural analysis. CA hexamers and pentamers are the fundamental building blocks of the capsid, however the pentameric state, in particular, remains poorly characterized. We have developed an efficient in vitro protocol for studying the assembly of Rous sarcoma virus (RSV) CA that involves mild acidification and produces structures modeling the authentic viral capsid. These structures include regular spherical particles with T = 1 icosahedral symmetry, built from CA pentamers alone. These particles were subject to cryoelectron microscopy (cryo-EM) and image processing, and a pseudo-atomic model of the icosahedron was created by docking atomic structures of the constituent CA domains into the cryo-EM-derived three-dimensional density map. The N-terminal domain (NTD) of CA forms pentameric turrets, which decorate the surface of the icosahedron, while the C-terminal domain (CTD) of CA is positioned underneath, linking the pentamers. Biophysical analysis of the icosahedral particle preparation reveals that CA monomers and icosahedra are the only detectable species and that these exist in reversible equilibrium at pH 5. These same acidic conditions are known to promote formation of a RSV CA CTD dimer, present within the icosahedral particle, which facilitates capsid assembly. The results are consistent with a model in which RSV CA assembly is a nucleation-limited process driven by very weak protein-protein interactions. PMID:20228062
S. Takeuchi
2006-01-01
Icosahedral quasicrystals are commonly plastically deformable at high temperatures, but the temperature ranges of the plastic deformation are largely different among different types of the quasicrystal. However, when we convert the upper yield stress vs. the temperature relations for various icosahedral quasicrystals into the non-dimensional stress normalised by Young's modulus E vs. the non-dimensional temperature normalised by (: the average
Structure of the icosahedral Ti-Zr-Ni quasicrystal R. G. Hennig*
Henley, Christopher L.
Structure of the icosahedral Ti-Zr-Ni quasicrystal R. G. Hennig* Department of Physics, Ohio State; published 7 April 2003 The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined of the quasicrystal. The decoration model is optimized using a method of structural analysis combining a least
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals R. G. Hennig
Henley, Christopher L.
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals R. G of the icosahedral TiZrNi quasicrystal. The complete ab initio zero-temperature ternary phase diagram is constructed, the icosahedral i-TiZrNi quasicrystal is approximated by periodic structures of up to 123 atoms/unit cell, based
NASA Astrophysics Data System (ADS)
Kurtuldu, Gven; Rappaz, Michel
2015-06-01
Recently, we have shown that minute Cr additions (typically 0.1 wt%) to Al-Zn alloys solidified in a uniform temperature field lead to the formation of fine equiaxed fcc Al grains [1]. Furthermore, these grains exhibit an unexpectedly large number of twin, or neartwin, relationships with their nearest neighbors and some of them even show a 5-fold symmetry multi-twin relationship with a common (110) direction. Similar observations have been made for yellow gold alloys (Au-12.5wt%Cu-12.5wt%Ag) inoculated with very small amounts of Ir (5-200 ppm) [2]. These results become fully consistent when one considers that the primary fcc phase forms on facets of icosahedral quasicrystals (iQC's), either by heteroepitaxy solidification or by peritectic transformation, with the following relationship: <111>fcc || 3-fold symmetry iQC axes, <110>fcc ? 2-fold symmetry iQC axes. The present study contributes to a better understanding of the frequency of twin boundary formation by the nucleation of fcc phase from an iQC template. A simple stereological model for the formation of equiaxed grains on such iQC templates has been derived. It is based on a 3D Voronoi tessellation of randomly distributed and oriented iQC template centers. Each iQC nucleation template site is the origin of 20 fcc grains with the heteroepitaxy relationships mentioned above on the 20 facets of the iQC. Therefore, the neighboring grains having a common iQC nucleation site contributes to the twin boundary frequency, while those coming from different iQC sites have random grain boundary orientations. The twin boundary frequency of the grains nucleated from iQC templates seen in 2D metallographic sections is compared with that measured in EBSD reconstructed grain structures.
New icosahedral quasicrystals formed in Cu-based ternary alloys
T. Honma; T. Ishimasa
2007-01-01
New Cu-based P-type icosahedral quasicrystals have been observed in the ternary Cu(Ga or Al)Sc alloy systems. The CuGaSc quasicrystal forms almost exclusively in a rapidly quenched Cu48Ga34Sc18 alloy, and has a six-dimensional lattice parameter a6D?=?0.6930?nm. The as-cast alloy with the same composition contains no quasicrystal but has a 1\\/1 bcc approximant as its main phase. The CuAlSc quasicrystal forms at
Dynamic and Kinetic Assembly Studies of an Icosahedral Virus Capsid
NASA Astrophysics Data System (ADS)
Lee, Kelly
2011-03-01
Hepatitis B virus has an icosahedrally symmetrical core particle (capsid), composed of either 90 or 120 copies of a dimeric protein building block. We are using time-resolved, solution small-angle X-ray scattering and single-molecule fluorescence microscopy to probe the core particle assembly reaction at the ensemble and individual assembly levels. Our experiments to date reveal the assembly process to be highly cooperative with minimal population of stable intermediate species. Solution conditions, particularly salt concentration, appears to influence the partitioning of assembly products into the two sizes of shells. Funding from NIH R00-GM080352 and University of Washington.
Melting of bcc Transition Metals and Icosahedral Clustering
Ross, M; Boehler, R; Japel, S
2006-05-26
In contrast to polyvalent metals, transition metals have low melting slopes(dT/dP) that are due to partially filled d-bands that allow for a lowering of liquid phase energy through s-d electron transfer and the formation of local structures. In the case of bcc transition metals we show the apparent discrepancy of DAC melting measurements with shock melting of Mo can be understood by reexamining the shock data for V and Ta and introducing the presence of an icosahedral short range order (ISRO) melt phase.
Xiong, Dongxia; Lu, Lu; Wang, Jianbo; Zhao, Dongshan; Sun, Yufeng
2013-01-01
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
NASA Astrophysics Data System (ADS)
Mohammad, Siti Afiqah; Ali, Nor Muhainiah Mohd; Sarmin, Nor Haniza; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah
2014-06-01
A Bieberbach group is a torsion free crystallographic group, which is an extension of a free abelian group of finite rank by a finite point group, while homological functors of a group include nonabelian tensor square, exterior square and Schur Multiplier. In this paper, some homological functors of a Bieberbach group of dimension four with dihedral point group of order eight are computed.
Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
Fernndez, Francisco M., E-mail: fernande@quimica.unlp.edu.ar; Garcia, Javier
2014-03-15
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. PT-symmetric multidimensional oscillators appear to show PT phase transitions. This transition was conjectured to be a high-energy phenomenon. We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.
NASA Astrophysics Data System (ADS)
Li, Han-Jung; Yeh, Chen-Hao; Ho, Jia-Jen
2013-10-01
Using density-functional theory, we investigated the adsorption and dissociation of CO2 on Ru19 clusters of nm size. According to our results, the CO2 molecule adsorbed on the rhombus-center region of a double icosahedral Ru19 nanocluster has the largest adsorption energy, -1.48 eV, and the greatest elongation of C-O bond. Dissociating the first C-O bond of a CO2 molecule we got a reaction barrier of 0.78 eV, smaller than that of adsorbed on otherwise octahedral and low-symmetry Ru19 cluster structures. To understand the electronic properties, we calculated the electron localization functions and local densities of states, and the result was explicable.
The atomic structure of the threefold surface of the icosahedral Ag-In-Yb quasicrystal.
Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fourne, V; Tsai, A P; McGrath, R; Sharma, H R
2012-11-01
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
Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
NASA Astrophysics Data System (ADS)
Satoh, M.; Matsuno, T.; Tomita, H.; Miura, H.; Nasuno, T.; Iga, S.
2008-03-01
A new type of ultra-high resolution atmospheric global circulation model is developed. The new model is designed to perform "cloud resolving simulations" by directly calculating deep convection and meso-scale circulations, which play key roles not only in the tropical circulations but in the global circulations of the atmosphere. Since cores of deep convection have a few km in horizontal size, they have not directly been resolved by existing atmospheric general circulation models (AGCMs). In order to drastically enhance horizontal resolution, a new framework of a global atmospheric model is required; we adopted nonhydrostatic governing equations and icosahedral grids to the new model, and call it Nonhydrostatic ICosahedral Atmospheric Model (NICAM). In this article, we review governing equations and numerical techniques employed, and present the results from the unique 3.5-km mesh global experimentswith O(10 9) computational nodesusing realistic topography and land/ocean surface thermal forcing. The results show realistic behaviors of multi-scale convective systems in the tropics, which have not been captured by AGCMs. We also argue future perspective of the roles of the new model in the next generation atmospheric sciences.
Unusual properties of icosahedral boron-rich solids
Emin, David [Department of Physics and Astronomy, 800 Yale Boulevard NE (MSC 07 4220), University of New Mexico, Albuquerque, NM 87131 (United States)]. E-mail: emin@unm.edu
2006-09-15
Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the 'self-healing' that underlies these materials' extraordinary radiation tolerance. Furthermore, boron carbides, a group of icosahedral boron-rich solids, possess unusual electronic, magnetic and thermal properties. For example, the charge carriers, holes, localize as singlet pairs on icosahedra. The unusual origin of this localization is indicated by the absence of a concomitant photo-ionization. The thermally assisted hopping of singlet pairs between icosahedra produces Seebeck coefficients that are unexpectedly large and only weakly dependent on carrier concentration. These properties are exploited in devices: (1) long-lived high-power high-capacity beta-voltaic cells (2) very high temperature thermoelectrics and (3) solid-state neutron detectors. - Graphical abstract: Very high-resolution transmission electron microscopy shows no damage to B{sub 12}P{sub 2} after an intense bombardment (10{sup 18} electrons/cm{sup 2} s) by 400 keV electrons to a net dose of about 10{sup 23} electrons/cm{sup 2}.
The symmetry of precession electron diffraction patterns.
Morniroli, J-P; Stadelmann, P; Ji, G; Nicolopoulos, S
2010-03-01
The integrated intensity of the diffracted beams present on microdiffraction precession patterns can be used to infer the 'ideal' symmetry, i.e. the symmetry which takes into account both the position and the intensity of the diffracted beams on a diffraction pattern. It is shown that this symmetry is connected with the 11 Laue classes on conventional electron precession patterns and with the centro- and non-centrosymmetrical point groups on unconventional precession patterns obtained without 'descan'. PMID:20500427
The Formation and Structure of Aluminum-Copper - (lithium, Magnesium) Icosahedral Alloys.
NASA Astrophysics Data System (ADS)
Shen, Yong
Quasicrystals have orientational order but lack periodic translational order. Sharp electron diffraction spots imply that they differ from amorphous materials. On the other hand, the aperiodic array of diffraction spots is inconsistent with conventional crystallography, which allows only two-, three-, four-, or sixfold symmetry axes. The discovery of the first icosahedral quasicrystal in a rapidly solidified Al-Mn alloy has created a flurry of activities in studying their structure and thermodynamics. AlCuLi icosahedral phase (i-phase) is the first stable quasicrystalline phase; and centimeter size quasicrystals can be obtained. Thus, AlCuLi i-phase is a model system for understanding the structure and thermodynamics of quasicrystalline materials. The research I have done consists of three parts: (1) Structural studies using high resolution x-ray diffraction. We found that Al(Cu) were decorated at the edge centers and vertices of two types of Penrose tiles, which are the basic units of Penrose tiling. Our results are the first successful determination of the atomic position in quasicrystalline materials, and prove that the Penrose tiling is a better description of quasicrystalline materials than other structural models. (2) Structural studies using pulsed neutron scattering. The dominant contribution to the AlCuLi x-ray spectrum comes from Al and Cu atoms since Li is a weak scatterer. However, the scattering length of the Li atom in neutron diffraction is comparable to that of Al(Cu). Furthermore, Li and Mg have opposite signs in scattering length. Thus, isomorphic substitution of Li by Mg results in contrast variation in neutron diffraction spectra, which demonstrates how Li atoms affect the diffraction. Using the pair distribution function analysis, we convincingly reveal the role of Li atoms in the structure. (3) Stability and formation. We investigate the formation of i-phase by varying preparation condition and stoichiometry. By using differential scanning calorimetry and x-ray diffraction, we established the thermodynamic relationship between the i-phase and the related crystalline phase.
Marzec, C J; Day, L A
1993-01-01
The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found. Images FIGURE 5 FIGURE 6 FIGURE 8 FIGURE 9 PMID:8312492
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
Partial pair distribution functions in icosahedral Al-Li-Cu quasicrystals
Boyer, Edmond
1689 Partial pair distribution functions in icosahedral Al-Li-Cu quasicrystals M. de Boissieu (1, 2 in a wealth of published papers. A bibliography of quasicrystals which chronicles the Article published online
Design and manufacture of an icosahedral virus model for educational use
Stach, Laurie A. (Laurie Anna)
2005-01-01
A model of an icosahedral virus was designed and manufactured. Much consideration was given to the design of different aspects of the part. though there were many uncertainties about some parameters that disallowed precise ...
Highly ordered structure of icosahedral quasicrystals in Zn-Mg-RE (RE ? rare earth metals) systems
A. P. Tsai; A. Niikura; A. Inoue; T. Masumoto; Y. Nishida; K. Tsuda; M. Tanaka
1994-01-01
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
Magnetic Properties of an Icosahedral Phase of Ga-Mg-Zn Alloy
Kaichi Saito; Susumu Matsuo; Tsutomu Ishimasa
1993-01-01
Magnetic properties of two kinds of Ga-Mg-Zn alloy samples were studied. One is Ga20Mg40Zn40 icosahedral phase which was thermally stable below about 615 K, the other is Ga18.5Mg41.5Zn40 alloy which exhibited amorphous-like X-ray diffraction pattern with no sharp peaks. The icosahedral phase showed a linear relationship between the magnetic susceptibility and the square of temperature. The improvement of the specimen
Magnetic properties of F- and P-type icosahedral quasicrystals of Al - Pd - Mn
Atsushi Kobayashi; Susumu Matsuo; Tsutomu Ishimasa; Hiroshi Nakano
1997-01-01
The magnetization of F- and P-type icosahedral Al - Pd - Mn was studied in the temperature region between 2 and 870 K in a magnetic field below 80 kOe. F-type icosahedral phase samples obtained by quenching from 1075 K were transformed to the low-temperature-phase form during the magnetic measurement above 600 K. The low-temperature phase is a P-type phase;
New group of stable icosahedral quasicrystals: structural properties and formation conditions
Tsutomu Ishimasa; Yasushi Kaneko; Hiroshi Kaneko
2004-01-01
Structural studies on the icosahedral quasicrystals in ZnMgSc, CuGaMgSc, and ZnMgTi alloys as well as their corresponding 1\\/1 cubic approximants, have revealed that these quasicrystals belong to a new structural group similar to Cd-based quasicrystals. This group is characterized by a triple-shell icosahedral cluster different from both Mackay- and Bergman-types. The presence of the atomic cluster has been deduced from
The formation condition of a stable CuGaMgSc icosahedral quasicrystal
Yasushi Kaneko; Ryo Maezawa; Tsutomu Ishimasa
2004-01-01
The formation condition and the stability of the CuGaMgSc icosahedral quasicrystal have been investigated in terms of the effects of Mg concentration and long time annealing. An addition of a few percent of Mg to the Cu3.7Ga2.3Sc-type cubic approximant causes the formation of an icosahedral quasicrystal. This quasicrystal is formed near the alloy composition of Cu48Ga34Mg3Sc15, and is regarded as
Cu-based icosahedral quasicrystal formed in Cu-Ga-Mg-Sc alloys
Yasushi Kaneko Ryomaezawa; Hiroshi Kaneko; Tsutomu Ishimasa
2002-01-01
The first-reported Cu-based icosahedral quasicrystal has been found as an almost single phase in Cu48Ga34Mg3Sc15 alloy annealed at 1043K for 61h. On the basis of our experiments, this icosahedral quasicrystal is expected to be one of the equilibrium phases in this alloy system. Powder X-ray diffraction and electron diffraction experiments revealed that the quasicrystal exhibits a high degree of structural
High-temperature magnetic properties of a stable Al65Cu20Fe15 icosahedral phase
S. Matsuo; T. Ishimasa; Hiroshi Nakano; Y. Fukano
1988-01-01
The field and temperature dependence of the magnetisation is studied in a stable Al-Cu-Fe icosahedral phase, in the temperature region between 77 and 1050 K and in magnetic fields up to 18 kOe. The sample shows a good quality of structural perfection in X-ray diffraction and electron microscope observations as compared with known icosahedral phases. The magnetic susceptibility shows an
Magnetic Property of Stable Icosahedral Quasicrystal in Zn-Fe-Sc Alloy
Shiro Kashimoto; Senni Motomura; Ryo Maezawa; Susumu Matsuo; Tsutomu Ishimasa
2004-01-01
We report the observation on the magnetic property of the stable Zn77Fe7Sc16 icosahedral quasicrystal discovered recently. As a result of measurements of magnetization, it became clear that the new Zn-based icosahedral quasicrystal has large local magnetic moments and exhibits spin glass behavior. The magnetization curves show Curie-like paramagnetism, where the magnetization M is 4.45 cgsemu\\/g at 5 K under 70
Anisotropic Magnetic Property of Single-Grained Al68Pd23Mn9 Icosahedral Quasicrystals
Susumu Matsuo; Hiroshi Nakano; Tsutomu Ishimasa; Masahiro Mori
1993-01-01
Magnetic properties were studied for single-grained Al68Pd23Mn9 icosahedral quasicrystals which had high degree of structural perfections. An anisotropy associated with the directional order in the icosahedral phase was found for the first time in the nonlinear region of the magnetization-vs-magnetic-field curve of the single-grained quasicrystal along 5-, 3-, and 2-fold axes below 40 K. No anisotropy was found in the
B. Bendjemil; A. Benaldjia; J. Bougdira; B. Malaman
2010-01-01
A systematic study on the formation and stability of the icosahedral quasicrystalline (IQC) Al70Cu20Fe10 alloy has been carried out using electrothermal explosion (ETE) reaction as a preparation method. The influence of added\\u000a elements on the formation of icosahedral phase has been investigated by Mssbauer spectroscopy, XRD, and field emission scanning\\u000a electron microscopy (FESEM). Combined ball milling and ETE reaction (BM-ETE)
Structure of Al-Li-Cu icosahedral crystals and Penrose tiling
Y. Shen; S. J. Poon; G. J. Shiflet; W. Dmowski; T. Egami
1987-01-01
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
NASA Astrophysics Data System (ADS)
Koelj, P.; Jazbec, S.; Vrtnik, S.; Jelen, A.; Dolinek, J.; Jagodi?, M.; Jagli?i?, Z.; Boulet, P.; de Weerd, M. C.; Ledieu, J.; Dubois, J. M.; Fourne, V.
2013-12-01
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.
The Triangle Pattern a New Quasiperiodic Tiling with Fivefold Symmetry
NASA Astrophysics Data System (ADS)
Baake, M.; Kramer, P.; Schlottmann, M.; Zeidler, D.
We introduce a quasiperiodic tiling with fivefold symmetry that is built from two types of triangles, an acute and an obtuse one. An easy to computerize construction algorithm based on the dualization scheme is presented that creates the pattern not pointwise but tile by tile directly. We present the vertex statistics, the inflation rule, and the Fourier analysis for selected decorations with pointlike atoms. A connection to the planar Penrose pattern and to the 3D icosahedral quasilattice is briefly discussed.
Icosahedral quasicrystal structure determination: Al-Cu-Li
Qiu, S.Y.
1992-01-01
This dissertation reports the theoretical study of the determination of quasicrystal atomic structures. A new method is developed for phasing the quasicrystal diffraction data (neutron, X-ray diffraction). A mathematical model is built which explicitly relates quasicrystals to their related periodic crystals. A test of the method is made on a simple theoretical system, the icosahedral quasiperiodic Ammann tiling decorated with point scatterers (Dirac [sigma] scattering potential) on vertices. A success is achieved in reconstructing the phases of the quasicrystal. The method is applied to a real quasicrystal system, the icosahedral quasicrystal i(Al[sub .570]Cu[sub .108]Li[sub .322]), where single-grain X-ray as well as neutron diffraction data are available, and the structure of the related large-unit-cell crystal of R(Al[sub .564]Cu[sub .116]Li[sub .320]), is well known. The reconstructed phases give the density of scatterers, which can then be used in the analysis of the atomic structure, and provide a guide to the final structure modeling. The validity of the method is evaluated with respect to the non-negativity of the resulting electron densities. In order to identify the negativity due to the intensity cut-off, the negativity is evaluated as a function of the cut-off and compared with the exact and reconstructed quasiperiodic Ammann tilings as well as with the experimental and model crystal data of R(Al[sub .564]Cu[sub .116]Li[sub .320]). It is concluded that the negativity of the reconstructed quasiperiodic electron density of i(Al[sub .570]Cu[sub .108]Li[sub .322]) is consistent with a cut-off effect. Modeling of the i(Al[sub .570]Cu[sub .108]Li[sub .322]) atomic structure in six-dimensional hyperspace is discussed. It is assumed that atomic surfaces can be modeled by polyhedra which can be described by a finite number of parameters. The authors successfully generated a model which agrees with the experimental data.
NSDL National Science Digital Library
Mrs. Neubert
2011-03-03
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 ...
An efficient code for calculation of the 6C, 9C and 12C symbols for C3v, T, and O point groups
NASA Astrophysics Data System (ADS)
Nikitin, A. V.
2012-03-01
A new code designed to calculate the 6 C, 9 C, and 12 C symbols for C3v, T, and O point groups is presented. The program is based on an algorithm that uses the symmetry property between pair and impair representations. This algorithm allows one to speed up the C-symbols calculation and increase the efficiency of spectroscopic programs based on the irreducible tensorial formalism. Program summaryProgram title: 6912C Catalogue identifier: AEKZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1214 No. of bytes in distributed program, including test data, etc.: 22 097 Distribution format: tar.gz Programming language: C++ Computer: Any computer with C, C++ compiler Operating system: Linux SUSE, Windows XP64 RAM: 400 Kb Classification: 4.2, 16.2, 16.3 Nature of problem: Spectroscopy of symmetric atmospheric molecules. Solution method: The program is based on an algorithm that uses the symmetry property between pair and impair representations. Running time: The test program provided takes a few seconds for C3v, a few minutes for T and a few days for O.
Magnetic Color Symmetry of Lattice Rotations in a Diamagnetic Material
S. Denev; A. Kumar; M. D. Biegalski; H. W. Jang; C. M. Folkman; A. Vasudevarao; Y. Han; I. M. Reaney; S. Trolier-McKinstry; C.-B. Eom; D. G. Schlom; V. Gopalan
2008-01-01
Oxygen octahedral rotations are the most common phase transitions in perovskite crystal structures. Here we show that the color symmetry of such pure elastic distortions is isomorphic to magnetic point groups, which allows their probing through distinguishing polar versus magnetic symmetry. We demonstrate this isomorphism using nonlinear optical probing of the octahedral rotational transition in a compressively strained SrTiO3 thin
On the symmetry of the quantum-mechanical particle in a cubic box
Francisco M. Fernndez
2014-12-25
In this paper we show that the point-group (geometrical) symmetry is insufficient to account for the degeneracy of the energy levels of the particle in a cubic box. The discrepancy is due to hidden (dynamical symmetry). We obtain the operators that commute with the Hamiltonian one and connect eigenfunctions of different symmetries. We also show that the addition of a suitable potential inside the box breaks the dynamical symmetry but preserves the geometrical one.The resulting degeneracy is that predicted by point-group symmetry.
SASS: a symmetry adapted stochastic search algorithm exploiting site symmetry.
Wheeler, Steven E; Schleyer, Paul V R; Schaefer, Henry F
2007-03-14
A simple symmetry adapted search algorithm (SASS) exploiting point group symmetry increases the efficiency of systematic explorations of complex quantum mechanical potential energy surfaces. In contrast to previously described stochastic approaches, which do not employ symmetry, candidate structures are generated within simple point groups, such as C2, Cs, and C2v. This facilitates efficient sampling of the 3N-6 Pople's dimensional configuration space and increases the speed and effectiveness of quantum chemical geometry optimizations. Pople's concept of framework groups [J. Am. Chem. Soc. 102, 4615 (1980)] is used to partition the configuration space into structures spanning all possible distributions of sets of symmetry equivalent atoms. This provides an efficient means of computing all structures of a given symmetry with minimum redundancy. This approach also is advantageous for generating initial structures for global optimizations via genetic algorithm and other stochastic global search techniques. Application of the SASS method is illustrated by locating 14 low-lying stationary points on the cc-pwCVDZ ROCCSD(T) potential energy surface of Li5H2. The global minimum structure is identified, along with many unique, nonintuitive, energetically favorable isomers. PMID:17362058
Pauling, Linus
1989-01-01
The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals. The first kind, represented by Al13Cu4Fe3, contains two very large icosahedral complexes, each of about 4680 atoms, in the body-centered arrangement, with six smaller icosahedral complexes (104 atoms each) in the principal interstices. The second kind, represented by Al5Mn, contains four of the very large complexes in the face-centered arrangement (cubic close packing), with four of the smaller clusters in the interstices. The third kind, represented by Al6CuLi3, contains eight icosahedral complexes, each of about 1350 atoms, in the ?-W arrangement. The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified. Images PMID:16594078
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...
ERIC Educational Resources Information Center
Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo
2008-01-01
We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple
NASA Astrophysics Data System (ADS)
Vikarchuk, A. A.; Dorogov, M. V.
2013-07-01
The effect of annealing on icosahedral small copper particles has been experimentally studied. The nanoporous structure and developed surface consisting of nanopores and nanowhiskers formed in the process of annealing of icosahedral small copper particles have been examined. Mechanisms of their formation have been proposed.
X-ray diffuse scattering in the icosahedral quasicrystal Al-Pd-Mn S. N. Ehrlich,2
Widom, Michael
X-ray diffuse scattering in the icosahedral quasicrystal Al-Pd-Mn Y. Zhang,1 S. N. Ehrlich,2 R source of diffuse scattering apart from Compton scattering . But in a quasicrystal the situation is quite to concentrate on icosahedral Al-Pd-Mn, be- cause it is a very ``perfect'' quasicrystal, in the sense
Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals
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
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.
Synthesis and characterization of monodispersed icosahedral Au using spherical aberration correction
NASA Astrophysics Data System (ADS)
Velazquez-Salazar, J. Jesus; Esparza, Rodrigo; Yacaman, Miguel Jose
2010-10-01
Monodisperse icosahedral Au nanoparticles were synthesized using one step protocol. The morphology and structural characteristics of the icosahedral Au nanoparticles with uniform size were studied in detail using ultra-high resolution scanning electron microscope (SEM) FEG Hitachi S-5500 (0.4 nm at 30 kV) with BF/DF Duo-STEM detector, high resolution transmission electron microscope (HRTEM) Jeol JEM-2010F with an accelerating voltage of 200 kV (resolution 0.19 nm point-to-point) and a scanning transmission electron microscope Jeol JEM-ARM200F (STEM) attachment with a spherical aberration corrector. The average size of the icosahedral Au nanoparticles was 10 nm. STEM Cs-corrected images showed the atomic structure of the nanoparticles, oriented mainly on the five and two fold exes. The nanoparticles were also characterized using UV/vis absorption spectrum.
Magnetic properties of icosahedral Al-Cr-Mn-Ge alloys
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
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.
NASA Astrophysics Data System (ADS)
Arribas, Victor; Casas, Llus; Estop, Eugnia; Labrador, Manuel
2014-01-01
Crystallography and X-ray diffraction techniques are essential topics in geosciences and other solid-state sciences. Their fundamentals, which include point symmetry groups, are taught in the corresponding university courses. In-depth meaningful learning of symmetry concepts is difficult and requires capacity for abstraction and spatial vision. Traditionally, wooden crystallographic models are used as support material. In this paper, we describe a new interactive tool, freely available, inspired in such models. Thirty-two PDF files containing embedded 3D models have been created. Each file illustrates a point symmetry group and can be used to teach/learn essential symmetry concepts and the International Hermann-Mauguin notation of point symmetry groups. Most interactive computer-aided tools devoted to symmetry deal with molecular symmetry and disregard crystal symmetry so we have developed a tool that fills the existing gap.
Schein, Stan; Gayed, James Maurice
2014-01-01
The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetrytetrahedral, octahedral, and icosahedralare the 5 Platonic polyhedra, the 13 Archimedean polyhedraincluding the truncated icosahedron or soccer balland the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, Goldberg polyhedra, which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a Goldberg triangle. We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Keplers rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry. PMID:24516137
Luo; Hashimoto
2000-10-01
A new ordered structure W' with a lattice parameter (a = 2.05 nm) about three times as large as that of the fundamental face-centered cubic W phase (a = 0.6848 nm) has been found in the Mg-Zn-Y system by means of transmission electron microscopy. The W' and W phases have the cube-to-cube orientation relationship. Moreover, the strong electron diffraction spots of the W' phase showed pseudoicosahedral symmetry, implying that it is a crystalline approximant of the Mg-Zn-Y icosahedral quasicrystal. In the high-resolution electron microscopic images of the W' phase, Penrose tiles of pentagons and boats with an edge length of a(p) = 0.481 nm can be identified. A binary tile of crown subunit has also been deduced from such a tiling. Translation domains of the W' phase have also been observed and the translation vectors at the domain boundary are: a(p), tau x a(p) and (1 + tau) x a(p), respectively, where (1 + tau) x a(p) equals to the edge length a(r) of the big obtuse rhombus of the W' phase and tau = (1 + square root of 5)/2, is the golden ratio. PMID:10831292
Calculation of vibrational spectra of an icosahedral quasicrystal AlCuFe
Rudenko, A. N., E-mail: ran@infoteck.ru; Mazurenko, V. G. [Ural State University (Russian Federation)
2007-11-15
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.
Magnetic and electrical properties of a new type ZnMgSc icosahedral quasicrystal
Senni Motomura; Yasushi Kaneko; Shiro Kashimoto; Hiroshi Nakano; Tsutomu Ishimasa; Susumu Matsuo
2004-01-01
The magnetic susceptibility of the ZnMgSc icosahedral quasicrystals, which have a new type of atomic cluster structure, was found to increase with a rise in temperature from 100 to 300 K. The increase of the susceptibility was accounted for by the temperature dependent term of the Pauli paramagnetism, which indicated a pseudogap in the electronic density of states (DOS) near
Technology Transfer Automated Retrieval System (TEKTRAN)
The inactivation mechanism of ultrashort pulsed laser irradiation at a wavelength of 425 nm has been studied using two different-sized, non-enveloped icosahedral viruses, murine norovirus-1 (MNV-1) and human papillomavirus-16 (HPV-16) pseudovirions. Our experimental results are consistent with a mo...
Global ocean simulations by HYCOM on icosahedral and logically rectangular grids
NASA Astrophysics Data System (ADS)
Sun, Shan; Bleck, Rainer
2015-04-01
iHYCOM, short for "icosahedral HYbrid Coordinate Ocean Model", is being developed at the NOAA Earth System Research Laboratory. The purpose of formulating HYCOM on an icosahedral grid is to allow coupling to an existing icosahedral weather prediction model ("FIM", see http://fim.noaa.gov) unencumbered by interpolation problems at the air-sea-ice interface. We have tested the traditional HYCOM, formulated on a Mercator grid augmented by a bipolar pole patch, with iHYCOM for several decades at comparable horizontal mesh sizes in the 0.5-1.0 deg range, employing the same vertical resolution of 26 potential density (sigma_1) layers. These comparison runs were forced by CORE (Common Ocean-Ice Reference Experiment) fields. Several performance measures indicate that formulating HYCOM on an icosahedral mesh is feasible, although a numerically stable barotropic-baroclinic mode splitting scheme is not available yet. We compare the large scale circulations simulated by both model versions and investigate the model sensitivity to different horizontal grids.
Transcritical bifurcation with O(3) symmetry
NASA Astrophysics Data System (ADS)
Matthews, P. C.
2003-07-01
Bifurcation from spherical symmetry occurs transcritically when the degree l of the spherical harmonics is even. In this case the leading-order bifurcation equations are completely determined by the symmetry. Several new results are presented concerning the existence or non-existence of solutions with dihedral symmetry in two-dimensional subspaces. For large l, there is an alternating arrangement of existence and non-existence of such solutions. Although all bifurcating branches of stationary solutions are unstable, a preferred solution is identified using a variational criterion; this solution also has only one positive eigenvalue. It is shown that the axisymmetric state is never the preferred solution according to this criterion. Results on the existence and stability of solution branches are given for even values of l up to l = 18, including all solutions in subspaces of dimension three or lower. For l = 6, 10 and 12, the preferred solution has icosahedral symmetry.
Symmetry, stability, and dynamics of multidomain and multicomponent?protein?systems
Blundell, Tom?L.; Srinivasan, N.
1996-01-01
Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions. PMID:8962033
Systematic mapping of icosahedral short-range order in a melt-spun Zr36Cu64 metallic glass.
Liu, A C Y; Neish, M J; Stokol, G; Buckley, G A; Smillie, L A; de Jonge, M D; Ott, R T; Kramer, M J; Bourgeois, L
2013-05-17
By analyzing the angular correlations in scanning electron nanodiffraction patterns from a melt-spun Zr(36)Cu(64) glass, the dominant local order was identified as icosahedral clusters. Mapping the extent of this icosahedral short-range order demonstrates that the medium-range order in this material is consistent with a face-sharing or interpenetrating configuration. These conclusions support results from atomistic modeling and a structural basis for the glass formability of this system. PMID:25167428
Tsutomu Ishimasa; Kei Oyamada; Yasuomi Arichika; Eiji Nishibori; Masaki Takata; Makoto Sakata; Kenichi Kato
2004-01-01
A structure analysis of the ZnMgHo icosahedral quasicrystal was carried out by the powder X-ray diffraction method using synchrotron radiation (?=0.73490 ) at SPring-8. The intensity distribution was analyzed by the Rietveld method modified for an icosahedral quasicrystal, in which simplified models were assumed: ellipsoid and spherical windows were assumed at five crystallographic sites in a F-type hypercubic unit cell.
'Broken symmetries' in macromolecular crystallography: phasing from unmerged data.
Schiltz, Marc; Bricogne, Grard
2010-04-01
The space-group symmetry of a crystal structure imposes a point-group symmetry on its diffraction pattern, giving rise to so-called symmetry-equivalent reflections. Instances in macromolecular crystallography are discussed in which the symmetry in reciprocal space is broken, i.e. where symmetry-related reflections are no longer equivalent. Such a situation occurs when the sample suffers from site-specific radiation damage during the X-ray measurements. Another example of broken symmetry arises from the polarization anisotropy of anomalous scattering. In these cases, the genuine intensity differences between symmetry-related reflections can be exploited to yield phase information in the structure-solution process. In this approach, the usual separation of the data merging and phasing steps is abandoned. The data are kept unmerged down to the Harker construction, where the symmetry-breaking effects are explicitly modelled and refined and become a source of supplementary phase information. PMID:20382998
Broken symmetries in macromolecular crystallography: phasing from unmerged data
Schiltz, Marc; Bricogne, Grard
2010-01-01
The space-group symmetry of a crystal structure imposes a point-group symmetry on its diffraction pattern, giving rise to so-called symmetry-equivalent reflections. Instances in macromolecular crystallography are discussed in which the symmetry in reciprocal space is broken, i.e. where symmetry-related reflections are no longer equivalent. Such a situation occurs when the sample suffers from site-specific radiation damage during the X-ray measurements. Another example of broken symmetry arises from the polarization anisotropy of anomalous scattering. In these cases, the genuine intensity differences between symmetry-related reflections can be exploited to yield phase information in the structure-solution process. In this approach, the usual separation of the data merging and phasing steps is abandoned. The data are kept unmerged down to the Harker construction, where the symmetry-breaking effects are explicitly modelled and refined and become a source of supplementary phase information. PMID:20382998
Scanning Tunneling Microscopy Studies of Surface Structures of Icosahedral Al-Cu-Fe Quasicrystals
Tanhong Cai
2002-12-31
Three papers are included in this dissertation. The first paper: ''Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies'', is in press with ''Surface Science''. The second paper: ''An STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface'' is submitted to ''Physical Review B, Rapid Communication''. The third paper: ''Pseudomorphic starfish: arrangement of extrinsic metal atoms on a quasicrystalline substrate'' is submitted to ''Nature''. Following the third paper are general conclusions and appendices that document the published paper ''Structural aspects of the three-fold surface of icosahedral Al-Pd-Mn'' (appearing in volume 461, issue 1-3 of ''Surface Science'' on page L521-L527, 2000), the design as well as the specifications of the aluminum evaporator used in the aluminum deposition study in this dissertation, an extended discussion of the aluminum deposition on the quasicrystalline surface, and the STM database.
Growth of Au on Pt icosahedral nanoparticles revealed by low-dose in situ TEM.
Wu, Jianbo; Gao, Wenpei; Wen, Jianguo; Miller, Dean J; Lu, Ping; Zuo, Jian-Min; Yang, Hong
2015-04-01
A growth mode was revealed by an in situ TEM study of nucleation and growth of Au on Pt icosahedral nanoparticles. Quantitative analysis of growth kinetics was carried out based on real-time TEM data, which shows the process involves: (1) deposition of Au on corner sites of Pt icosahedral nanoparticles, (2) diffusion of Au from corners to terraces and edges, and (3) subsequent layer-by-layer growth of Au on Au surfaces to form Pt@Au core-shell nanoparticles. The in situ TEM results indicate diffusion of Au from corner islands to terraces and edges is a kinetically controlled growth, as evidenced by a measurement of diffusion coefficients for these growth processes. We demonstrated that in situ electron microscopy is a valuable tool for quantitative study of nucleation and growth kinetics and can provide new insight into the design and precise control of heterogeneous nanostructures. PMID:25723499
Formation of a well ordered ultrathin aluminum oxide film on icosahedral AlPdMn quasicrystal
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
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.
Magnetic Color Symmetry of Lattice Rotations in a Non-magnetic Material
Sava Denev; A. Kumar; M. D. Biegalski; H. W. Jang; C. M. Folkman; A. Vasudevarao; Y. Han; I. M. Reaney; S. Trolier-McKinstry; C.-B. Eom; D. G. Schlom; V. Gopalan
2009-01-01
Oxygen octahedral rotations are the most common phase transitions in perovskite crystal structures. Here we show that the color symmetry of such pure elastic distortions is isomorphic to magnetic point groups, which allows their probing through distinguishing polar versus magnetic symmetry. We demonstrate this isomorphism using nonlinear optical probing of the octahedral rotational transition in a compressively strained SrTiO3 thin
Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy
Grigorieff, Nikolaus; Harrison, Stephen C.
2011-01-01
Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfill predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3 4 resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry. PMID:21333526
A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, Jin
2013-11-01
The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM uses innovations in model formulation similar to its hydrostatic version of the Flow-following Icosahedral Model (FIM) developed by Earth System Research Laboratory (ESRL) which has been tested and accepted for future use by the National Weather Service as part of their operational global prediction ensemble. Innovations from the FIM used in the NIM include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, et al., 2010), * All differentials evaluated as finite-volume integrals around the cells, *Icosahedral grid optimization (Wang and Lee, 2011) NIM extends the two-dimensional finite-volume operators used in FIM into the three-dimensional finite-volume solvers designed to improve pressure gradient calculation and orographic precipitation over complex terrain. The NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as warm bubble, density current, internal gravity wave, and mountain waves. Physical parameterizations have been incorporated into the NIM dynamic core and successfully tested with multimonth aqua-planet simulations. Recent results from NIM simulations will be presented at the Symposium.
B12Hn and B12Fn: planar vs icosahedral structures
2012-01-01
Using density functional theory and quantum Monte Carlo calculations, we show that B12Hn and B12Fn (n = 0 to 4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we show that the fully planar B12F6 cluster is more stable than the three-dimensional counterpart. These results open up the possibility of designing larger boron-based nanostructures starting from quasi-planar or fully planar building blocks. PMID:22546348
Stacking faults in high-temperature-deformed Al-Pd-Mn icosahedral quasicrystals
Renhui Wang; Michael Feuerbacher; Wenge Yang; Knut Urban
1998-01-01
Stacking-fault contrasts were observed by transmission electron microscopy in high-temperature, plastically deformed Al-Pd-Mn icosahedral quasicrystals. Bright- and dark-field contrast and trace analysis experiments show that there are two types of stacking-fault contrast. One has a fault plane perpendicular to a twofold axis and a displacement vector parallel to the fault plane normal, while the other has a fault plane perpendicular
Stacking faults in high-temperature-deformed Al-Pd-Mn icosahedral quasicrystals
Renhuiwang
1998-01-01
Stacking-fault contrasts were observed by transmission electron microscopy in high-temperature, plastically deformed Al-Pd-Mn icosahedral quasicrystals. Bright-and dark-field contrast and trace analysis experiments show that there are two types of stacking-fault contrast. One has a fault plane perpendicular to a twofold axis and a displacement vector parallel to the fault plane normal, while the other has a fault plane perpendicular to
Magnetic and electrical properties of a stable Zn-Mg-Ho icosahedral quasicrystal
S. Kashimoto; S. Matsuo; Hiroshi Nakano; T. Shimizu; T. Ishimasa
1998-01-01
We investigated the electrical resistivity and the magnetism of heavy-rare-earth-based Zn60Mg30Ho10 F-type icosahedral quasicrystals in the temperature region between 2K and room temperature below 80kOe in magnetic field. The maximum value of the electrical resistivity is 159?? cm which is comparatively lower than other quasicrystal systems. Below 15K, the magnetic-field dependence exhibits a magnetoresistance maximum which has not been observed
Icosahedral quasicrystal and 1\\/1 cubic approximant in Au-Al-Yb alloys
Tsutomu Ishimasa; Yukinori Tanaka; Shiro Kashimoto
2011-01-01
A P-type icosahedral quasicrystal is formed in Au-Al-Yb alloy of which 6-dimensional lattice parameter a6D = 7.448 {\\\\AA}. The composition of the quasicrystal was analyzed to be Au51Al34Yb15. This quasicrystal is formed in as-cast alloys, and is regarded as metastable because of decomposition into other crystalline phases by annealing at 700 \\\\degree C. Among Tsai-type quasicrystals, this quasicrystal is situated
Ten-fold-like magnetic anisotropy in electrical conductivity of AlPdMn icosahedral quasicrystal
Takayuki Mizutani; Hiroshi Nakano; Shiro Kashimoto; Yukihiro Takatani; Masahiro Mori; Tsutomu Ishimasa; Susumu Matsuo
2002-01-01
Ten-fold-like magnetic anisotropy is reproducibly observed in electrical conductivity of Al71Pd21Mn8 icosahedral quasicrystal. The voltage V is measured, where the current I is along a five-fold axis of the sample and is perpendicular to the magnetic field H. The voltage difference ?V=V(+I)+V(?I) has angle dependences at H=30?80 kOe and the temperature T=2?8 K. ?V is about 3000 times smaller than
Microdomain Structure in the Disordered Zn-Mg-Ho Icosahedral Phase
Tsutomu Ishimasa; Takayuki Shimizu
2000-01-01
Diffuse scattering related to F-type superlattice ordering was observed in the disordered icosahedral phase formed in Zn60Mg35Ho5 alloy annealed at 562C. Real space analysis of the diffuse scattering was carried out using high-resolution electron microscopy and a Fourier filtering method. Processed images revealed the presence of microdomains related to weak F-type ordering. The domain diameters range between 30 and 170
Synthesis of Stable Icosahedral Quasicrystals in Zn-Sc Based Alloys and Their Magnetic Properties
S. Kashimoto; T. Ishimasa
2006-01-01
We have measured magnetic properties of stable icosahedral quasicrystals Zn-M-Sc (M = Fe, Co and Ag). These quasicrystals were formed in Zn-Sc based alloys and possess high structural perfection which was confirmed by X-ray powder diffraction and selected-area electron diffraction. The magnetic susceptibility of the Zn74.5Ag9.5Sc16 quasicrystal shows an increase with a rise in temperature over 80 K, which is
Icosahedral quasicrystals in Zn-T-Sc (T = Mn, Fe, Co or Ni) alloys
Ryo Maezawa; Shiro Kashimoto; Tsutomu Ishimasa
2004-01-01
Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a6D
Susumu Matsuo; Tsutomu Ishimasa; Hiroshi Nakano
1997-01-01
Time dependence of the magnetic susceptibility of two kinds of Al?Pd?Mn icosahedral quasicrystals was studied to investigate the phason relaxation in the anneal after water quench. Al70Pd21.5Mn8.5 remained in the f-type structure and Al71Pd21Mn8 transformed to p-type. A universal time dependence was found in the initial decrease in the susceptibility characterized by square root of time. The whole time dependence
Antiferromagnetic orders in Ising model simulations in an icosahedral ZnMgHo structure
Susumu Matsuo; Tsutmu Ishimasa; Hiroshi Nakano
2000-01-01
Antiferromagnetic orders were investigated in an icosahedral ZnMgHo model structure in simulated annealing of 12524 and 67896 Ising spins interacting via a RudermanKittelKasuyaYosida (RKKY)-like alternating exchange. Magnetic orders were analyzed by means of diffraction patterns arising from spin-dependent elastic scattering amplitudes. The diffraction patterns from the magnetic structure consisted of spots at low temperatures in the case of an antiferromagnetic
Superlattice ordering in the low-temperature icosahedral phase of Al-Pd-Mn
T. Ishimasa
1995-01-01
The low-temperature icosahedral phase, which forms below approximately 700C near the alloy composition Al71Pd21Mn8 has been investigated by means of electron diffraction. Precise analysis of diffraction patterns indicates that the Bravais lattice of the low-temperature phase is P type, different from the formerly proposed F type. The six-dimensional lattice parameter of this new P-type lattice is determined to be aP
Electrical Properties of a Stable Icosahedral Quasicrystal Zn-Fe-Sc
Senni Motomura; Shiro Kashimoto; Ryo Maezawa; Tsutomu Ishimasa; Susumu Matsuo
2004-01-01
The electrical resistivity of a recently discovered stable icosahedral quasicrystal Zn77Fe7Sc16 was found to have a T1\\/2 dependence in low temperature region between 2 and 16 K, while it increased gradually by 6.8% with the decrease in temperature from 270 to 2 K. The increase is considered to arise from the weak localization of conduction electrons. Negative magnetoresistance was found
Orientation relation between icosahedral and crystalline phases in Al-Mn alloys
C. Beeli; T. Ishimasa; H.-U. Nissen
1988-01-01
A transmission-electron-microscope investigation of the orientation relations between faceted icosahedral quasicrystals and crystalline f.c.c. matrix in rapidly cooled alloys of Al-Mn reveals three different orientation relations:In the third relation the f.c.c.[111] axis cannot be exactly parallel to the twofold axis i2 because of geometrical restrictions. Most of the observed relations can be ideally classified into these three classes (with deviations
Resonant photoemission study of the Al-Cu-Fe icosahedral phase
M. Mori; K. Kamiya; S. Matsuo; T. Ishimasa; Hiroshi Nakano; H. Fujimoto; H. Inokuchi
1992-01-01
Photoemission spectra of the valence band in an Al-Cu-Fe icosahedral phase are studied at excitation photon energies near the Fe threshold. The constant-initial-state spectra in the binding energy region between 0-2 eV show a resonant characteristic. The spectrum has an asymmetric shape, in which the weak peak is on the lower photon energy side and the strong dip is on
Electrical transport, magnetic and thermal properties of icosahedral AlPdMn quasicrystals
A. Poddar; S. Das; D. Plachke; H. D. Carstanjen
2006-01-01
We report measurements of electrical resistivity (?), Hall coefficient (RH), magnetization (M) and specific heat (Cp(T)) of high-quality icosahedral Al70.4Pd20.8Mn8.8 phases with different thermal treatment. An improvement in the quasi-crystallinity upon the annealing treatment caused a drastic increase in ? up to 7000??cm accompanied by a very small electronic specific heat coefficient ?. The low temperature ?(T) data has been
Computational self-assembly of a one-component icosahedral quasicrystal.
Engel, Michael; Damasceno, Pablo F; Phillips, Carolyn L; Glotzer, Sharon C
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems. PMID:25485986
Computational self-assembly of a one-component icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Engel, Michael; Damasceno, Pablo F.; Phillips, Carolyn L.; Glotzer, Sharon C.
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.
Dynamic Paper Constructions for Easier Visualization of Molecular Symmetry
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2010-01-01
A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The
Lowe, M; Yadav, T P; Fourne, V; Ledieu, J; McGrath, R; Sharma, H R
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol. PMID:25747095
Hiroyuki Shimizu; Takashi Nishida; Hiroaki Takeda; Tadashi Shiosaki
2009-01-01
Rare-earth calcium oxoborate RCa4O(BO3)3 (R=La, Gd, Y) piezoelectric single crystals were successfully grown by a conventional RF-heating Czochralski (Cz) technique. They belong to the monoclinic system with point group m, and have 27 independent material constants. We developed the determination scheme (cuts and vibration modes) of the material constants in point group m. Their material constants were evaluated on the
Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes
M. Damnjanovic; I. Milosevic; T. Vukovic; R. Sredanovic
1999-01-01
The full symmetry groups for all single-wall and multiwall carbon nanotubes are found. As for the single-wall tubes, the symmetries form non-Abelian nonsymorphic line groups, enlarging the groups reported in the literature. In the multiwall case, any type of line and axial point groups can be obtained, depending on single-wall constituents and their relative position. The isogonal symmetry is related
Boyer, Edmond
KINETICS OF ICOSAHEDRAL PARTICLES IN GOLD FILMS CONDENSED ON NaCl SUBSTRATE M. GILLET and A. RENOU size is often greater than the one of c.f.c. particles. In a first stsige of growth we suppose'experience. Abstract. -Gold particles condensed on alkali halides have sometimes icosahedral structure. Particles
Vasconcelos, Wolmer
More Stuff on Groups Groups Acting on Itself Icosahedral Group Operations on Subsets Sylow Theorems Homework Math 451: Abstract Algebra I Wolmer V. Vasconcelos Set 3 Fall 2009 #12;More Stuff on Groups Groups Acting on Itself Icosahedral Group Operations on Subsets Sylow Theorems Homework Outline 1 More Stuff
Gähler, Franz
-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant. Marc de Boissieu1 ** , Sonia Francoual 1 author : Marc.de-boissieu@ltpcm.inpg.fr Abstract: Quasicrystals are long range ordered materials which scattering experiments on single grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn
Projective symmetry of partons in Kitaev's honeycomb model
NASA Astrophysics Data System (ADS)
Mellado, Paula
2015-03-01
Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of Kitaev's honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities reflect not the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group. We acknowledge Fondecyt under Grant No. 11121397, Conicyt under Grant No. 79112004, and the Simons Foundation (P.M.); the Max Planck Society and the Alexander von Humboldt Foundation (O.P.); and the US DOE Grant No. DE-FG02-08ER46544 (O.T.).
Mg32(Zn,Al)49-type icosahedral quasicrystals formed by solid-state reaction and rapid solidification
NASA Astrophysics Data System (ADS)
Cassada, W. A.; Shen, Y.; Poon, S. J.; Shiflet, G. J.
1986-11-01
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.
High Pressure X-ray Diffraction Study on Icosahedral Boron Arsenide (B12As2)
J Wu; H Zhu; D Hou; C Ji; C Whiteley; J Edgar; Y Ma
2011-12-31
The high pressure properties of icosahedral boron arsenide (B12As2) were studied by in situ X-ray diffraction measurements at pressures up to 25.5 GPa at room temperature. B12As2 retains its rhombohedral structure; no phase transition was observed in the pressure range. The bulk modulus was determined to be 216 GPa with the pressure derivative 2.2. Anisotropy was observed in the compressibility of B12As2-c-axis was 16.2% more compressible than a-axis. The boron icosahedron plays a dominant role in the compressibility of boron-rich compounds.
Dynamical x-ray diffraction from an icosahedral Al-Pd-Mn quasicrystal
Kycia, S.
1996-04-23
Primary extinction effects in diffraction from single grains of Al-Pd- Mn, and presumably many other FCI alloys, may be significant and should be corrected for prior to use of diffraction data in structural determinations. Probes based on dynamical diffraction effects, such as x-ray standing wave fluorescence, multiple beam interference, and x-ray transmission topographs, may now be used to study the bulk and surface structure of some quasicrystals. The observation of dynamical diffraction from icosahedral Al-Pd-Mn is a striking confirmation of the fact that quasicrystals can present a degree of structural perfection comparable to that found in the best periodic intermetallic crystals.
Millimeter-Sized Single Icosahedral Quasicrystal of Zn-Mg-Sc Alloy
Yasushi Kaneko; Tsutomu Ishimasa
2002-01-01
Millimeter-sized single icosahedral quasicrystals were produced by slow cooling from melt in Zn80.5Mg4.2Sc15.3 alloy. The alloy ingots were melted at 835C for 1 h and then slowly cooled to an annealing temperature of 750C at the cooling rates of 28 K\\/h and 60 K\\/h. Scanning electron microscopy, electron back-scattered diffraction, and selected-area electron diffraction and powder X-ray diffraction experiments revealed
Magnetic and electrical properties of a CuGaMgSc icosahedral quasicrystal
Hidetoshi Yamada; Senni Motomura; Ryo Maezawa; Yasushi Kaneko; Tsutomu Ishimasa; Hiroshi Nakano; Susumu Matsuo
2004-01-01
We have investigated the magnetic susceptibility and the electrical resistivity of a new P-type icosahedral quasicrystal Cu48.2Ga33.8Mg3Sc15 and a cubic phase Cu49Ga36Sc15, interpreted as a 1\\/1 approximant crystal of the quasicrystal. The magnetic susceptibility of the Cu48.2Ga33.8Mg3Sc15 quasicrystal showed an increase from ?3.5110?4 to ?2.7810?4 m3kg?1 with a rise in temperature from 120 to 300 K. The Cu49Ga36Sc15 cubic phase
A metastable icosahedral quasicrystal in the Zn--Mg--Yb alloy system
T. Mitani; T. Ishimasa
2006-01-01
The formation conditions for a ZnMgYb icosahedral quasicrystal, which is primitive (P) type and has a six-dimensional lattice parameter a6D?=?7.371?, have been studied. This quasicrystal is formed only by quenching from a temperature higher than 650C in the narrow composition region between approximately Zn76Mg9Yb15 and Zn71Mg17Yb12. On annealing, this quasicrystal transforms to the Zn17Yb3-type cubic phase and the hexagonal Z
Solution growth of a binary icosahedral quasicrystal of Sc[subscript 12]Zn[subscript 88
Canfield, P.C.; Caudle, M.L.; Ho, C.-S.; Kreyssig, A.; Nandi, S.; Kim, M.G.; Lin, X.; Kracher, A.; Dennis, K.W.; McCallum, R.W.; Goldman, A.I. (Iowa State)
2010-07-23
We report the discovery of a binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra, and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order. The discovery of i-Sc{sub 12}Zn{sub 88} suggests that a re-examination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other binary quasicrystalline phases.
Icosahedral packing of polymer-tethered nanospheres and stabilization of the Gyroid Phase
NSDL National Science Digital Library
Iacovella, Christopher R.
2006-05-17
We present results of molecular simulations that predict the phases formed by the selfassembly of model nanospheres functionalized with a single polymer tether. Microphase separation of the immiscible tethers and nanospheres induces the formation of the double gyroid, perforated lamella and crystalline bilayer phases. Confinement effects promote the formation of icosahedral arrangements of nanoparticles that help to stabilize the gyroid and perforated lamella phases. We also present a new metric for determining the local arrangement of particles in liquid and solid configurations.
Preprint, link to published version can be found below.
Very large thermal rectification in bulk composites consisting partly of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Takeuchi, Tsunehiro
2014-12-01
The bulk thermal rectifiers usable at a high temperature above 300 K were developed by making full use of the unusual electron thermal conductivity of icosahedral quasicrystals. The unusual electron thermal conductivity was caused by a synergy effect of quasiperiodicity and by a narrow pseudogap at the Fermi level. The rectification ratio, defined by TRR = |{{{\\boldsymbol{J}} }large}|/|{{{\\boldsymbol{J}} }small}|, reached vary large values exceeding 2.0. This significant thermal rectification would lead to new practical applications for the heat management.
Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary 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
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.
Nol, Yves; De La Pierre, Marco; Zicovich-Wilson, Claudio M; Orlando, Roberto; Dovesi, Roberto
2014-07-14
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
The structure of the NTPase that powers DNA packaging into Sulfolobus turreted icosahedral virus 2.
Happonen, Lotta J; Oksanen, Esko; Liljeroos, Lassi; Goldman, Adrian; Kajander, Tommi; Butcher, Sarah J
2013-08-01
Biochemical reactions powered by ATP hydrolysis are fundamental for the movement of molecules and cellular structures. One such reaction is the encapsidation of the double-stranded DNA (dsDNA) genome of an icosahedrally symmetric virus into a preformed procapsid with the help of a genome-translocating NTPase. Such NTPases have been characterized in detail from both RNA and tailed DNA viruses. We present four crystal structures and the biochemical activity of a thermophilic NTPase, B204, from the nontailed, membrane-containing, hyperthermoacidophilic archaeal dsDNA virus Sulfolobus turreted icosahedral virus 2. These are the first structures of a genome-packaging NTPase from a nontailed, dsDNA virus with an archaeal host. The four structures highlight the catalytic cycle of B204, pinpointing the molecular movement between substrate-bound (open) and empty (closed) active sites. The protein is shown to bind both single-stranded and double-stranded nucleic acids and to have an optimum activity at 80C and pH 4.5. The overall fold of B204 places it in the FtsK-HerA superfamily of P-loop ATPases, whose cellular and viral members have been suggested to share a DNA-translocating mechanism. PMID:23698307
Cluster packing geometry for Al-based F-type icosahedral alloys
Nobuhisa Fujita; Hikari Takano; Akiji Yamamoto; An-Pang Tsai
2013-01-29
This paper presents a new highly stable periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al-Pd-TM (TM=transition metals). The structure of this intermetallic Al-Pd-Cr-Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be Pa-3 and the lattice constant 40.5 angstrom. The structure is well described as a dense packing of clusters of two kinds, which are known in the literature as the pseudo-Mackay type and the Bergman type clusters. The clusters are centered at the vertices of a canonical cell tiling, in which the parity of each vertex determines the kind of the associated cluster. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the crystal can be designated as a 2x2x2 superstructure of the ordinary cubic 3/2 rational approximant. The superlattice ordering is shown to be of a different kind from the P-type superlattice ordering previously reported in i-Al-Pd-Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.
The Structure of the NTPase That Powers DNA Packaging into Sulfolobus Turreted Icosahedral Virus 2
Happonen, Lotta J.; Oksanen, Esko; Liljeroos, Lassi; Goldman, Adrian; Kajander, Tommi
2013-01-01
Biochemical reactions powered by ATP hydrolysis are fundamental for the movement of molecules and cellular structures. One such reaction is the encapsidation of the double-stranded DNA (dsDNA) genome of an icosahedrally symmetric virus into a preformed procapsid with the help of a genome-translocating NTPase. Such NTPases have been characterized in detail from both RNA and tailed DNA viruses. We present four crystal structures and the biochemical activity of a thermophilic NTPase, B204, from the nontailed, membrane-containing, hyperthermoacidophilic archaeal dsDNA virus Sulfolobus turreted icosahedral virus 2. These are the first structures of a genome-packaging NTPase from a nontailed, dsDNA virus with an archaeal host. The four structures highlight the catalytic cycle of B204, pinpointing the molecular movement between substrate-bound (open) and empty (closed) active sites. The protein is shown to bind both single-stranded and double-stranded nucleic acids and to have an optimum activity at 80C and pH 4.5. The overall fold of B204 places it in the FtsK-HerA superfamily of P-loop ATPases, whose cellular and viral members have been suggested to share a DNA-translocating mechanism. PMID:23698307
The Architecture and Chemical Stability of the Archaeal Sulfolobus Turreted Icosahedral Virus ?
Khayat, Reza; Fu, Chi-yu; Ortmann, Alice C.; Young, Mark J.; Johnson, John E.
2010-01-01
Viruses utilize a diverse array of mechanisms to deliver their genomes into hosts. While great strides have been made in understanding the genome delivery of eukaryotic and prokaryotic viruses, little is known about archaeal virus genome delivery and the associated particle changes. The Sulfolobus turreted icosahedral virus (STIV) is a double-stranded DNA (dsDNA) archaeal virus that contains a host-derived membrane sandwiched between the genome and the proteinaceous capsid shell. Using cryo-electron microscopy (cryo-EM) and different biochemical treatments, we identified three viral morphologies that may correspond to biochemical disassembly states of STIV. One of these morphologies was subtly different from the previously published 27--resolution electron density that was interpreted with the crystal structure of the major capsid protein (MCP). However, these particles could be analyzed at 12.5- resolution by cryo-EM. Comparing these two structures, we identified the location of multiple proteins forming the large turret-like appendages at the icosahedral vertices, observed heterogeneous glycosylation of the capsid shell, and identified mobile MCP C-terminal arms responsible for tethering and releasing the underlying viral membrane to and from the capsid shell. Collectively, our studies allow us to propose a fusogenic mechanism of genome delivery by STIV, in which the dismantled capsid shell allows for the fusion of the viral and host membranes and the internalization of the viral genome. PMID:20592081
NASA Astrophysics Data System (ADS)
Pudykiewicz, Janusz A.
2011-03-01
The shallow water equations coupled to the set of reaction-advection-diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.
Kentaro Hori; Cumrun Vafa
2000-01-01
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
Martin R. Zirnbauer
2010-01-05
Physical systems exhibiting stochastic or chaotic behavior are often amenable to treatment by random matrix models. In deciding on a good choice of model, random matrix physics is constrained and guided by symmetry considerations. The notion of 'symmetry class' (not to be confused with 'universality class') expresses the relevance of symmetries as an organizational principle. Dyson, in his 1962 paper referred to as the Threefold Way, gave the prime classification of random matrix ensembles based on a quantum mechanical setting with symmetries. In this article we review Dyson's Threefold Way from a modern perspective. We then describe a minimal extension of Dyson's setting to incorporate the physics of chiral Dirac fermions and disordered superconductors. In this minimally extended setting, where Hilbert space is replaced by Fock space equipped with the anti-unitary operation of particle-hole conjugation, symmetry classes are in one-to-one correspondence with the large families of Riemannian symmetric spaces.
D. Reinhard; B. D. Hall; P. Berthoud; S. Valkealahti; R. Monot
1997-01-01
Unsupported nanometer-sized copper particles in a molecular beam of inert carrier gas have been studied using electron diffraction. A distinct separation in the size distributions of fcc and icosahedral particles is observed: Icosahedra occur at sizes well below a diameter limit of 3.8 nm predicted for copper by molecular dynamics simulations, while fcc particles occur close to this limit or
S. Matsuo; Hiroshi Nakano; T. Ishimasa; Y. Fukano
1989-01-01
The stable Al-Cu-Fe icosahedral phase showed almost no local magnetic moment at low temperatures, and a dependence of the magnetic susceptibility linear to the square of the temperature above about 150 K. The former is interpreted by the condition of the local magnetic moment formation according to the theory of Friedel and Anderson, and the latter affords strong experimental evidence
Nematic phases and the breaking of double symmetries
Mathy, C.J.M. [Department of Physics, Princeton University, Jadwin Hall, Princeton, NJ 08544 (United States)]. E-mail: cmathy@princeton.edu; Bais, F.A. [Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)]. E-mail: bais@science.uva.nl
2007-03-15
In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra T{sub r} and the symmetry algebra U characterizing the effective 'low energy' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP. Physical parameterizations such as those used by GFS have been incorporated into NIM dynamic core and successfully tested with multi-months aqua-planet simulations as well as real data simulations. NIM has been implemented on GPUs and CPUs. Efficiency tests show GPU significantly speeds up model calculations.
P. Danielewicz
2006-07-15
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal densities.
Thermal conductivity and Seebeck coefficients of icosahedral boron arsenide films on silicon carbide
NASA Astrophysics Data System (ADS)
Gong, Y.; Zhang, Y.; Dudley, M.; Zhang, Y.; Edgar, J. H.; Heard, P. J.; Kuball, M.
2010-10-01
The thermal conductivity of icosahedral boron arsenide (B12As2) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3? technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 ?V/K and 136 ?V/K for samples grown at 1350 C with AsH3/B2H6 flow ratio equals to 1:1 and 3:5, respectively.
Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface
Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.
2007-07-21
Nucleation of Ag islands on the five-fold surface of icosahedral Al-Pd-Mn is influenced strongly by trap sites. Submonolayers of Ag prepared by deposition at 365 K and with a flux of 1 x 10{sup -3} monolayers/s exhibit a variation in Ag island densities across different terraces. Comparisons with previous work and with rate equation analysis indicate that trap sites are not saturated under these experimental conditions and that the difference in island densities is not necessarily due to variation in trap densities. While it could have a number of different origins, our results point to a terrace-dependent value of the effective diffusion barrier for Ag adatoms.
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Cout, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-01-01
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 ?m in diameter and adeninethymine (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 guaninecytosine-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; Cout, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-03-18
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 ?m in diameter and adenine-thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 ?m in length and guanine-cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 ?m in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))
1988-07-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, noise) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals.
Spinless Topological Insulators without Time-Reversal Symmetry A. Alexandradinata,1
Gilbert, Matthew
Spinless Topological Insulators without Time-Reversal Symmetry A. Alexandradinata,1 Chen Fang,2, 3 surface modes. For n = 3, 4 and 6 of the Cnv groups, we find the first-known 3D topological insulators) We explore the 32 crystallographic point groups and identify topological phases of matter with robust
R. Aldrovandi; R. R. Cuzinatto; L. G. Medeiros
2007-08-30
A detailed examination of the Killing equations in Robertson-Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product U = (a^2)(dH/dt) of the squared scale parameter by the time-derivative of the Hubble function encapsulates the relationship between the two cases: the symmetry is maximal when U is a constant, and reduces to the six-parameter symmetry of a generic Friedmann-Robertson-Walker model when it is not. As the fields physical interpretation is not clear in these coordinates, comparison is made with the Killing fields in static coordinates, whose interpretation is made clearer by their direct relationship to the Poincare group generators via Wigner-Inonu contractions.
Magnetic color symmetry of lattice rotations in a diamagnetic material.
Denev, S; Kumar, A; Biegalski, M D; Jang, H W; Folkman, C M; Vasudevarao, A; Han, Y; Reaney, I M; Trolier-McKinstry, S; Eom, C-B; Schlom, D G; Gopalan, V
2008-06-27
Oxygen octahedral rotations are the most common phase transitions in perovskite crystal structures. Here we show that the color symmetry of such pure elastic distortions is isomorphic to magnetic point groups, which allows their probing through distinguishing polar versus magnetic symmetry. We demonstrate this isomorphism using nonlinear optical probing of the octahedral rotational transition in a compressively strained SrTiO3 thin film that exhibits ferroelectric (4mm) and antiferrodistortive (4{'}mm{'}) phases evolving through independent phase transitions. The approach has broader applicability for probing materials with lattice rotations that can be mapped to color groups. PMID:18643702
Full Symmetry of Single- and Multi-wall Nanotubes
M. Damnjanovic; I. Milosevic; T. Vukovic; R. Sredanovic
1999-02-17
The full symmetry groups for all single- and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case, any type of the line and the axial point groups can be obtained, depending on single-wall constituents and their relative position. Several other consequences are discussed: quantum numbers and related selection rules, electronic and phonon bands, and their degeneracy, application to tensor properties.
S. Kashimoto; S. Motomura; S. Francoual; S. Matsuo; T. Ishimasa
2006-01-01
We have investigated the magnetic properties of Zn-based Tsai-type icosahedral quasicrystals (i-QCs) and their approximants by measuring the field-and temperature-dependence of magnetization. The quasicrystals are formed by an addition of the third element M (M?=?Mg, Mn, Fe, Co, Ni, Cu, Pd, Ag, Pt or Au) to a Zn17Sc3 1\\/1 cubic approximant crystal. The remarkable feature of the Zn-M-Sc series is
Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1\\/1 approximant
Marc de Boissieu; Sonia Francoual; Marek Mihalkovic; Kaoru Shibata; Alfred Q. R. Baron; Yvan Sidis; Tsutomu Ishimasa; Dongmei Wu; Thomas Lograsso; Louis-Pierre Regnault; Franz Ghler; Satoshi Tsutsui; Bernard Hennion; Pierre Bastie; Taku J. Sato; Hiroyuki Takakura; Roland Currat; An-Pang Tsai
2007-01-01
Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1\\/1 approximant, with the aim of studying the respective influence of the local order and of the long-range
M. de Boissieu; S. Francoual; Y. Kaneko; T. Ishimasa
2005-01-01
We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Qper2 dependence. Moreover, when compared to
Long-range and short-range F-type ordering in ZnMgHo icosahedral phase
T Ishimasa; T Shimizu
2000-01-01
The behavior of the F-type superlattice in the ZnMgHo icosahedral phase was studied with respect to long-range ordering and short-range ordering. At the composition Zn60Mg30Ho10, a gradual decrease in intensities of superlattice reflections was observed in the alloys annealed at high temperatures, i.e. at 544, 549, 559 and 563C. This observation indicated that the long-range order parameters decrease in the
Atomic model of anti-phase boundaries in a face-centred icosahedral Zn Mg Dy quasicrystal
Jianbo Wang; Wenge Yang; Renhui Wang
2003-01-01
An atomic model in the physical space for an anti-phase boundary (APB) in the ordered face-centred icosahedral Zn-Mg-Dy quasicrystal phase is presented, based on a six-dimensional model suggested by Ishimasa and Shimizu (2000 Mater. Sci. Eng. A 294-296 232, Ishimasa 2001 private communication). The physical space atomic positions of the defected structure were used for the calculation of the corresponding
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the
NASA Astrophysics Data System (ADS)
Stagno, Vincenzo; Bindi, Luca; Shibazaki, Yuki; Tange, Yoshinori; Higo, Yuji; Mao, H.-K.; Steinhardt, Paul J.; Fei, Yingwei
2014-07-01
The first natural-occurring quasicrystal, icosahedrite, was recently discovered in the Khatyrka meteorite, a new CV3 carbonaceous chondrite. Its finding raised fundamental questions regarding the effects of pressure and temperature on the kinetic and thermodynamic stability of the quasicrystal structure relative to possible isochemical crystalline or amorphous phases. Although several studies showed the stability at ambient temperature of synthetic icosahedral AlCuFe up to ~35 GPa, the simultaneous effect of temperature and pressure relevant for the formation of icosahedrite has been never investigated so far. Here we present in situ synchrotron X-ray diffraction experiments on synthetic icosahedral AlCuFe using multianvil device to explore possible temperature-induced phase transformations at pressures of 5 GPa and temperature up to 1773 K. Results show the structural stability of i-AlCuFe phase with a negligible effect of pressure on the volumetric thermal expansion properties. In addition, the structural analysis of the recovered sample excludes the transformation of AlCuFe quasicrystalline phase to possible approximant phases, which is in contrast with previous predictions at ambient pressure. Results from this study extend our knowledge on the stability of icosahedral AlCuFe at higher temperature and pressure than previously examined, and provide a new constraint on the stability of icosahedrite.
Aalto, Antti P.; Bitto, David; Ravantti, Janne J.; Bamford, Dennis H.; Huiskonen, Juha T.; Oksanen, Hanna M.
2012-01-01
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 virushost pair isolated from a hypersaline environment: an icosahedral, membrane-containing double-stranded DNA virusSalisaeta 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 PRD1adenovirus 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 virushost 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
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
Nsz, Istvn; Adm, Eva
2005-10-01
Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino acids--are in symmetrical location. Every kind of polypeptide forms also a separately symmetrical network in the capsid distributed according to their functions in the inner and outer side and inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four hexons according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each group of four hexons orient towards the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the group of four hexons: the hexons surround either a polypeptide IX or a polypeptide IIIa. The two versions of group of four hexons on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of the hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the anti-symmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an anti-symmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide subunits of the polypeptide IX centered group of four hexons have identical counter-clockwise orientation but the orientation of the neighbouring facets is always opposite compared to each other. On the five-fold symmetry axis, any facet can be "turned on" to the adjacent facet or "rotated" to all the others and will take the symmetry and orientation of the facet it got turned on or rotated to. Thus, every facet together with the polypeptides attached to it shows a twenty-fold symmetry and multiplicity. Another type of symmetry and multiplicity in the capsid is that perpendicular to the 6 five-fold rotation axes a geodetic (equatorial) ribbon like motif (superfieces) altogether six made up of 10-10 triangular facets and bent ten-times with an angle of 36 degrees. A triangular facet participates in forming three ribbon-like motifs, which intersect with each other on the given facet but the same three motifs intersect only on the anti-symmetrically located facet. PMID:16304803
None
2011-02-24
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not renormalizable. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged vector particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of massless modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a massive SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic vector field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are scalar fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a renormalizab
Proteomic Analysis of Sulfolobus solfataricus During Sulfolobus Turreted Icosahedral Virus Infection
Maaty, Walid S.; Selvig, Kyla; Ryder, Stephanie; Tarlykov, Pavel; Hilmer, Jonathan K.; Heinemann, Joshua; Steffens, Joseph; Snyder, Jamie C.; Ortmann, Alice C.; Movahed, Navid; Spicka, Kevin; Chetia, Lakshindra; Grieco, Paul A.; Dratz, Edward A.; Douglas, Trevor; Young, Mark J.; Bothner, Brian
2012-01-01
Where there is life, there are viruses. The impact of viruses on evolution, global nutrient cycling, and disease has driven research on their cellular and molecular biology. Knowledge exists for a wide range of viruses, however, a major exception are viruses with archaeal hosts. Archaeal virus-host systems are of great interest because they have similarities to both eukaryotic and bacterial systems and often live in extreme environments. Here we report the first proteomics-based experiments on archaeal host response to viral infection. Sulfolobus Turreted Icosahedral Virus (STIV) infection of Sulfolobus solfataricus P2 was studied using 1D and 2D differential gel electrophoresis (DIGE) to measure abundance and redox changes. Cysteine reactivity was measured using novel fluorescent zwitterionic chemical probes that, together with abundance changes, suggest that virus and host are both vying for control of redox status in the cells. Proteins from nearly 50% of the predicted viral open reading frames were found along with a new STIV protein with a homolog in STIV2. This study provides insight to features of viral replication novel to the archaea, makes strong connections to well described mechanisms used by eukaryotic viruses such as ESCRT-III mediated transport, and emphasizes the complementary nature of different omics approaches. PMID:22217245
Maaty, Walid S; Selvig, Kyla; Ryder, Stephanie; Tarlykov, Pavel; Hilmer, Jonathan K; Heinemann, Joshua; Steffens, Joseph; Snyder, Jamie C; Ortmann, Alice C; Movahed, Navid; Spicka, Kevin; Chetia, Lakshindra; Grieco, Paul A; Dratz, Edward A; Douglas, Trevor; Young, Mark J; Bothner, Brian
2012-02-01
Where there is life, there are viruses. The impact of viruses on evolution, global nutrient cycling, and disease has driven research on their cellular and molecular biology. Knowledge exists for a wide range of viruses; however, a major exception are viruses with archaeal hosts. Archaeal virus-host systems are of great interest because they have similarities to both eukaryotic and bacterial systems and often live in extreme environments. Here we report the first proteomics-based experiments on archaeal host response to viral infection. Sulfolobus Turreted Icosahedral Virus (STIV) infection of Sulfolobus solfataricus P2 was studied using 1D and 2D differential gel electrophoresis (DIGE) to measure abundance and redox changes. Cysteine reactivity was measured using novel fluorescent zwitterionic chemical probes that, together with abundance changes, suggest that virus and host are both vying for control of redox status in the cells. Proteins from nearly 50% of the predicted viral open reading frames were found along with a new STIV protein with a homologue in STIV2. This study provides insight to features of viral replication novel to the archaea, makes strong connections to well-described mechanisms used by eukaryotic viruses such as ESCRT-III mediated transport, and emphasizes the complementary nature of different omics approaches. PMID:22217245
Bulk electronic structure of Zn-Mg-Y and Zn-Mg-Dy icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Nayak, J.; Maniraj, M.; Gloskovskii, A.; Kraj?, M.; Sebastian, S.; Fisher, I. R.; Horn, K.; Barman, S. R.
2015-06-01
We use bulk sensitive hard x-ray photoelectron spectroscopy to provide unambiguous evidence for a pseudogap in the density of states around the Fermi level in icosahedral Zn-Mg-Y and Zn-Mg-Dy quasicrystals, in agreement with our density functional theory calculations. The pseudogap in these Zn-based quasicrystals is less pronounced compared to the Al-based ones such as Al-Pd-Mn and Al-Cu-Fe [J. Nayak et al., Phys. Rev. Lett. 109, 216403 (2012), 10.1103/PhysRevLett.109.216403]. This observation is in agreement with transport studies that indicate a larger charge carrier concentration in the Zn-based quasicrystals. Compared to Zn-Mg-Dy, the pseudogap is somewhat deeper in Zn-Mg-Y. The larger width of the Mg 1 s and Zn 2 p core-level spectra in Zn-Mg-Y is explained by different configurations of the local atomic surrounding compared to Zn-Mg-Dy.
Icosahedral quasicrystals in Zn-T-Sc (T = Mn, Fe, Co or Ni) alloys
NASA Astrophysics Data System (ADS)
Maezawa, Ryo; Kashimoto, Shiro; Ishimasa, Tsutomu
2004-04-01
Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a6D ranging from 7.044 to 7.107 . They have valence electron concentrations e/a ranging from 2.01 to 2.14, and almost the same ratios between the edge length aR of the Penrose tile and the averaged atomic diameter
NASA Astrophysics Data System (ADS)
Dykeman, Eric C.; Sankey, Otto F.
2010-02-01
We describe a technique for calculating the low-frequency mechanical modes and frequencies of a large symmetric biological molecule where the eigenvectors of the Hessian matrix are determined with full atomic detail. The method, which follows order N methods used in electronic structure theory, determines the subset of lowest-frequency modes while using group theory to reduce the complexity of the problem. We apply the method to three icosahedral viruses of various T numbers and sizes; the human viruses polio and hepatitis B, and the cowpea chlorotic mottle virus, a plant virus. From the normal-mode eigenvectors, we use a bond polarizability model to predict a low-frequency Raman scattering profile for the viruses. The full atomic detail in the displacement patterns combined with an empirical potential-energy model allows a comparison of the fully atomic normal modes with elastic network models and normal-mode analysis with only dihedral degrees of freedom. We find that coarse-graining normal-mode analysis (particularly the elastic network model) can predict the displacement patterns for the first few (10) low-frequency modes that are global and cooperative.
Thermal conductivity and Seebeck coefficients of icosahedral boron arsenide films on silicon carbide
Gong, Y.; Kuball, M. [H.H. Wills Physics Laboratory, Centre for Device Thermography and Reliability (CDTR), University of Bristol, Bristol BS8 1TL (United Kingdom); Zhang, Y.; Dudley, M. [Department of Materials Science and Engineering, Stony Brook University, Stony Brook, New York 11794-2275 (United States); Zhang, Y.; Edgar, J. H. [Department of Chemical Engineering, Kansas State University, Manhattan, Kansas 66506 (United States); Heard, P. J. [Interface Analysis Centre, University of Bristol, Bristol BS2 8BS (United Kingdom)
2010-10-15
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 deg. C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {mu}V/K and 136 {mu}V/K for samples grown at 1350 deg. C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Lee, Kelly K.; Tang, Jinghua; Taylor, Derek; Bothner, Brian; Johnson, John E.
2004-01-01
Nudaurelia ? capensis virus (N?V) capsids were previously characterized in two morphological forms, a T=4, 485--diameter round particle with large pores and a tightly sealed 395- icosahedrally shaped particle with the same quasi-symmetric surface lattice. The large particle converts to the smaller particle when the pH is lowered from 7.6 to 5, and this activates an autocatalytic cleavage of the viral subunit at residue 570. Here we report that both 1-anilino-8 naphthalene sulfonate (ANS) and the covalent attachment of the thiol-reactive fluorophore, maleimide-ANS (MIANS), inhibit the structural transition and proteolysis at the lower pH. When ANS is exhaustively washed from the particles, the maturation proceeds normally; however, MIANS-modified particles are still inhibited after the same washing treatment, indicating that covalent attachment targets MIANS to a critical location for inhibition. Characterization of the low-pH MIANS product by electron cryo-microscopy (cryo-EM) and image reconstruction demonstrated a morphology intermediate between the two forms previously characterized. A pseudoatomic model of the intermediate configuration was generated by rigid body refinement of the X-ray structure of the subunits (previously determined in the assembled capsid) into the cryo-EM density, allowing a quantitative description of the inhibited intermediate and a hypothesis for the mechanism of the inhibition. PMID:15194797
Pauling, Linus
1988-01-01
Single-grain precession x-ray diffraction photographs of Al6CuLi3 have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 , 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. PMID:16593929
Nsz, I; Adm, Eva
2006-03-01
Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino-acids--are in symmetrical location. Every kind of polypeptide forms a separately also symmetrical network in the capsid distributed according to their functions in the inner and outer side and the inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four (GOF) according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each GOF orient toward the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the GOFs: the hexons surround either a polypeptide IX or a polypeptide IlIa. The two versions of GOFs on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the antisymmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an antisymmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide subunits of polypeptide IX centered GOF hexons have identical counter-clockwise orientation but the orientation of the neighbouring facets is always opposite compared to each other. On the five-fold symmetry axis, any facet can be "turned on" to the adjacent facet or "rotated" to all the others and will take the symmetry and orientation of the facet it got turned on or rotated to. Thus, every facet together with the polypeptides attached to it shows a twenty-fold symmetry and multiplicity. An other type of symmetry and multiplicity in the capsid is that perpendicular to the 6 five-fold rotation axes run a geodetic (equatorial) ribbon like motif (superfieces) altogether six made up of 10 x 10 triangular facets and bent ten-times with an angle of 36 degrees. A triangular facet participates in forming three ribbon-like motifs, which intersect with each other on the given facet, but the same three motifs intersect repeatedly only on the antisymmetrically located facet. PMID:16696547
Linus Pauling
1988-01-01
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.
Pauling, Linus
1988-01-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals. PMID:16593990
Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))
1988-11-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals.
Symmetry detection through local skewed symmetries
Tat-jen Cham; Roberto Cipolla
1995-01-01
We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by consider- ing the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetri- city is introduced, which is based on Mahalanobis distances from the tangent-curvature states of
Symmetry detection through local skewed symmetries
Cham, Tat Jen
Symmetry detection through local skewed symmetries Tat-Jen Cham and Roberto Cipolla We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by consider- ing the tangents and curvatures of local
A highly symmetric four-dimensional quasicrystal
Veit Elser; N. J. A. Sloane
1987-01-01
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.
Evidence for time-reversal symmetry breaking in the noncentrosymmetric superconductor LaNiC2.
Hillier, A D; Quintanilla, J; Cywinski, R
2009-03-20
Muon spin relaxation experiments on the noncentrosymmetric intermetallic superconductor LaNiC2 are reported. We find that the onset of superconductivity coincides with the appearance of spontaneous magnetic fields, implying that in the superconducting state time-reversal symmetry is broken. An analysis of the possible pairing symmetries suggests only four triplet states compatible with this observation, all of them nonunitary. They include the intriguing possibility of triplet pairing with the full point group symmetry of the crystal, which is possible only in a noncentrosymmetric superconductor. PMID:19392234
Evidence for Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor LaNiC2
NASA Astrophysics Data System (ADS)
Hillier, A. D.; Quintanilla, J.; Cywinski, R.
2009-03-01
Muon spin relaxation experiments on the noncentrosymmetric intermetallic superconductor LaNiC2 are reported. We find that the onset of superconductivity coincides with the appearance of spontaneous magnetic fields, implying that in the superconducting state time-reversal symmetry is broken. An analysis of the possible pairing symmetries suggests only four triplet states compatible with this observation, all of them nonunitary. They include the intriguing possibility of triplet pairing with the full point group symmetry of the crystal, which is possible only in a noncentrosymmetric superconductor.
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.
NASA Astrophysics Data System (ADS)
Klein, P. B.; Nwagwu, Ugochukwu; Edgar, J. H.; Freitas, J. A.
2012-07-01
The indirect band gap of icosahedral B12As2 (IBA) has been determined by variable temperature photoluminescence measurements (8 K-294 K) on solution-grown bulk samples. In addition, evidence of three shallow acceptor levels and one shallow donor level is reported. The low-temperature spectra were characterized by broad and intense deep defect emission, donor-acceptor pair (DAP) bands, and exciton recombination. The appearance of DAP emission verifies the incorporation of a donor in IBA, which has not been reported previously. The temperature dependence of the free exciton (FE) intensity reflected a FE binding energy of 45 meV. The variation of the FE peak position with temperature was fitted with both Varshni and Pssler models to determine an expression for the temperature dependence of the indirect band gap. The resulting low and room temperature band gaps are Eg(0) = 3.470 eV and Eg(294 K) = 3.373 eV, respectively. The latter is not consistent with previous reports of the room temperature band gap, 3.20 eV and 3.47 eV, derived from band structure calculations and optical absorption, respectively. The origin of these discrepancies is discussed. The DAP spectra reveal three relatively shallow acceptors with binding energies of ?175, 255, and 291 meV, and a shallow donor with binding energy ?25 meV. Although the identity of the individual acceptors is not known, they appear to be associated with the light-hole band. The small donor binding energy is suggestive of an interstitial donor impurity, which is suspected to be Ni.
THOR-ICO: a General Circulation Model for Exoplanets on an Icosahedral Grid
NASA Astrophysics Data System (ADS)
Mendonca, J.; Heng, K.; Grimm, S.
2014-04-01
The study of extrasolar planets has become important since the discovery of a large number of these astronomical objects. The diversity of planetary characteristics observed raises questions about the variety of climates. The influence of the astronomical and planetary bulk parameters in driving the atmospheric circulations continues to be poorly understood. In the solar system the results from planetary spacecraft missions have demonstrated how different the planetary climate and atmospheric circulations can be. The study of exoplanets is going to require a study of a far greater range of physical and orbital parameters than the ones that characterise our neighbour planets (in the solar system). For this reason the study of exoplanets will involve an even greater diversity of circulation and climate regimes. We are developing a dedicated General Circulation Model (GCM) for extrasolar planets called "Exoclimes Simulation Platform". This model will solve the complex physical and dynamical equations that include fundamental principles of atmospheric fluid dynamics and various idealisations of, for example, radiative transfer [1] and dry or moist convection. The interpretation and analysis of the results from this complex model will help us to have a better understanding on the diversity of climates and atmospheric circulations. Here we present the first results of our recent scheme which represents the fluid dynamical phenomena in the atmosphere. This new code solves the atmospheric fluid equations in a rotating sphere (fully compressible - elastic - nonhydrostatic system) using an icosahedral grid. The grid is also modified to improve the uniformity of the grid point distribution applying a method called spring dynamics [2]. The results shown include 3D experiments of gravity and acustic waves, Held-Suarez test case [3] and an idealized hot-Jupiter case.
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
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.
Magnetic and electrical properties of the single-grained Al-Cu-Fe icosahedral phase
S. Matsuo; T. Ishimasa; M. Mori; Hiroshi Nakano
1992-01-01
Magnetization of a single-grained quasi-crystal of nominal composition 66.32 at.% Al-20.41 at.% Cu-13.27 at.% Fe was investigated in the temperature range from 2 to 250 K and for magnetic fields below 5 T along fivefold, threefold and twofold axes. No anisotropy was found, which is consistent with the symmetry consideration based on the symmetry of the diffraction spots. Electrical conductivity
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
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.}
Simulation of ion-beam channeling in icosahedral Al[sub 63]Cu[sub 25]Fe[sub 12
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
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.
Magnetic and Electrical Properties of a Single-Grained Al70Pd21Mn9 Icosahedral Quasicrystal
Kaichi Saito; Susumu Matsuo; Hiroshi Nakano; Tsutomu Ishimasa; Masahiro Mori
1994-01-01
The magnetization of a stable single-grainedAl70Pd21Mn9 icosahedral quasicrystal has beeninvestigated in the temperature region between 2 and 600 Kbelow the magnetic field 80 kOe. The susceptibility yields aCurie constant 1.7510-4 cgsemuK\\/g, a Curietemperature -1.62 K, and a constant susceptibility contribution-0.2510-8 cgsemu\\/g. Magnetization curves at lowtemperatures suggest that only about 1% of the Mn atoms aremagnetic. The temperature dependence of the
A New Series of Icosahedral Quasicrystals in Zn-M-Sc (M = Ag, Au, Pd, Pt) Alloys
Shiro Kashimoto; Ryo Maezawa; Yoko Kasano; Tomokazu Mitani; Tsutomu Ishimasa
2003-01-01
A new series of icosahedral quasicrystals has been found in Zn75M10Sc15 (M = Ag, Au, Pd and Pt) as-cast alloys. Electron and powder X-ray diffraction analyses indicated that these quasicrystals are of the P-type (primitive type) and have six-dimensional lattice parameters a6D=0.7112--0.7151 nm. The quasicrystals are formed as main phases in these alloys. In the Zn80Ag5Sc15 alloy annealed at 981
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
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.
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.
Yeh, Chen-Hao; Lin, Yu-Chieh; Ho, Jia-Jen
2014-04-28
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
Wei, Lu; Zhou, Zhi-You; Chen, Sheng-Pei; Xu, Chang-Deng; Su, Dangsheng; Schuster, Manfred Erwin; Sun, Shi-Gang
2013-12-11
Pt triambic icosahedral nanocrystals (TIH NCs) enclosed by {771} high-index facets were successfully synthesized electrochemically, for the first time, in ChCl-urea based deep eutectic solvents, and exhibited higher electrocatalytic activity and stability towards ethanol electrooxidation than a commercial Pt black catalyst. PMID:24084858
D. Reinhard; B. D. Hall; D. Ugarte; R. Monot
1997-01-01
The structure of free silver clusters, produced in an inert-gas-aggregation source and flowing in a molecular beam has been studied by electron diffraction. Large clusters (up to 11 nm in diameter) of both icosahedral and fcc structure are observed. Cluster structure is investigated as a function of evaporation temperature and molecular weight of the inert gas in the source. An
Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi
2013-08-23
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
NASA Astrophysics Data System (ADS)
Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi
2013-08-01
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
Zheng Yang; Ivet Bahar; Michael Widom
2009-01-01
Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-01-01
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structuresand investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of bodybar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in bodybar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains. PMID:24379431
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N. [MS 283, Los Alamos National Laboratory, Los Alamos, NM, 87545 (United States)
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
NASA Astrophysics Data System (ADS)
Sharma, H. R.; Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.; McGrath, R.
2014-05-01
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage.
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
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.
Sharma, H R; Smerdon, J A; Nugent, P J; Ribeiro, A; McLeod, I; Dhanak, V R; Shimoda, M; Tsai, A P; McGrath, R
2014-05-01
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage. PMID:24811658
de Boissieu, M; Francoual, S; Kaneko, Y; Ishimasa, T
2005-09-01
We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Q(2)(per) dependence. Moreover, when compared to previous measurements carried out on the i-AlPdMn phase, we find that the amount of diffuse scattering is smaller in the i-ZnMgSc phase, in agreement with larger phason elastic constants in this phase. This is confirmed by the observation of a large number of weak Bragg peaks having a high Q(per) reciprocal space component. PMID:16196940
Symmetry Breaking NICTA and UNSW
Walsh, Toby
Symmetry Breaking Toby Walsh NICTA and UNSW #12;Outline What What is symmetry? Why Why is symmetry a problem? How How do we deal with symmetry? #12;Apology Symmetry in constraint programming workshop, Nantes 2006 1st International Symmetry Conference, Edinburgh 2007 #12;Symmetry Within objects
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Geometric intrinsic symmetries
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl; Szulerecka, A.; Pedrak, A. [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)] [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Henley, E.M.
1992-12-31
Violations of symmetries have been used to determine (or test) the theoretical dynamics or to study structure. Recent experiments on parity non-conservation and time reversal symmetry, and that depend on spin properties, are used to illustrate both applications.
Henley, E.M.
1992-01-01
Violations of symmetries have been used to determine (or test) the theoretical dynamics or to study structure. Recent experiments on parity non-conservation and time reversal symmetry, and that depend on spin properties, are used to illustrate both applications.
Jianmin Jiang; Jinzhao Wu
2005-01-01
For event structures as a major branch of concurrent models, no one notices their symmetries. It is very likely that someone thinks that symmetry reduction over an event structure can be replaced by the (largest) autobisimulation reduction. We show that, given an event structure, there are some differences between the symmetric quotient model induced by symmetry reduction and the bisimilar
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or
Symmetry Breaking Toby Walsh #
Walsh, Toby
Symmetry Breaking Toby Walsh # National ICT Australia and School of CSE, University of New South Wales, Sydney, Australia, tw@cse.unsw.edu.au Symmetry occurs in many problems in aritifical intelligence be able to swap them around without changing the performance of the computer. Symmetries come in many di
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
M. Krajc; J. Hafner
2000-01-01
The electronic and magnetic structure of hexagonal rare-earth-zinc-magnesium compounds closely related to the icosahedral phases has been investigated by local density approximation (LDA) and LDA + U calculations. It is shown that both non-magnetic Y-Zn-Mg and antiferromagnetic Gd-Zn-Mg are stabilized by a Hume-Rothery-like electronic mechanism, the formation of a deep structure-induced pseudogap at the Fermi level being effected by an
S. Kashimoto; C. Masuda; S. Motomura; S. Matsuo; T. Ishimasa
2007-01-01
Icosahedral quasicrystals containing heavy lanthanoids L, namely Ho, Er or Tm, have been discovered in the Zn77Fe7Sc16xLx alloy systems. The solubility limit of the lanthanoid is approximately half of the Sc atoms. All these quasicrystals belong to p-type and are stable at approximately 973?K. The temperature dependence of the magnetic susceptibility of the Zn77Fe7Sc8Tm8 quasicrystal follows the CurieWeiss law and
Shiro Kashimoto; Hiroshi Nakano; Yasuomi Arichika; Tsutomu Ishimasa; Susumu Matsuo
2000-01-01
Electrical resistivity and magnetoresistance were measured in Zn60Mg30Ho10 icosahedral quasicrystals annealed at various temperatures that have different degrees of long-range F-type ordering. In the temperature dependence of the electrical resistivity, the sample annealed at 832K (higher annealing temperature) exhibits a broad maximum at 125K, which can be interpreted on the basis of the weak localization theory under strong spin-orbit effect.
H. R. Sharma; M. Shimoda; A. R. Ross; T. A. Lograsso; A. P. Tsai
2006-01-01
We present an analysis of Sn film growth on the fivefold surface of the icosahedral AlCuFe quasicrystal at multilayer coverage. Scanning tunnelling microscopy of the Sn-deposited surface revealed that film morphology differed from terrace to terrace. Most terraces exhibited flat-topped clusters with preferential growth at the step edges, while a minority of terraces showed a smooth film. The height, lateral
H. R. Sharma; M. Shimoda; A. R. Ross; T. A. Lograsso; A. P. Tsai
2006-01-01
We present an analysis of Sn film growth on the fivefold surface of the icosahedral Al-Cu-Fe quasicrystal at multilayer coverage. Scanning tunnelling microscopy of the Sn-deposited surface revealed that film morphology differed from terrace to terrace. Most terraces exhibited flat-topped clusters with preferential growth at the step edges, while a minority of terraces showed a smooth film. The height, lateral
Meng Zhang; Xiao-Yan Gu; Wen-Li Zhang; Li-Na Zhao; Li-Ming He; You-Hua Luo
2010-01-01
The geometries, electronic, and magnetic properties of the 3d, 4d, 5d impurities encapsulated in an icosahedral Ag12 cage have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. The general features of the properties of 3d, 4d, 5d transition-metal atoms doped Ag12 clusters are probed and compared. It is found that the most stable structure
NASA Astrophysics Data System (ADS)
Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; Willett, Brian
2015-02-01
A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ( q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
Improved Statistics for Determining the Patterson Symmetry fromUnmerged Diffraction Intensities
Sauter, Nicholas K.; Grosse-Kunstleve, Ralf W.; Adams, Paul D.
2006-01-09
We examine procedures for detecting the point-group symmetryof macromolecular datasets and propose enhancements. To validate apoint-group, it is sufficient to compare pairs of Bragg reflections thatare related by each of the group's component symmetry operators.Correlation is commonly expressed in the form of a single statisticalquantity (such as Rmerge) that incorporates information from all of theobserved reflections. However, the usual practice of weighting all pairsof symmetry-related intensities equally can obscure the fact that thevarious symmetry operators of the point-group contribute differingfractions of the total set. In some cases where particular symmetryelements are significantly under-represented, statistics calculatedglobally over all observations do not permit conclusions about thepoint-group and Patterson symmetry. The problem can be avoided byrepartitioning the data in a way that explicitly takes note of individualoperators. The new analysis methods, incorporated into the programLABELIT (cci.lbl.gov/labelit), can be performed early enough during dataacquisition, and are quick enough, that it is feasible to pause tooptimize the data collection strategy.
Brumfield, Susan K.; Ortmann, Alice C.; Ruigrok, Vincent; Suci, Peter; Douglas, Trevor; Young, Mark J.
2009-01-01
Little is known about the replication cycle of archaeal viruses. We have investigated the ultrastructural changes of Sulfolobus solfataricus P2 associated with infection by Sulfolobus turreted icosahedral virus (STIV). A time course of a near synchronous STIV infection was analyzed using both scanning and transmission electron microscopy. Assembly of STIV particles, including particles lacking DNA, was observed within cells, and fully assembled STIV particles were visible by 30 h postinfection (hpi). STIV was determined to be a lytic virus, causing cell disruption beginning at 30 hpi. Prior to cell lysis, virus infection resulted in the formation of pyramid-like projections from the cell surface. These projections, which have not been documented in any other host-virus system, appeared to be caused by the protrusion of the cell membrane beyond the bordering S-layer. These structures are thought to be sites at which progeny virus particles are released from infected cells. Based on these observations of lysis, a plaque assay was developed for STIV. From these studies we propose an overall assembly model for STIV. PMID:19357174
NASA Astrophysics Data System (ADS)
Maniraj, M.; Rai, Abhishek; Barman, S. R.; Kraj?, M.; Schlagel, D. L.; Lograsso, T. A.; Horn, K.
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.150.1)me and tracks the change in the work function is assigned to an image potential resonance because our density functional calculation shows an absence of band gap in the respective energy region. We show that Sn grows pseudomorphically on i-Al-Pd-Mn as predicted by density functional theory calculations, and the energy of the image potential resonance tracks the change in the work function with Sn coverage. The image potential resonance appears much weaker in the spectrum from the related crystalline Al-Pd-Mn surface, demonstrating that its strength is related to the compatibility of the quasiperiodic wave functions in i-Al-Pd-Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above EF provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
Lattice dynamics of the Zn-Mg-Sc icosahedral quasicrystal and its Zn-Sc periodic 1/1 approximant.
de Boissieu, Marc; Francoual, Sonia; Mihalkovic, Marek; Shibata, Kaoru; Baron, Alfred Q R; Sidis, Yvan; Ishimasa, Tsutomu; Wu, Dongmei; Lograsso, Thomas; Regnault, Louis-Pierre; Ghler, Franz; Tsutsui, Satoshi; Hennion, Bernard; Bastie, Pierre; Sato, Taku J; Takakura, Hiroyuki; Currat, Roland; Tsai, An-Pang
2007-12-01
Quasicrystals are long-range-ordered materials that lack translational invariance, so the study of their physical properties remains a challenging problem. Here, we have carried out inelastic-X-ray- and neutron-scattering experiments on single-grain samples of the Zn-Mg-Sc icosahedral quasicrystal and of the Zn-Sc periodic cubic 1/1 approximant, with the aim of studying the respective influence of the local order and of the long-range order (periodic or quasiperiodic) on lattice dynamics. Besides the overall similarities and the existence of a pseudo-gap in the transverse dispersion relation, marked differences are observed, the pseudo-gap being larger and better defined in the approximant than in the quasicrystal. This can be qualitatively explained using the concept of a pseudo-Brillouin-zone in the quasicrystal. These results are compared with simulations on atomic models and using oscillating pair potentials, and the simulations reproduce in detail the experimental results. This paves the way for a detailed understanding of the physics of quasicrystals. PMID:17982466
New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal
Lin, Qisheng; Corbett, John D.
2006-01-01
The refined x-ray crystal structure of the phase Mg27Al10.7(2)Zn47.3(2) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al2 dimer. This phase exhibits the same long-range order as recently established for the Tsai-type ScMgZn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements. PMID:16950873
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.
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
NASA Astrophysics Data System (ADS)
Alexandradinata, A.; Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
2014-09-01
We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n=3,4, and 6 of the Cnv groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups; i.e., the relevant symmetries are purely crystalline and do not include time reversal. To describe these Cnv systems, we introduce the notions of (a) a halved mirror chirality, an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number, the traditional Thouless-Kohmoto-Nightingale-den Nijs invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities. In addition to electronic systems without spin-orbit coupling, our findings also apply to intrinsically spinless systems such as photonic crystals and ultracold atoms.
Better Verification Through Symmetry
C. Norris Ip; David L. Dill
1996-01-01
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
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged
NSDL National Science Digital Library
2012-07-09
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.
Better Verification Through Symmetry
C. Norris Ip
1993-01-01
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
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
NSDL National Science Digital Library
2007-01-01
In this simulation, you will learn about axial symmetry and the difference between the axes. Just drag and drop the shapes onto the grid and choose between the different axes of symmetry to see the effect it has on the various shapes.
Symmetry and Topological Order
Zohar Nussinov; Gerardo Ortiz
2014-10-22
We prove sufficient conditions for Topological Quantum Order at both zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries (that notably extend and differ from standard local gauge symmetries) and their associated defects, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges), discuss associated braiding, and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on certain suggested quantum computing schemes and lead to "thermal fragility". Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
David Wallace
2009-07-03
A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are applied to gain a greater insight into the phenomenon of antimatter.
Nested polytopes with non-crystallographic symmetry as projected orbits of extended Coxeter groups
Motiejus Valiunas; Emilio Zappa; Briony Thomas; Reidun Twarock
2015-01-27
We construct nested polytopes with non-crystallographic symmetry from the orbits of groups containing a non-crystallographic Coxeter group $W$ via projection. For this, we embed $W$ into the point group $\\mathcal{P}$ of a higher dimensional lattice, and study the orbits of the subgroups of $\\mathcal{P}$ which contain $W$. The projection of these orbits into a lower dimensional subspace invariant under $W$ consists of nested shell arrangements with non-crystallographic symmetry. We study the properties of these structures and classify them in the case of extensions of $W$, i.e. subgroups of $\\mathcal{P}$ that contain $W$ as a normal subgroup. Geometrically, the convex hulls of these orbits represent nested polytopes with non-crystallographic symmetry. These have interesting applications in physics (quasicrystals), biology (viruses) and carbon chemistry (fullerenes).
Temperature-reflection symmetry
NASA Astrophysics Data System (ADS)
Ba?ar, Gke; Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2015-05-01
We point out the presence of a T ?-T temperature-reflection (T -reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of T -reflection symmetry in systems with exactly calculable partition functions. We show that T -reflection symmetry is present in a variety of conformal and nonconformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under T -reflections. An interesting property of the T -reflection symmetry is that it can be broken by shifts of the vacuum energy.
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
We have observed dynamical diffraction in the
Lander, Gabriel C.; Baudoux, Anne-Claire; Azam, Farooq; Potter, Clinton S.; Carragher, Bridget; Johnson, John E.
2012-01-01
We report the sub nanometer cryo-electron microscopy (cryoEM) reconstruction of a novel marine siphovirus, the Vibrio phage SIO-2. This phage is lytic for related Vibrio species with significant ecological importance including the broadly antagonistic bacterium Vibrio sp. SWAT3. The three dimensional structure of the 800 SIO-2, icosahedrally averaged, head of the tailed particle revealed a novel T=12 quasi-symmetry not previously described in a bacteriophage. Two, morphologically distinct, types of auxiliary proteins were also identified; one species bound to the surface of hexamers and the other bound to pentamers. The secondary structure, evident in the electron density, shows that the major capsid protein has the HK97-like fold. The three-dimensional structure of the procapsid form, also presented here, has no decoration proteins and reveals a novel capsomer organization due to the constraints of the T=12 symmetry. PMID:22405008
Lin, Qisheng; Corbett, John D
2010-11-15
The realm of Tsai-type (YCd(6)-type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca(15.0(5))Au(60.0(4))Sn(25.0(2)) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca(3)Au(14.36(3))Sn(4.38(5)) in space group Im3, a = 15.131(1) , whereas a representative 2/1 AC gives Ca(13)Au(47.2(1))Sn(28.1(1)), Pa3 and a = 24.444(1) . 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
Atomic model of anti-phase boundaries in a face-centred icosahedral Zn Mg Dy quasicrystal
NASA Astrophysics Data System (ADS)
Wang, Jianbo; Yang, Wenge; Wang, Renhui
2003-03-01
An atomic model in the physical space for an anti-phase boundary (APB) in the ordered face-centred icosahedral Zn-Mg-Dy quasicrystal phase is presented, based on a six-dimensional model suggested by Ishimasa and Shimizu (2000 Mater. Sci. Eng. A 294-296 232, Ishimasa 2001 private communication). The physical space atomic positions of the defected structure were used for the calculation of the corresponding exit-plane wavefunction and high-resolution transmission electron microscopy images. The analysis of the defect by inverse Fourier transformation reveals that when superstructure reflection spots are used for back-transformation, then at the APB, bright lattice fringes are found to turn into dark ones, and vice versa. When fundamental reflections are used, the APB is not visible. This phenomenon is the same as the corresponding experimental study recently published by Heggen et al(2001a Phys. Rev. B 64 014202). Based on this atomic model it is found that the APB perpendicular to a fivefold axis A5 (APB-A5) is a non-conservative boundary, while the APB perpendicular to a pseudo-twofold axis A2P (APB-A2P) is a conservative one. This fact is consistent with the experimental observation (Heggen et al2002 J. Alloys Compounds 342 330) that the frequency of occurrence of APB-A5 is 90% in the heat-treated samples compared with that in the deformed samples (45%), while the frequency of occurrence of APB-A2P is 34% in the deformed samples compared with that in the heat-treated samples.
NASA Astrophysics Data System (ADS)
Keunen, R.; Cathcart, N.; Kitaev, V.
2014-06-01
A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of icosahedral nuclei in precursor NPs. Violet light (401-410 nm) is crucial to promote plasmonic selection of near-spherical AgIhNPs. Oxidative etching with hydrogen peroxide and photochemical reduction with citrate establishes a red-ox equilibrium for the photochemical selection of AgIhNPs. The addition of chloride ions improves size- and shape-selectivity. Finally, the demonstration of 1-D growth of AgIhNPs to pentagonal pins initiated at AgIhNP pentagonal-twinned defects highlights a universal role of twinned defects for the formation of anisotropic nanoparticles.A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of icosahedral nuclei in precursor NPs. Violet light (401-410 nm) is crucial to promote plasmonic selection of near-spherical AgIhNPs. Oxidative etching with hydrogen peroxide and photochemical reduction with citrate establishes a red-ox equilibrium for the photochemical selection of AgIhNPs. The addition of chloride ions improves size- and shape-selectivity. Finally, the demonstration of 1-D growth of AgIhNPs to pentagonal pins initiated at AgIhNP pentagonal-twinned defects highlights a universal role of twinned defects for the formation of anisotropic nanoparticles. Electronic supplementary information (ESI) available: Additional information on the synthesis series. See DOI: 10.1039/c4nr01477d
John H. Schwarz
1995-03-20
A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities, underlies string theory. It is my hope that an understanding of these symmetries will suggest the right way to formulate non-perturbative string theory. Whether or not this hope is realized, it has already been demonstrated that this line of inquiry leads to powerful new tools for understanding gauge theories and new evidence for the uniqueness of string theory, as well as deep mathematical results.
Tarumi, Ryuichi
2013-01-01
We investigated free-vibration acoustic resonance (FVAR) of two-dimensional St VenantKirchhoff-type hyperelastic materials and revealed the existence and structure of colour symmetry embedded therein. The hyperelastic material is isotropic and frame indifferent and includes geometrical nonlinearity in its constitutive equation. The FVAR state is formulated using the principle of stationary action with a subsidiary condition. Numerical analysis based on the Ritz method revealed the existence of four types of nonlinear FVAR modes associated with the irreducible representations of a linearized system. Projection operation revealed that the FVAR modes can be classified on the basis of a single colour (black or white) and three types of bicolour (black and white) magnetic point groups: , , and . These results demonstrate that colour symmetry naturally arises in the finite amplitude nonlinear FVAR modes, and its vibrational symmetries are explained in terms of magnetic point groups rather than the irreducible representations that have been used for linearized systems. We also predicted a grey colour nonlinear FVAR mode which cannot be derived from a linearized system. PMID:24204182
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
Symmetry Restoration By Acceleration
P. Castorina; M. Finocchiaro
2012-07-16
The restoration of spontaneous symmetry breaking for a scalar field theory for an accelerated observer is discussed by the one-loop effective potential calculation and by considering the effective potential for composite operators. Above a critical acceleration, corresponding to the critical restoration temperature,T_c, for a Minkowski observer by Unruh relation, i.e. a_c/2\\pi=T_c, the symmetry is restored. This result confirms other recent calculations in effective field theories that symmetry restoration can occur for an observer with an acceleration larger than some critical value. From the physical point of view, a constant acceleration is locally equivalent to a gravitational field and the critical acceleration to restore the spontaneous symmetry breaking corresponds to a huge gravitational effect which, therefore, prevents boson condensation.
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
Classification of Arnold-Beltrami Flows and their Hidden Symmetries
Pietro Fre; Alexander S. Sorin
2015-01-19
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the ABC-flow introduced by Beltrami, Arnold and Childress. Beltrami equation is the eigenstate equation for the first order Laplace-Beltrami operator *d, which we solve by using harmonic analysis. Taking torus T^3 constructed as R^3/L, where L is a crystallographic lattice, we present a general algorithm to construct solutions of Beltrami equation which utilizes as main ingredient the orbits under the action of the point group P_L of three-vectors in the momentum lattice L*. We introduce the new notion of a Universal Classifying Group GU_L which contains all crystallographic space groups as proper subgroups. We show that the *d-eigenfunctions are naturally arranged into irreducible representations of GU_L and by means of a systematic use of the branching rules with respect to various possible subgroups H of GU_L we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group P_L is the proper octahedral group O_24 and the Universal Classifying Group is finite group G_1536 of order 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O_24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G_1536. In this way we obtain an exhaustive classification of all generalized ABC-flows and of their hidden symmetries. We make several conceptual comments about the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that possibly make contact with M-theory and the geometry of flux-compactifications.
Matthias Neubert
1994-01-01
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
Symmetries Wider than Supersymmetry
DIMITRY LEITESH; Vera Serganova
\\u000a We observe that supersymmetries do not exhaust all the symmetries of the supermanifolds. On a generalization of supermanifolds\\u000a (called metamanifolds), the functions form a metaabelean algebra, i.e., the one for which [[ x, y],z] = 0 with respect to the usual commutator. The superspaces considered as metaspaces admit symmetries wider than supersymmetries.\\u000a Conjecturally, infinitesimal transformations of these metaspaces constitute Volichenko
Steven Louis Rugari
1992-01-01
We have carried out a search for broken reflection symmetry in the exotic nucleus ^{114 }Xe. Evidence for broken reflection symmetry has been previously observed in the actinide region, most notably Ra-Th nuclei, and more recently in the neutron rich nuclei ^{144}Ba, ^{146}Ce, and ^{146,148}Nd. This evidence has been discussed in terms of two conceptually different theoretical frameworks, namely alpha
Finite group symmetry breaking
G. Gaeta
2005-10-02
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and field theory. The breaking of finite groups symmetry has thus been thoroughly studied, and general approaches exist to investigate it. In Landau theory, the state of a system is described by a finite dimensional variable (the {\\it order parameter}), and physical states correspond to minima of a potential, invariant under a group. In this article we describe the basics of symmetry breaking analysis for systems described by a symmetric polynomial; in particular we discuss generic symmetry breakings, i.e. those determined by the symmetry properties themselves and independent on the details of the polynomial describing a concrete system. We also discuss how the plethora of invariant polynomials can be to some extent reduced by means of changes of coordinates, i.e. how one can reduce to consider certain types of polynomials with no loss of generality. Finally, we will give some indications on extension of this theory, i.e. on how one deals with symmetry breakings for more general groups and/or more general physical systems.
On the symmetry of three identical interacting particles in a one-dimensional box
Paolo Amore; Francisco M. Fernndez
2015-04-07
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh-Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.
Internal Symmetry Marijn Heule1
Flener, Pierre
Internal Symmetry Marijn Heule1 and Toby Walsh2 1 Delft University of Technology, The Netherlands studying the internal symmetries within an individual solution of a constraint satisfaction problem [1]. Such inter- nal symmetries can be compared with solution symmetries which map between different solutions
Symmetry in Numbers David Marshall
Marshall, David
Symmetry in Numbers David Marshall Monmouth University April 13, 2005 808 -2 3 + 3 -169 54 + 1007 18 + 3 -169 54 - 1007 18 Typeset by FoilTEX #12;Symmetry One of the guiding principles group of symmetries. -Paul Yale, in Geometry and Symmetry 2. Due or just proportion; harmony of parts
Crystal Symmetry Algorithms in a High-Throughput Framework for Materials
NASA Astrophysics Data System (ADS)
Taylor, Richard
The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.
NASA Astrophysics Data System (ADS)
Tsuji, Masaharu; Nakamura, Nozomi; Tang, Xinling; Uto, Keiko; Matsunaga, Mika
2014-11-01
We previously reported that trapezoid, plate-like and mono- or bi-tetrahedral Ag-flag structures are evolved from side facets of Ag-nanorod (NR) seeds when AgNO3 was reduced in N,N-dimethylformamide (DMF) in the presence of polyvinylpyrrolidone (PVP). In this study, we examined what shapes are grown by further growth of bitetrahedral flags based on TEM and SEM observations. For this purpose, we initially studied effects of the reaction temperature, concentrations of PVP, and molecular weights of PVP for the shape evolution of flag types of Ag nanostructures from Ag-NR seeds. Results show that shape and size of flags can be controlled by changing these parameters and reaction times. Under an appropriate experimental condition, we found that decahedral and icosahedral flags and their intermediates having {1 1 1} facets were finally grown by stepwise growth of tetrahedral units, although yield of perfect decahedral and icosahedral flags were low because of occurrence of homogenous nucleation at high AgNO3 concentration.
Wayne Isami Imaino
1980-01-01
Triply degenerate F modes in the Raman spectrum of Bi(,12)GeO(,20), which has the cubic point group symmetry T, are studied as a function of the magnitude of the phonon wave-vector q. The small splittings, due to the long range polarization field (LO-TO splitting) and linear q-effects near the zone center are resolved using the high resolution of a piezoelectrically scanned
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. PMID:11223922
NASA Astrophysics Data System (ADS)
Kuprievich, V. A.; Kapitanchuk, O. L.; Shramko, O. V.
2003-04-01
Recent achievements in the synthesis of novel substances and materials raise specific problems in computational quantum chemistry demanding to consider electronic structure multiatomic molecular systems in excited and ionic states beyond one-electron approaches. The proposed computational treatment of problem of electron correlation with emphasis on the symmetry-induced degeneracy of molecular states is discussed. It is essentially based on the theory of symmetry molecular invariants that supposes (i) use of fixed reference symmetry base and (ii) determination of invariant expansions for two-electron integrals and energies. The method successively takes full advantage of the relations between the integrals defined on symmetry molecular orbitals (MO). Using the symmetry-similarity principle within the model with two-center electron - electron interaction a simple computational technique is elaborated enabling to represent each integral from complete set as an expansion of a few independent integrals [1,2]. The technique is specified for the most complicated case of icosahedral (Ih) symmetry which is inherent to fullerene C60. It is considered for (i) the configurations (t1u + t1g), the symmetries of two lowest vacant MOs and (ii) for upper occupied hu-shell. The reference symmetry basis sets (mostly with integer components) are presented enabling to obtain the most results in a mathematically rigorous form thus avoiding round-off errors. Energy functionals constructed for all multiplet states of multi-charged ions are reduced to simple form involving only five (h-shell) or six ((t1u + t1g) case) independent integrals (instead of 120 or 231, respectively, in the general case) thus enabling to reduce full-CI or multiconfigurational self-consistent-field calculations of multicharged ions within the corresponding orbital spaces. Applications of the proposed approach are presented to the C60 anion states, which are the case in superconducting fullerides K3C60 and Rb3C60. Some effects of electron interactions within quasi-pi-electron model with different interelectron potentials are considered [3].
David Brown
2008-08-19
The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth--order finite difference implementation of the equations.
Killing Tensors and Symmetries
David Garfinkle; E. N. Glass
2010-03-10
A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin's magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.
NASA Astrophysics Data System (ADS)
Maes, Christian; Salazar, Alberto
2014-01-01
In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary-driven particle systems such as the open Kawasaki lattice gas and the zero-range model. As a measure of time-symmetric dynamical activity over time T we count the difference (N? - Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo-type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.
Dynamical (super) symmetry breaking
Murayama, Hitoshi
2000-10-03
Dynamical Symmetry Breaking (DSB) is a concept theoristsrely on very often in the discussions of strong dynamics, model building,and hierarchy problems. In this talk, I will discuss why this is such apermeating concept among theorists and how they are used in understandingphysics. I also briefly review recent progress in using dynamicalsymmetry breaking to construct models of supersymmetry breaking andfermion masses.
ERIC Educational Resources Information Center
McGehe, Carol
1991-01-01
Presents math activities, problems, and games for teaching elementary students to recognize the world's natural symmetry and understand the mathematical qualities it represents; suggests activities with construction paper, blocks, and calculators. Instructions for using the calculator to create palindromes are included. (SM)
Tessellations: Geometry and Symmetry
NSDL National Science Digital Library
2010-01-01
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.
E. Allen Emerson; A. Prasad Sistla
1993-01-01
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.
Ergin Sezgin
We review the structure of W? algebras, their super and topological extensions, and their contractions down to (super) w?. Emphasis is put on the field theoretic realisations of these algebras. We also review the structure of w? and W? gravities and comment on various applications of W? symmetry.
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
Invariant Features from Interest Point Groups
Salvaggio, Carl
detectors used are not scale-invariant, and the correlation measures are not invariant to viewpoint, scale can form feature descriptors which are invariant to any 2D projective transformation (similarity of scale-invariant interest point detectors in their implemen- tation. Groups of interest points which
Topologic symmetry and real symmetry in framework silicates
G. Gottardi
1979-01-01
Summary The topologic symmetry of a framework silicate is reduced to topochemical symmetry by an ordering inside the tetrahedra; each further reduction of symmetry may be due to one of the following three causes: 1 ordered distribution of extraframework cations, 2 squeezing of the framework, 3 repulsion of extraframework cations.
Hari Krovi
2007-11-12
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. We derive an expression for hitting time using superoperators, and numerically evaluate it for the walk on the hypercube for various coins and decoherence models. We show that, by contrast to classical walks, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition for their existence. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Symmetries of a graph, given by its automorphism group, can be inherited by the evolution operator. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. Symmetry can also cause the walk to be confined to a subspace of the original Hilbert space for certain initial states. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph and we give an explicit construction of the quotient graph. We conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speed-up. Finally, we use symmetry and the theory of decoherence-free subspaces to determine when the subspace of the quotient graph is a decoherence-free subspace of the dynamics.
NASA Astrophysics Data System (ADS)
Zhu, B.; Wang, Y.; Atanasov, I. S.; Cheng, D.; Hou, M.
2012-04-01
Metropolis Monte Carlo sampling in the semi-grand canonical ensemble with empirical potentials is used to predict equilibrium ordered structures and segregation properties of small icosahedral Au-Pd nanoclusters and helical nanowire segments over the whole range of compositions at low temperatures. The cases of free-standing clusters and wires are compared with the same systems encapsulated in carbon nanotubes. A number of chemically ordered structures and segregation states are identified and found to be consistent with the same interplay between size mismatch, mixing enthalpy and surface energies of elemental metals which determines the thermodynamic equilibrium of binary metal alloys. Encapsulation has the effect of modifying the surface energies of nanoclusters and wires, with considerable consequences on their thermodynamic states, although the metal-graphite interaction strength is low as compared with the metal cohesive energy and the carbon-carbon binding energy.
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
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}
Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M
2014-02-01
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
NASA Astrophysics Data System (ADS)
Sato, K.; Kobayashi, Y.; Arinuma, K.; Kanazawa, I.; Tamura, R.; Shibuya, T.; Takeuchi, S.
2004-09-01
Previously, we showed that the icosahedral quasicrystal Cd5.7Yb possesses similar structural vacancies to those in its cubic 1/1 -approximant Cd6Yb by positron lifetime measurements [K. Sato, H. Uchiyama, K. Arinuma, I. Kanazawa, R. Tamura, T. Shibuya, and S. Takeuchi, Phys. Rev. B 66, 052201 (2002)]. In the present paper, the local chemical environment around the structural vacancies is specifically investigated by two-detector coincident Doppler broadening spectroscopy. Essentially the same annihilation sites with Cd-rich chemical environments are identified for the two phases. This strongly suggests that the quasicrystal is composed of the same cluster as the approximant. The difference in the structural vacancy density between the two phases is examined by positron diffusion experiments using a slow positron beam. The structural vacancy density in the quasicrystal is found to be 20% lower than that in the approximant.
Jana, Partha P; Lidin, Sven
2015-02-01
The ? phase in the Au-Cd binary system has been synthesized, and the structure has been analyzed by single-crystal X-ray diffraction. The compound ?-AuCd(4) crystallizes in the hexagonal space group P6(3)/m (No. 176). The unit cell contains ?273 atoms. The compound AuCd(4) represents a ?3a ?3a c superstructure of the AgMg(4) type. The structure can be well described by icosahedral and trigonal-prismatic clusters. A phase transition to the high-temperature ? phase occurs exothermically at around 578 K. The compound is formed at a sharp valence electron concentration of 1.8 e/a. The compound can be understood within the framework of the Hume-Rothery stabilization mechanism. PMID:24934260
Persson, K.; Schneider, G.; Jordan, D. B.; Viitanen, P. V.; Sandalova, T.
1999-01-01
Lumazine synthase catalyzes the penultimate step in the synthesis of riboflavin in plants, fungi, and microorganisms. The enzyme displays two quaternary structures, the pentameric forms in yeast and fungi and the 60-meric icosahedral capsids in plants and bacteria. To elucidate the structural features that might be responsible for differences in assembly, we have determined the crystal structures of lumazine synthase, complexed with the inhibitor 5-nitroso-6-ribitylamino-2,4-pyrimidinedione, from spinach and the fungus Magnaporthe grisea to 3.3 and 3.1 A resolution, respectively. The overall structure of the subunit and the mode of inhibitor binding are very similar in these enzyme species. The core of the subunit consists of a four-stranded parallel beta-sheet sandwiched between two helices on one side and three helices on the other. The packing of the five subunits in the pentameric M. grisea lumazine synthase is very similar to the packing in the pentameric substructures in the icosahedral capsid of the plant enzyme. Two structural features can be correlated to the differences in assembly. In the plant enzyme, the N-terminal beta-strand interacts with the beta-sheet of the adjacent subunit, thus extending the sheet from four to five strands. In fungal lumazine synthase, an insertion of two residues after strand beta1 results in a completely different orientation of this part of the polypeptide chain and this conformational difference prevents proper packing of the subunits at the trimer interface in the icosahedron. In the spinach enzyme, the beta-hairpin connecting helices alpha4 and alpha5 participates in the packing at the trimer interface of the icosahedron. Another insertion of two residues at this position of the polypeptide chain in the fungal enzyme disrupts the hydrogen bonding in the hairpin, and the resulting change in conformation of this loop also interferes with proper intrasubunit contacts at the trimer interface. PMID:10595538
Dynamical Symmetries in Classical Mechanics
ERIC Educational Resources Information Center
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that
Reflections on Symmetry and Proof
ERIC Educational Resources Information Center
Merrotsy, Peter
2008-01-01
The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical
Symmetry as a Continuous Feature
Hagit Zabrodsky; Shmuel Peleg; David Avnir
1995-01-01
Symmetry is treated as a continuous featureand a Continuous Measure of Distance from Symmetry inshapes is defined. The Symmetry Distance (SD) of a shape isdefined to be the minimum mean squared distance requiredto move points of the original shape in order to obtain asymmetrical shape. This general definition of a symmetrymeasure enables a comparison of the "amount" of symmetryof different
Symmetry Energy in Nuclear Surface
Pawel Danielewicz; Jenny Lee
2008-12-25
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
Nonlinear Realizations of Supersymmetry and Other Symmetries
S. T. Love
2005-10-21
Simultaneous nonlinear realizations of spontaneously broken supersymmetry in conjunction with other spontaneous and/or explicitly broken symmetries including R symmetry, global chiral symmetry, dilatations and the superconformal symmetries is reviewed.
A Reflective Symmetry Descriptor Michael Kazhdan,
Funkhouser, Thomas A.
A Reflective Symmetry Descriptor Michael Kazhdan, Bernard Chazelle, David Dobkin, Adam Finkelstein, and Thomas Funkhouser Princeton University, Princeton NJ 08544, USA Abstract. Computing reflective symmetries, we introduce a new reflective symmetry descriptor that repre- sents a measure of reflective symmetry
Dark discrete gauge symmetries
NASA Astrophysics Data System (ADS)
Batell, Brian
2011-02-01
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.
Mass independent textures and symmetry
Lam, C. S. [Department of Physics, McGill University, Montreal, QC, Canada H3A 2T8 and Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 (Canada)
2006-12-01
A mass-independent texture is a set of linear relations of the fermion mass-matrix elements which imposes no constraint on the fermionic masses nor the Majorana phases. Magic and 2-3 symmetries are examples. We discuss the general construction and the properties of these textures, as well as their relation to the quark and neutrino mixing matrices. Such a texture may be regarded as a symmetry, whose unitary generators of the symmetry group can be explicitly constructed. In particular, the symmetries connected with the tribimaximal neutrino mixing matrix are discussed, together with the physical consequence of breaking one symmetry but preserving another.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Guo, Fei; Liu, Zheng; Vago, Frank; Ren, Yue; Wu, Weimin; Wright, Elena T.; Serwer, Philip; Jiang, Wen
2013-01-01
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. PMID:23580619
Simple and collective twisted symmetries
Giuseppe Gaeta
2014-10-29
After the introduction of $\\lambda$-symmetries by Muriel and Romero, several other types of so called "twisted symmetries" have been considered in the literature (their name refers to the fact they are defined through a deformation of the familiar prolongation operation); they are as useful as standard symmetries for what concerns symmetry reduction of ODEs or determination of special (invariant) solutions for PDEs and have thus attracted attention. The geometrical relation of twisted symmetries to standard ones has already been noted: for some type of twisted symmetries (in particular, $\\lambda$ and $\\mu$-symmetries), this amounts to a certain kind of gauge transformation. In a previous review paper [G. Gaeta, "Twisted symmetries of differential equations", {\\it J. Nonlin. Math. Phys.}, {\\bf 16-S} (2009), 107-136] we have surveyed the first part of the developments of this theory; in the present paper we review recent developments. In particular, we provide a unifying geometrical description of the different types of twisted symmetries; this is based on the classical Frobenius reduction applied to distribution generated by Lie-point (local) symmetries.
NASA Astrophysics Data System (ADS)
Kumar, Vijay
2009-02-01
We report results of ab initio pseudopotential calculations on the nanocoating of gold on an icosahedral Al13 cluster and the findings of icosahedrally symmetric endohedral Al@Al12Au20- and empty cage Al12Au202- compound fullerenes formed of metal atoms. Twelve Al atoms cap the pentagonal faces of a dodecahedral Au20 cage in which each Au atom has three Al atoms and three Au atoms as nearest neighbors. Mixing of Al13 and Au20 magic clusters leads to a large heat of formation of 0.55 eV/atom and high stability of the Al@Al12Au20 compound fullerene. The binding energies of Al12Au20 and Al@Al12Au20 are 3.017 and 3.007 eV/atom, respectively, which are much larger than 2.457 eV/atom for Au32 fullerene, leading to the possibility of their high abundance.
Oxidizing Borcherds symmetries
Axel Kleinschmidt; Jakob Palmkvist
2013-01-07
The tensor hierarchy of maximal supergravity in D dimensions is known to be closely related to a Borcherds (super)algebra that is constructed from the global symmetry group E(11-D). We here explain how the Borcherds algebras in different dimensions are embedded into each other and can be constructed from a unifying Borcherds algebra. The construction also has a natural physical explanation in terms of oxidation. We then go on to show that the Hodge duality that is present in the tensor hierarchy has an algebraic counterpart. For D>8 the Borcherds algebras we find differ from the ones existing in the literature although they generate the same tensor hierarchy.
Thermal symmetry in isoscaling
NASA Astrophysics Data System (ADS)
Escudero, C. R.; Lpez, J. A.; Dorso, C. O.
2007-02-01
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
Symmetry and perturbation theory
NASA Astrophysics Data System (ADS)
Gaeta, Giuseppe
A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler-Lagrange equations -- Regularity of pseudogroup orbits -- Relaxation times to equilibrium in Fermi-Pasta-Ulam system -- Energy cascade in Fermi-Pasta-Ulam models -- On Birkhoff method for integrable lagrangian systems -- Symmetry of singularities and orbit spaces of compact linear groups -- Symmetric solutions in molecular potentials -- Variational approach to soliton generation and stability analysis of multidimensional nonlinear Schrodinger equation -- Differential invariants for infinite-dimensional algebras.
Galileons with Gauge Symmetries
Shuang-Yong Zhou; Edmund J. Copeland
2012-02-08
Galileon models arise in certain braneworld scenarios as modifications to General Relativity, and are also interesting as field theories in their own right. We show how the galileon model can be naturally generalized to include local gauge symmetries, by allowing for couplings to Yang-Mills fields. The resulting theories have at most second order spacetime derivatives in any representation of the gauge group, thereby avoiding Ostrogradski ghosts. We also extend the models to include curved space, and show how in that case we need to include non-minimal couplings between the galileons and the curvature tensors for the theory to retain its second order nature.
Holographic heavy quark symmetry
NASA Astrophysics Data System (ADS)
Hashimoto, Koji; Ogawa, Noriaki; Yamaguchi, Yasuhiro
2015-06-01
We investigate the heavy quark spin symmetry, i.e. the mass degeneracy of pseudo-scalar and vector quarkonia at heavy quark limit, by using the gauge/gravity correspondence. We allow generic D3-like geometry with a flavor D7-brane, to avoid supersymmetric mass degeneracy. For geometries admitting physical QCD-like properties, we find that the mass degeneracy is generically achieved in a good accuracy, up to a few percent mass splitting. We also compute spectra of excited quarkonia states, and discuss comparisons with experiments and quark-model calculations.
Pauling, L
1991-01-01
The low-Q peaks on three pulsed-neutron powder patterns (total, U differential, and Pd differential) of the icosahedral quasicrystal Pd3SiU have been indexed on the basis of an assumed cubic structure of the crystals that by icosahedral twinning form the quasicrystal. The primitive unit cube is found to have edge length 56.20 A and to contain approximately 12,100 atoms. Similar analyses of pulsed-neutron patterns of Al55Cu10Li35, Al55Cu10Li30Mg5, and Al510Cu125Li235Mg130 give values of the cube edge length 58.3, 58.5, and 58.4 A, respectively, with approximately 11,650 atoms in the unit cube. It is suggested that the unit contains eight complexes in the beta-W positions, plus some small interstitial groups of atoms, with each complex consisting of a centered icosahedron of 13 clusters, each of 116 atoms with the icosahedral structure found in the body-centered cubic crystal Mg32(Al,Zn)49. PMID:11607201
Neutrinos, axions and conformal symmetry
Krzysztof A. Meissner; Hermann Nicolai
2008-01-01
We demonstrate that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the standard model\\u000a with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry,\\u000a which naturally gives rise to an axion-like particle with some unusual features. The couplings of this axion to standard\\u000a model particles, in particular photons and gluons, are entirely
Symmetry planes of Paleozoic crinoids
Lane, N. G.; Webster, G. D.
1967-11-30
THE UNIVERSITY OF KANSAS PALEONTOLOGICAL CONTRIBUTIONS November 30, 1967 Paper 25 SYMMETRY PLANES OF PALEOZOIC CRINOIDS N. GARY LANE and G. D. WEBsTER University of California, Los Angeles, and San Diego State College ABSTRACT The homocrinid (E... three planes of bilateral symmetry in the crowns of Paleozoic crinoids. The most widely prevalent of these is the so-called madreporite (M) plane of BATHER. The other two planes, called homocrinid and heterocrinid symmetry planes by UBAGHS, are most...
Trovato, Antonio; Hoang, Trinh Xuan; Banavar, Jayanth R.; Maritan, Amos
2007-01-01
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of ?/(32)?0.7405. Much more recently, an unusually high-density packing of ?0.770732 was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of ?/4. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at c*=2?1. PMID:18032605
Givental graphs and inversion symmetry
P. Dunin-Barkowski; S. Shadrin; L. Spitz
2012-12-17
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Unal, Baris
2008-12-01
The present work in this dissertation mainly focuses on the clean fivefold surfaces of i-Al-Pd-Mn quasicrystals as well as the nucleation and growth of Ag films on these surfaces. In addition, Ag film growth on NiAl(110) has been explored in the frame of this dissertation. First, we have investigated the equilibration of a fivefold surface of icosahedral Al-Pd-Mn quasicrystal at 900-915 K and 925-950 K, using Omicron variable temperature scanning tunneling microscope (STM). Annealing at low temperatures resulted in many voids on some terraces while the others were almost void-free. After annealing at 925-950K, void-rich terraces became much rarer. Our STM images suggest that through growth and coalescence of the voids, a different termination becomes exposed on host terraces. All of these observations in our study indicate that even after the quasicrystalline terrace-step structure appears, it evolves with time and temperature. More specifically, based on the STM observations, we conclude that during the annealing a wide range of energetically similar layers nucleate as surface terminations, however, with increasing temperature (and time) this distribution gets narrower via elimination of the metastable void-rich terraces. Next, we have examined the bulk structural models of icosahedral Al-Pd-Mn quasicrystal in terms of the densities, compositions and interplanar spacings for the fivefold planes that might represent physical surface terminations. In our analyses, we mainly have focused on four deterministic models which have no partial or mixed occupancy but we have made some comparisons with an undeterministic model. We have compared the models with each other and also with the available experimental data including STM, LEED-IV, XPD and LEIS. In all deterministic models, there are two different families of layers (a pair of planes), and the nondeterministic model contains similar group of planes. These two families differ in terms of the chemical decoration of their top planes. Hence, we name them as Pd+(with Pd) and Pd-(without Pd). Based on their planer structure and the step height, it can be said that these two families can be viable surface terminations. However, besides the Pd content, these two sets differ in terms of relative densities of their top planes as well as the gap separating the layer from the nearest atomic plane. The experimental data and other arguments lead to the conclusion that the Pd- family is favored over the Pd+. This has an important implication on the interpretation of local motifs seen in the high resolution STM images. In other words, the dark stars are not formed by cut-Bergmans rather they are formed by cut-Mackays.
Robert B. Howlett Chapter 1: Symmetry
Howlett, Robert Brian
Aspects of Symmetry Robert B. Howlett #12;Contents Chapter 1: Symmetry §1a An example of abstract symmetry 2 §1b Structure preserving transformations 3 §1c The symmetries of some structured sets 7 §1d Some and inadmissibility proofs 105 Index of notation 110 Index 111 iv #12;1Symmetry Of the following geometrical objects
Almor, Amit
Gender Symmetry, Sexism, & Intimate Partner Violence 1 Running Head: Gender Symmetry, Sexism, & Intimate Partner Violence Gender Symmetry, Sexism, & Intimate Partner Violence Christopher T. Allen University of New York #12;Gender Symmetry, Sexism, & Intimate Partner Violence 2 Abstract The current study
Symmetry in context: Salience of mirror symmetry in natural Elias H. Cohen # $
Tong, Frank
Symmetry in context: Salience of mirror symmetry in natural patterns Elias H. Cohen # $ Psychology Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments
Noether symmetries in Bianchi universes
Salvatore Capozziello; Giuseppe Marmo; Claudio Rubano; Paolo Scudellaro
1996-06-17
We use our N\\"other Symmetry Approach to study the Einstein equations minimally coupled with a scalar field, in the case of Bianchi universes of class A and B. Possible cases, when such symmetries exist, are found and two examples of exact integration of the equations of motion are given in the cases of Bianchi AI and BV.
NSDL National Science Digital Library
2011-01-01
This website provides text, images, animations, and interactive Java applets to teach bilateral and rotational symmetry. Learners are given drawing and painting challenges as well as recreational activities such as making a virtual kaleidoscope. Clicking on the first button 'Best Symmetry Animation' takes students through the entire sequence.
Symmetry and Tilings: An Exploration
NSDL National Science Digital Library
James Rutledge
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.
Symmetry and Condensed Matter Physics
M. El-Batanouny; F. Wooten
2008-01-01
Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography, experimental methods capitalizing on symmetry aspects, non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems, as well as concepts and techniques behind the
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smoli?, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Kaneko, Y; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M
2013-03-20
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 molecular dynamics study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare it to recently published results obtained for the cubic 1/1-approximant Zn(6)Sc. Both phases, quasicrystal and approximant, are built up from large atomic clusters which contain a tetrahedral shell at the cluster centre and are packed either quasiperiodically or on a bcc lattice. Using quasielastic neutron scattering and atomic scale simulations, we show that in the quasicrystal the tetrahedra display a dynamics similar to that observed in the 1/1-approximant: the tetrahedra behave as a 'single molecule' and reorient dynamically on a timescale of the order of a few ps. The tetrahedra reorientation is accompanied by a large distortion of the surrounding cluster shells which provide a unique dynamical flexibility to the quasicrystal. However, whereas in the 1/1-approximant the tetrahedron reorientation is observed down to T(c) = 160 K, where a phase transition takes place, in the quasicrystal the tetrahedron dynamics is gradually freezing from 550 to 300 K, similarly to a glassy system. PMID:23411496
Shukla, A. K.; Dhaka, R. S.; Biswas, C.; Banik, S.; Barman, S. R.; Horn, K.; Ebert, Ph.; Urban, K. [UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore, 452017, Madhya Pradesh (India); Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin (Germany); Institut fuer Festkoerperforschung, Forschungszentrum Juelich GmbH, 52425 Juelich (Germany)
2006-02-01
We report x-ray photoelectron spectroscopy (XPS) study of Na and K adlayers on icosahedral Al{sub 70.5}Pd{sub 21}Mn{sub 8.5} (i-Al-Pd-Mn) quasicrystal. The Na 1s core-level exhibits a continuous linear shift of 0.8 eV towards lower binding energies (BE) with increasing coverage up to one monolayer (ML) saturation coverage. In the case of K/i-Al-Pd-Mn, a similar linear shift in the K 2p spectra towards lower BE is observed. In both cases, the plasmon related loss features are observed only above 1 ML. The substrate core-level peaks, such as Al 2p, do not exhibit any shift with the adlayer deposition up to the highest coverage. Based on these experimental observations and previous studies of alkali metal growth on metals, we conclude that below 1 ML, both Na and K form a dispersed phase on i-Al-Pd-Mn and there is hardly any charge transfer to the substrate. The variation of the adlayer and substrate core-level intensities with coverage indicates layer by layer growth.
Doronin, Yu. S.; Libin, M. Yu.; Samovarov, V. N.; Vakula, V. L. [B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Avenue, Kharkiv, 61103 (Ukraine)
2011-08-15
Supersonic-jet luminescence spectroscopy was applied to study vibronic transitions in icosahedral N{sub 2} and Ar-N{sub 2} clusters having from 100 to 400 particles per cluster. In the case of mixed Ar-N{sub 2} clusters, the w {sup 1}{Delta}{sub u}{yields} X {sup 1}{Sigma}{sub g}{sup +} transitions were observed to occur in single N{sub 2} molecules in an Ar environment, in very much the same way as in Ar-N{sub 2} bulk samples. In N{sub 2} clusters, however, a band series was detected which, to our knowledge, was never observed earlier. In the spectra of Ar-N{sub 2} clusters, this series coexisted with the ''bulk''w {sup 1}{Delta}{sub u}{yields} X{sup 1}{Sigma}{sub g}{sup +} transitions. Our analysis demonstrated that the series should be assigned to emission of van der Waals (N{sub 2}){sub 2} dimers from inside clusters. Earlier, such dimers were only observed in molecular beams and gaseous nitrogen; this paper reports their observation in the solid phase of nitrogen. Our results can be of interest from the viewpoint of producing polymeric nitrogen since (N{sub 2}){sub 2} dimers can be considered to be a starting species for its synthesis.
NASA Astrophysics Data System (ADS)
Goto, D.; Nakajima, T.; Masaki, S.
2014-12-01
Air pollution has a great impact on both climate change and human health. One effective way to tackle with these issues is a use of atmospheric aerosol-chemistry models with high-resolution in a global scale. For this purpose, we have developed an aerosol-chemistry model based on a global cloud-resolving model (GCRM), Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Tomita and Satoh, Fluid. Dyn. Res. 2004; Satoh et al., J. Comput. Phys. 2008, PEPS, 2014) under MEXT/RECCA/SALSA project. In the present study, we have simulated aerosols and tropospheric ozone over Japan by our aerosol-chemistry model "NICAM-Chem" with a stretched-grid system of approximately 10 km resolution, for saving the computer resources. The aerosol and chemistry modules are based on Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS; Takemura et al., J. Geophys. Res., 2005) and Chemical AGCM for Study of Atmospheric Environment and Radiative Forcing (CHASER; Sudo et al., J. Geophys. Res., 2002). We found that our model can generally reproduce both aerosols and ozone, in terms of temporal variations (daily variations of aerosols and diurnal variations of ozone). Under MEXT/RECCA/SALSA project, we also have used these results obtained by NICAM-Chem for the assessment of their impact on human health.
Symmetry in Nonlinear Mathematical Physics 1997, V.1, 130137. Nonclassical Potential Symmetries
Popovych, Roman
Symmetry in Nonlinear Mathematical Physics 1997, V.1, 130137. Nonclassical Potential Symmetries Puerto Real, Cadiz, Spain E-mail: mlgand@merlin.uca.es Abstract In this paper, new classes of symmetries symmetries called nonclassical potential symmetries, are neither potential symmetries nor nonclassical
Stillness in Motion The Essence of Symmetry
Lee, Carl
Carl Lee Symmetry October 2014 7 / 39 #12;Textiles (Peruvian Skirt) Carl Lee Symmetry October 2014 8 / 39 #12;Textiles (Peruvian Skirt) Motion: Reflection across a line Carl Lee Symmetry October 2014 9
Symmetry Theory of the Flexomagnetoelectric Effect in the Bloch Lines
B. M. Tanygin
2011-09-02
It was shown, that there are 48 magnetic point groups of the Bloch lines including 22 (11 time-invariant and 11 time-noninvariant) enantimorphic and 26 non-enantiomorphic groups. The Bloch lines with the time-noninvariant enantiomorphism have identical types (parities) of the magnetization and polarization dependences. The soliton like Bloch lines are 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 walls has been suggested. New type of the flexomagnetoelectric coupling, 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 multiple states Bloch line based magnetoelectric/multiferroic memory is proposed. It can be considered as a concept of the magnetoelectric enhancement of existing Bloch line memory invention.
Classification of Arnold-Beltrami Flows and their Hidden Symmetries
Fre, Pietro
2015-01-01
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the ABC-flow introduced by Beltrami, Arnold and Childress. Beltrami equation is the eigenstate equation for the first order Laplace-Beltrami operator *d, which we solve by using harmonic analysis. Taking torus T^3 constructed as R^3/L, where L is a crystallographic lattice, we present a general algorithm to construct solutions of Beltrami equation which utilizes as main ingredient the orbits under the action of the point group P_L of three-vectors in the momentum lattice L*. We introduce the new notion of a Universal Classifying Group GU_L which contains all crystallographic space groups as proper subgroups. We show that the *d-eigenfunctions are naturally arranged into irreducible representations of GU_L and by means of a systematic use of the branching rules with respect to various possible subgroups H of GU_L we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lat...
Spectral theorem and partial symmetries
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
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.
Strangeness and Chiral Symmetry Breaking
Harleen Dahiya; Neetika Sharma
2010-11-04
The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model ($\\chi$CQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson-nucleon sigma terms. The $\\chi$CQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.
CKM matrix and flavor symmetries
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Ishida, Hiroyuki; Ishimori, Hajime; Kobayashi, Tatsuo; Ogasahara, Atsushi
2013-11-01
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both ?13 and ?23 or only ?13 are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The Z7 symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the ?(6N2) series are also briefly discussed.
Symmetries of homogeneous cosmologies
Spiros Cotsakis; Peter Leach; Hara Pantazi
2000-11-06
We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi-scalar field equations become subsets of the second Bianchi jet bundle, $J^2$, and every Bianchi cosmology is naturally extended to live on a variety of $J^2$. We are interested in the existence and behaviour of extensions of arbitrary Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector fields corresponding to both Bianchi classes $A$ and $B$. We give examples of functions defined on Bianchi jet bundles which are constant along some Bianchi models (first integrals) and use these to find particular solutions in the Bianchi total space. We discuss how our approach could be used to shed new light to questions like isotropization and the nature of singularities of homogeneous cosmologies by examining the behaviour of the variational vector fields and also give rise to interesting questions about the `evolution' and nature of the cosmological symmetries themselves.
Pairing-Symmetry Selection in a Weakly Doped Canted Antiferromagnet on the Triangular Lattice
NASA Astrophysics Data System (ADS)
Wrbel, P.; Suleja, W.
2008-07-01
The mechanism of superconductivity generation by spin fluctuations in the electron doped canted antiferromagnet on the triangular lattice was analyzed. The underlying assumption is that the formation of the bound state is the prerequisite of pairing. The outcome of this analysis is also valid if an additional isotropic attraction is active but the anisotropic spin-fluctuation mediated force decides on the symmetry of the two-particle bound state. When the canted antiferromagnetic state is generated, the symmetry of the point group C6v for the triangular lattice is lowered to the symmetry of C3v. It is demonstrated that spin fluctuations definitely favor the p-wave bound state, which transforms according to the E representation of C3v. Since the inversion is not an element of C3v, the parity is not a good quantum number and thus the predicted paired state will be a mixture of singlet and triplet. Such a scenario may be relevant to physics of superconducting triangular cobaltates or organics.
Higgs family symmetry and supersymmetry
Patt, Brian Lawrence
2006-01-01
In this thesis we investigate building models of family symmetry that give the Higgs fields family structure. We construct several models, starting with 2 generation models then moving onto 3 generation models. These models ...
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Hidden symmetry of the Galileon
NASA Astrophysics Data System (ADS)
Hinterbichler, Kurt; Joyce, Austin
2015-07-01
We show that there is a special choice of parameters for which the Galileon theory is invariant under an enhanced shift symmetry whose nonlinear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one with only even powers of the field, with no free coefficients, and accounts for the improved soft-limit behavior observed in the quartic Galileon S -matrix.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; Rodrguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
Nonholonomic mechanical systems with symmetry
Anthony M. Bloch; P. S. Krishnaprasad; Jerrold E. Marsden; Richard M. Murray
1996-01-01
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d'Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin
Contrapositive symmetry of fuzzy implications
J' Anos C. Fodor
1995-01-01
Contrapositive symmetry of R- and QL-implications defined from t-norms, t-conorms and strong negations is studied. For R-implications, characterizations of contrapositive symmetry are proved when the underlying t-norm satisfies a residuation condition. Contrapositive symmetrization of R-implications not having this property makes it possible to define a conjunction so that the residuation principle is preserved. Cases when this associated conjunction is a
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
Symmetry breaking from Lorentz transformation
Bin-Guang Ma
2005-08-10
Symmetry breaking is discussed in this paper which comes from the Lorentz transformation of special relativity and changes our view that two relatively moving bodies always have the relative speed equal in magnitude and opposite in direction. An appeal was made for the test of Lorentz transformation in a multimedia environment which has the fundamental significance that it may reveal the origin of symmetry breaking in many physical phenomena.
NASA Astrophysics Data System (ADS)
Dai, Tie; Shi, Guangyu; Nakajima, Teruyuki
2015-06-01
Aerosol optical properties are simulated using the Spectral Radiation Transport Model for Aerosol Species (SPRINTARS) coupled with the Non-hydrostatic ICosahedral Atmospheric Model (NICAM). The 3-year global mean all-sky aerosol optical thickness (AOT) at 550 nm, the ngstrm Exponent (AE) based on AOTs at 440 and 870 nm, and the single scattering albedo (SSA) at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Aerosol Robotic Network (AERONET). The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the opposite is found over regions dominated by hydrophobic aerosol.
Teo, Boon K; Strizhev, Alex
2002-12-01
A new and simple method for assessing the relative stabilities of various positional isomers of a given heteronuclear cluster is described. The method is based on a tight-binding approach in conjunction with an adjacent matrix methodology (TBAM). The usefulness of the method is illustrated by bond energy calculations of a number of binary icosahedral clusters, including noncentered icosahedral A(n)B(12)(-)n clusters comprising main-group elements B, C, N, and S as well as B- and A-centered icosahedral A(n)B(13)(-)n clusters that consist of transition metals, Au, Ag, Ni, and Pt atoms. The latter results are compared with the previously reported molecular mechanics calculations based on Lennard-Jones potential and with experimental results, whenever possible. The trends of the total bond energies obtained by the two methods are nearly parallel in all cases, indicating that the relative stabilities predicted by the two methods follow the same order. The TBAM approach provides a simple and efficient way of predicting the relative stabilities of various positional isomers of a given cluster, particularly for clusters where the number of positional isomers is so large that it cannot be handled manually. The total bond energies exhibit a stepwise progression. Each step is characterized by a set of A-A, B-B, and A-B bonds which uniquely determines the total bond energy and, hence, the stability. The step formation implies that positional isomers of a given cluster geometry can be categorized by sets of numbers of A-A, B-B, and A-B bonds, or simply the numbers of the minority (either A-A or B-B) bonds. Three site preference rules, the strong-bond rule, the heterobond rule, and the big-hole rule, were formulated based on these model calculations. These rules are useful in rationalizing and/or predicting the relative stabilities of various positional isomers of a given cluster geometry. PMID:12444776
About the concept and definition of "noncrystallographic symmetry"
Souvignier, Bernd
of "noncrystallographic symmetry" in structur- al biology is inconsistent with the accepted definitionAbout the concept and definition of "noncrystallographic symmetry" Massimo Nespolo*, I , Bernd symmetry / Local symmetry / Partial symmetry / Groupoid Abstract. The definition of "noncrystallographic
Do symmetry constraints yield exact solutions?
Wen-Xiu Ma; Min Chen
2007-01-01
Two classes of natural symmetry constraints are introduced and analyzed for the SharmaTassoOlver equation. Through those symmetry constraints, the phenomenon is exhibited that symmetry constraints do not always yield exact solutions. It is also explained why such phenomenon can happen in the symmetry theory.
Braided Quantum Field Theories and Their Symmetries
Yuya Sasai; Naoki Sasakura
2007-01-01
Braided quantum field theories, proposed by Oeckl, can provide a framework for quantum field theories that possess Hopf algebra symmetries. In quantum field theories, symmetries lead to non-perturbative relations among correlation functions. We study Hopf algebra symmetries and such relations in the context of braided quantum field theories. We give the four algebraic conditions among Hopf algebra symmetries and braided
Symmetries of the Robinson-Trautman equation
Wlodzimierz Natorf; Jacek Tafel
2006-09-02
We study point symmetries of the Robinson--Trautman equation. The cases of one- and two-dimensional algebras of infinitesimal symmetries are discussed in detail. The corresponding symmetry reductions of the equation are given. Higher dimensional symmetries are shortly discussed. It turns out that all known exact solutions of the Robinson--Trautman equation are symmetric.
Exploiting Symmetry in Temporal Logic Model Checking
Edmund M. Clarke; Somesh Jha; Reinhard Enders; Thomas Filkorn
1996-01-01
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
Symmetry properties in polarimetric remote sensing
S. V. Nghiem; S. H. Yueh; R. Kwok; F. K. Li
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by
Exploiting Symmetry In Temporal Logic Model Checking
Edmund M. Clarke; Thomas Filkorn; Somesh Jha
1993-01-01
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
Partial Symmetry Breaking Iain McDonald
Rossi, Francesca
Partial Symmetry Breaking Iain McDonald University of St Andrews, Fife, Scotland, iain@dcs.st-and.ac.uk Abstract. In this paper I de#12;ne partial symmetry breaking, a concept that has been used in many previous of partial symmetry breaking in constraint programming. I show experimentally that performing symmetry
Symmetry in Matrix Models Pierre Flener
Walsh, Toby
Symmetry in Matrix Models Pierre Flener , Alan Frisch , Brahim Hnich , Zeynep Kiziltan models, sym- metry is an important feature. We study and generalise symmetry-breaking techniques with symmetry in such models in a uniform way. We thereby reduce the burden on the user of eliminating symmetry
The symmetry of wallpaper David Morawski
Weinberger, Hans
The symmetry of wallpaper David Morawski University of Minnesota Math Club, University of Minnesota 25 March, 2011 #12;"Symmetry is everywhere" In art: The Alhambra, Spain David Morawski (UMN) The symmetry of wallpaper 25 March, 2011 2 / 35 #12;"Symmetry is everywhere" In architecture: Apartment
Rotational symmetry breaking for spiral waves
Victor G LeBlanc
2002-01-01
We continue our investigation of the effects of forced symmetry breaking on the dynamics of spiral waves in excitable media. In a previous paper, we have studied the effects of breaking the translation symmetry, while keeping the rotation symmetries in the Euclidean equivariant models for spiral waves. In this paper, we will investigate the effects of breaking the rotational symmetry
Hennig, R. G. [Department of Physics, Ohio State University, Columbus, Ohio 43210, U.S.A. (United States); Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States); Majzoub, E. H. [Sandia National Laboratories, Livermore, California 94550, U.S.A. (United States); Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States); Kelton, K. F. [Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States)
2006-05-01
We present a determination of hydrogen sites in the 1/1 approximant structure of the icosahedral TiZrNi quasicrystal. A Rietveld refinement of neutron and x-ray diffraction data determines the locations of interstitial hydrogen atoms. Density-functional methods calculate the energy of hydrogen on all possible interstitial sites. The Rietveld refinement shows that the hydrogen atoms are preferentially located in the two lowest-energy sites. The filling of the remaining hydrogen sites is dominated by the repulsive hydrogen-hydrogen interaction at short distances.
O'Hanlon actions by Noether symmetry
F. Darabi
2015-04-14
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials respecting Noether symmetry in O'Hanlon action in Einstein frame.
Symmetry protected topological orders and the group cohomology of their symmetry group
Wen, Xiao-Gang
Symmetry protected topological orders and the group cohomology of their symmetry group Xie Chen,1 Canada Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G, which can all be smoothly connected to the same trivial product state if we break the symmetry
Symmetry protected topological orders and the group cohomology of their symmetry group
Chen, Xie
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase ...
Chiral Symmetry Breaking in Graphene
Gordon W. Semenoff
2011-08-19
The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.
Aspects of Dynamical Symmetry Breaking
NASA Astrophysics Data System (ADS)
Cohler, Lucien Eugene
In order to develop some insight into dynamical symmetry breaking in four dimensional nonabelian theories, a toy model is examined that exhibits some of the features of the more realistic model but remains tractable. The model that is studied is that of QED in three dimensions with N fermion flavors. It will be shown that there are configurations that dynamically break the chiral symmetry of the model. By taking a large number of flavors, a 1/N expansion may be used to simplify the problem which is approached by numerically solving the Schwinger-Dyson equations for the fermion self energy. By comparing the effective potentials of the broken and unbroken solutions it will be shown that the dynamics favors symmetry breaking. In addition, the low energy impact of having a composite Higgs sector will be examined by estimating its contribution to the (rho) parameter.
Neutrino Mixing from CP Symmetry
Chen, Peng; Ding, Gui-Jun
2015-01-01
The neutrino mass matrix has remnant CP symmetry expressed in terms of the lepton mixing matrix, and vice versa the remnant CP transformations allow us to reconstruct the mixing matrix. We study the scenario that all the four remnant CP transformations are preserved by the neutrino mass matrix. The most general parameterization of remnant CP transformations is presented. The lepton mixing matrix is completely fixed by the remnant CP, and its explicit form is derived. The necessary and sufficient condition for conserved Dirac CP violating phase is found. If the Klein four flavor symmetry generated by the postulated remnant CP transformations arises from a finite flavor symmetry group, the phenomenologically viable lepton flavor mixing would be the trimaximal pattern, both Dirac CP phase $\\delta_{CP}$ and Majorana phase $\\alpha_{31}$ are either $0$ or $\\pi$ while another Majorana phase $\\alpha_{21}$ is a rational multiple of $\\pi$. These general results are confirmed to be true in the case that the finite flavo...
Flavored Peccei-Quinn symmetry
NASA Astrophysics Data System (ADS)
Ahn, Y. H.
2015-03-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a ? - ? power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the ? - ? power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma?2.53 1 0-5 eV and the axion coupling to photon ga ? ??1.33 1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Order Symmetry of Weak Measurements
Lars M. Johansen; Pier A. Mello
2009-07-30
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement. We show that this generalized concept of weak measurements displays a symmetry under reversal of measurement order. We show that the conditions for order symmetry are the same as in classical mechanics. We also find that the imaginary part of the weak value has a counterpart in classical mechanics. This scheme suggests new experimental possibilities.
Polarization and Symmetry of Electronic Transitions in Long Fluorescence Lifetime Triangulenium Dyes
Thyrhaug, Erling; Srensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W.
2013-01-01
To fully exploit the capabilities of fluorescence probes in modern experiments, where advanced instrumentation is used to probe complex environments, other photophysical properties than emission color and emission intensity are monitored. Each dye property can be addressed individually as well as collectively to provide in-depth information unavailable from the standard intensity measurements. Dyes with long emission lifetimes and strongly polarized transitions enable the monitoring of lifetime changes as well as emission polarization (or anisotropy). Thus experiments can be designed to follow slow dynamics. In this article the UV and visible electronic transitions of a series of red emitting dyes based on the triangulenium motif are investigated. We resolve overlapping features in the spectra and assign transition moment of the molecular axes. The result is the complete Jablonski diagram for the UV and visible spectral region. The symmetries of the studied dyes are shown to have a large influence on the optical response and they are clearly separated into two groups of symmetry by their photophysical properties. The C2v symmetric dyes: azadioxatriangulenium (ADOTA+) and diazaoxatriangulenium (DAOTA+) have high emission anisotropies, fluorescence lifetimes around 20 ns, and fluorescence quantum yields of ~50%. The trioxatriangulenium (TOTA+) and triazatriangulenium (TATA+) dyesnominally of D3h symmetryhave fluorescence lifetimes around 10 ns lifetimes and fluorescence quantum yields of 10-15%. However, the D3h-symmetry is shown to be lowered to a point group, where the axes transform uniquely such that the degeneracy of the E-states is lifted. PMID:23391292
Charge Symmetry at the Partonic Level
J. T. Londergan; J. C. Peng; A. W. Thomas
2009-07-14
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 [Formula: see text] maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Axions and family symmetry breaking
Frank Wilczek
1982-01-01
Possible advantages of replacing the Peccei-Quinn U(1) quasisymmetry by a group of genuine flavor symmetries are pointed out. Characteristic neutral Nambu-Goldstone bosons will arise, which might be observed in rare K or ..mu.. decays. The formulation of Lagrangians embodying these ideas is discussed schematically.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative
Symmetry structure and phase transitions
Ashok Goyal; Meenu Dahiya; Deepak Chandra
2002-01-22
We study chiral symmetry structure at finite density and temperature in the presence of external magnetic field and gravity, a situation relevant in the early Universe and in the core of compact stars. We then investigate the dynamical evolution of phase transition in the expanding early Universe and possible formation of quark nuggets and their survival.
From symmetries to number theory
Tempesta, P., E-mail: p.tempesta@fis.ucm.e [Universidad Complutense, Departamento de Fisica Teorica II, Facultad de Fisicas (Spain)
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
GAPLex: Generalised Static Symmetry Breaking
Chris Jefferson; Tom Kelsey; Steve Linton; Karen Petrie
We describe a novel algorithm that statically breaks symmetry in CSPs by using computa- tional group theory during search. This algo- rithm extends and generalises the commonly used double lex method for breaking sym- metry in matrices. We show that our new sym- metry breaking method, GAPLex, is sound (will neither lose solutions nor return incor- rect solutions) and complete
Asymptotic Symmetries in Gravitational Theory
R. Sachs
1962-01-01
It is pointed out that the definition of the inhomogeneous Lorentz group as a symmetry group breaks down in the presence of gravitational fields even when the dynamical effects of gravitational forces are completely negligible. An attempt is made to rederive the Lorentz group as an \\
SYMMETRIES OF QUASICRYSTALS Charles Radin *
SYMMETRIES OF QUASICRYSTALS by Charles Radin * Department of Mathematics, University of Texas, Austin, TX 78712 Abstract We consider tiling models of ``round quasicrystals'' which would have supported in part by NSF Grant No. DMS9531584 and Texas ARP Grant 003658152 #12; Quasicrystals were
Kohn's theorem and Galilean symmetry
P-M. Zhang; P. A. Horvathy
2011-07-08
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, $e_a/m_a=\\epsilon$ 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 Schroedinger symmetry, augmented with independent internal rotations. All these properties follow from the cohomological structure of the Galilei group, as explained by Souriau's "d\\'ecomposition barycentrique"
$?$-$?$ reflection symmetry and radiative corrections
Ye-Ling Zhou
2014-09-30
The $\\mu$-$\\tau$ reflection symmetry is compatible with current neutrino oscillation data and easily realized under family symmetries. We prove that this symmetry preserves $\\theta_{23}=45^\\circ$, $\\delta=\\pm90^\\circ$, $\\rho,\\sigma=0,90^\\circ$, and can be embedded into the seesaw mechanism. The $\\mu$-$\\tau$ reflection symmetry preserved at a high energy scale $\\Lambda_\\text{FS}$ will be broken by radiative corrections and result in deviations of $\\theta_{23}$ from $45^\\circ$ and $\\delta$ from $\\pm90^\\circ$ at the electroweak scale. We develop an analytical method to derive the corrections to all the mixing parameters. We perform a numerical analysis in the MSSM for $\\delta=-90^\\circ$ at $\\Lambda_\\text{FS}$, and observe that $\\theta_{23}>45^\\circ$ in the normal mass ordering, $\\theta_{23}<45^\\circ$ in the inverted mass ordering, and the sizable correction to $\\delta$ prefers a negative sign. These deviations have definite directions and can be tested in the future neutrino oscillation experiments.
Book Reviews A Fearful Symmetry
Denardo, Dale
Conservation Soci- ety, and the Smithsonian's National Zoo, that wild tigers occupy 40% less habitat in 2006Book Reviews A Fearful Symmetry Tiger Bone & Rhino Horn: the Destruction of Wildlife for Tradi for understand- ing a new and rapidly unfolding effort to stem illegal wildlife trade. Accord- ing to the U
Basic logic: reflection, symmetry, visibility.
Sambin, Giovanni
Basic logic: reflection, symmetry, visibility. Giovanni Sambin - Giulia Battilotti - Claudia Faggian Abstract We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non
Symmetry within Solutions Marijn Heule
Kuzmanov, Georgi
need to take account of symmetry. For ex- ample, when finding magic squares (prob019 in CSPLib (Gent there exists such that (A) = B. Running example. The magic squares problem is to label a n by n square so magic square contains the integers 1 to n2 . We model this with n2 variables Xi,j where Xi,j = k iff
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical
Fundamental Symmetries and Conservation Laws
W. C. Haxton
2009-02-09
I discuss recent progress in low-energy tests of symmetries and conservation laws, including parity nonconservation in atoms and nuclei, electric dipole moment tests of time-reversal invariance, beta-decay correlation studies, and decays violating separate (family) and total lepton number.
Local symmetries and conservation laws
A. M. Vinogradov
1984-01-01
Starting with Lie's classical theory, we carefully explain the basic notions of the higher symmetries theory for arbitrary systems of partial differential equations as well as the necessary calculation procedures. Roughly speaking, we explain what analogs of higher KdV equations are for an arbitrary system of partial differential equations and also how one can find and use them. The cohomological
Unitary Symmetry and Leptonic Decays
Nicola Cabibbo
1963-01-01
An analysis of leptonic decays based on unitary symmetry for strong ; interactions (eightfold way) and the V-A theory for weak interactions is ; presented. An explanation for the observed predominance of the LAMBDA yields ; + e⁻ + nu decay over the LAMBDA ⁻ yields n + e⁻ + nu ; decay is obtained. Branching ratios predicted for electron
Symmetry and separation of variables
W Miller; W. Jr
1977-01-01
This book is concerned with the relation between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions by the separation of variables, and the properties of the special functions that arise in this manner. Some modern group-theoretic twists in the separation of variables method that can be used to
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest
Walsh, Toby
, red => green, .. E.g. AvB => AvC, CvD => BvD (Z[1],Z[2],..) => ((Z[1]),(Z[2]),..) #12;Symmetry propagator for this global constraint based on a ternary decomposition #12;Adding constraints Same method
Inflation, symmetry, and B-modes
Hertzberg, Mark Peter
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing ...
A Quantitative Evaluation of Symmetry Detection Algorithms
important cues for human and machine perception of the chaotic real world. For over three decades now, reflection and glide-reflection), the detection of bilateral reflection symmetry (mirror-symmetry) and its
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Tunneling through Quantum Dots with Discrete Symmetries
Yshai Avishai; Konstantin Kikoin
2008-01-01
We describe in this short review the influence of discrete symmetries in complex quantum dots on the Kondo co-tunneling through these nano-objects. These discrete symmetries stem from the geometrical structure of the tunneling devices (e.g spatial symmetry of multivalley quantum dot in a tunneling contact with leads). They affect the dynamical symmetry of spin multiplets characterizing the ground state and
Tunneling Through Quantum Dots with Discrete Symmetries
Yshai Avishai; Konstantin Kikoin
2009-01-01
We describe in this short review the influence of discrete symmetries in\\u000acomplex quantum dots on the Kondo co-tunneling through these nano-objects.\\u000aThese discrete symmetries stem from the geometrical structure of the tunneling\\u000adevices (e.g spatial symmetry of multivalley quantum dot in a tunneling contact\\u000awith leads). They affect the dynamical symmetry of spin multiplets\\u000acharacterizing the ground state and
Symmetry numbers and chemical reaction rates
Antonio Fernndez-Ramos; Benjamin A. Ellingson; Rubn Meana-Paeda; Jorge M. C. Marques; Donald G. Truhlar
2007-01-01
This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them\\u000a to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational\\u000a symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i)\\u000a if the reaction
Symmetry-Breaking Predicates for Search Problems
James M. Crawford; Matthew L. Ginsberg; Eugene M. Luks; Amitabha Roy
1996-01-01
Many reasoning and optimization problemsexhibit symmetries. Previous work hasshown how special purpose algorithms canmake use of these symmetries to simplifyreasoning. We present a general schemewhereby symmetries are exploited by adding"symmetry-breaking" predicates to the theory.Our approach can be used on any propositionalsatisfiability problem, and can beused as a pre-processor to any (systematicor non-systematic) reasoning method. In thegeneral case adding...
T-duality versus Gauge Symmetry
Olaf Hohm
2011-01-18
We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the theory, which can be viewed as an `O(D,D) covariantization' of the low-energy effective space-time action of closed string theory. We discuss its symmetries with a special emphasis on the relation between global duality symmetries and local gauge symmetries.
Quasicrystalline decagonal and related crystalline approximant structures
Daulton, T.L.
1992-01-01
The icosahedral phase is a condensed phase of matter that has a noncrystallographic point group with long range orientational and translational order but lacks strict periodicity. Periodicity is replaced in all dimensions by a mathematically well defined quasiperiodicity. Two and one dimensional quasicrystals also form in the same metallic-alloy systems as does the icosahedral quasicrystal. The decagonal phase is an example of a two-dimensional quasicrystal that occurs with dicrete one dimensional periodicites of approximately 4 [angstrom] x (1, 2, 3, and 4). The different periodicity decagonal phases are studied with an analytical transmission electron microscope (TEM), using high resolution electron microscopy (HREM), convergent beam electron diffraction (CBED), selected area diffraction (SAD), energy-dispersive x-ray spectroscopy (EDXS), and electron energy-loss spectroscopy (EELS). X-ray powder diffraction studies are also presented. Closely related crystalline structures that approximate well the noncrystallographic symmetries of quasicrystals, were also studied. These crystals also exhibit the same discrete periodicities present in the decagonal phases. The striking similarities between the different periodicity decagonal phases, the icosahedral phase, and the crystalline approximant structures suggest that they all contain similar fundamental atomic clusters. Further, the discrete decagonal periodicities observed suggest that the decagonal structures are formed by different stacking sequences of similar atomic clusters. An atomic model that is based on distorted icosahedrally symmetric clusters that are stacked with different interpenentration depths to form the different periodicity decagonal phases is presented.
From additional symmetries to linearization of Virasoro symmetries
NASA Astrophysics Data System (ADS)
Wu, Chao-Zhong
2013-04-01
We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. Considered as certain reductions of the two-component BKP hierarchy, the Drinfeld-Sokolov hierarchies of type D are proved to possess symmetries written as the linear action of a series of Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhangs hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.
From Additional Symmetries to Linearization of Virasoro Symmetries
Chao-Zhong Wu
2011-12-01
We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. We also show that the Drinfeld-Sokolov hierarchies of type D, which are reduced from the two-component BKP hierarchy, possess symmetries written as the action of a series of linear Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhang's hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.
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.
Symmetry in Chinese Arts Yip Lixia, Sabrina
Aslaksen, Helmer
Symmetry in Chinese Arts Done by: Group 3 Lim Li Yan Yip Lixia, Sabrina Lee Weitian, Ivan Zhong Shengmin Goh Yoon Keong 1 #12;2 CONTENTS · Introduction · Symmetry in Chinese Literature · Chinese Paper Cuttings · Symmetry in Chinese buildings · Chinese Music · Conclusion · Bibliography #12;3 Introduction
Symmetry-Breaking Constraints for Matrix Models
Flener, Pierre
Symmetry-Breaking Constraints for Matrix Models Zeynep Kiziltan1 and Barbara M. Smith2 1 Department their rows and/or columns. Eliminating all such symmetry can be very costly as there are in general exponentially many symme- tries. Cost-effective methods have been proposed to break much of the symmetry
Symmetry violation in nuclei Vladimir Gudkov1
Symmetry violation in nuclei Vladimir Gudkov1 1 Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208 The study of symmetry violation in nuclei, including parity (PV of the fundamental symmetries tests and a search for new physics is underlined in the third recommendation
Symmetry examples in open quantum dynamics
Thomas F. Jordan; San Ha Seo
2014-08-19
Dependent symmetries, a new kind of symmetry of the open quantum dynamics of a subsystem, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. Each symmetry implies a particular form for the results of the open dynamics. The forms exhibit the symmetries very simply. It is shown directly, without assuming anything about the symmetry, that the dynamics produces the form, but knowing the symmetry and the form it implies can reduce what needs to be done to work out the dynamics; pieces can be deduced from the symmetry rather that calculated from the dynamics. Symmetries can be related to constants of the motion in new ways. A quantity might be a dependent constant of the motion, constant only for particular situations of the subsystem in the larger system. In particular, a generator of dependent symmetries could represent a quantity that is a dependent constant of the motion for the same situations as for the symmetries. The examples present a variety of possibilities. Sometimes a generator of dependent symmetries does represent a dependent constant of the motion. Sometimes it does not. Sometimes no quantity is a dependent constant of the motion. Sometimes every quantity is.
Conditional Symmetry Breaking Ian P. Gent1
Miguel, Ian
Conditional Symmetry Breaking Ian P. Gent1 , Tom Kelsey1 , Steve A. Linton1 , Iain McDonald1 , Ian,tom,sal,iain,ianm}@dcs.st-and.ac.uk, bms@4c.ucc.ie Abstract. We introduce the study of Conditional symmetry breaking in constraint-problem satisfies some condition under which additional symetries hold. Conditional symmetry can cause redun- dancy
The Symmetry Detection Mechanisms are Color Selective
Chen, Chein Chung
The Symmetry Detection Mechanisms are Color Selective Chia-Ching Wu1 & Chien-Chung Chen2 1 of the symmetry detection mechanism. In each trial, a vertical symmetric target was randomly presented in one increased. This suggests that the symmetry detection mechanisms are color selective and only extract local
Horizontal Symmetry from the Bottom Up
C. S. Lam
2010-03-02
A general method to derive horizontal symmetry from a mixing matrix is reviewed. The technique has been applied to deduce leptonic symmetry from the tri-bimaximal neutrino mixing matrix and three of its variations. The question of how the quark mixing can be accommodated within the leptonic symmetry group is discussed, including in this connection an example based on the group $D_4$.
Detecting Symmetry and Symmetric Constellations of Features
Gareth Loyand; Jan-olof Eklundh
2006-01-01
A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and evaluated, and how these can be grouped into symmetric constellations that specify the domi-
Popovych, Roman
Symmetry in Nonlinear Mathematical Physics 1997, V.1, 8997. Lie Symmetries and Preliminary) of the form u (k) n (t) = Fn(t, un+a, . . . , un+b) with k 2 are studied for Lie symmetries and preliminary classification. Explicit forms of equations are given for those admitting at least one intrinsic Lie symmetry
Symmetry in Nonlinear Mathematical Physics 1997, V.2, 321327. Higher Symmetries of the Wave Equation
Nikitin, Anatoly
Symmetry in Nonlinear Mathematical Physics 1997, V.2, 321327. Higher Symmetries of the Wave@apmat.freenet.kiev.ua Abstract Higher order symmetry operators for the wave equation with scalar and vector po- tentials are investigated. All scalar potentials which admit second order symmetry operators are found explicitly
Instantaneous Symmetry and Symmetry on Average in the CouetteTaylor and Faraday
Instantaneous Symmetry and Symmetry on Average in the CouetteTaylor and Faraday Experiments November 16, 1993 Abstract We describe some recent results on symmetry of attractors for dy namical systems with symmetry and consider the implications for the CouetteTaylor experiment and the Faraday
ess5011 Robert J. Serfling MULTIVARIATE SYMMETRY AND
Serfling, Robert
a delightful and wide-ranging treatment of "symmetry," from bilateral symmetry in Greek sculpture to Kant: 62G99 CONCEPTS OF SYMMETRY The idea of "symmetry" has served from ancient times as a conceptual
Measuring complexity through average symmetry
NASA Astrophysics Data System (ADS)
Alamino, Roberto C.
2015-07-01
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principlemeasuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures
Neutrino mixing and discrete symmetries
NASA Astrophysics Data System (ADS)
Hu, Bo
2013-02-01
In this paper we discuss a new way to derive neutrino mixing patterns, which originates from the idea proposed in a recent article by Hernandez and Smirnov. Its applications to various cases are discussed. We first present the complete set of possible mixing patterns for the minimal case where unbroken residual symmetries of the Majorana neutrino and left-handed charged-lepton mass matrices obey some general assumptions that are also satisfied by many models based on discrete symmetries. We find that they are either well-known mixing patterns or phenomenologically disfavored ones. It shows clearly that, for full-mixing matrices to fit the mixing data with small or negligible corrections, it is necessary to go beyond the minimal scenario. We present an explicit formalism for a rather general nonminimal case. Some applications and phenomenological implications are discussed. Several new mixing patterns are derived.
Symmetry restoration and quantumness reestablishment
Guo-Mo Zeng; Lian-Ao Wu; Hai-Jun Xing
2014-09-18
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.
Space symmetries draw elasticity theory
Chaouqi Misbah; Sofia Biagi; Paolo Politi
2013-04-08
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions are of short range and are therefore localized at the boundary); (ii) the stress tensor must be symmetric in order to prevent spontaneous rotation of the material points. These two requirements are presented to be necessary in classical textbooks on elasticity theory. By using only basic spatial symmetries it is shown that elastodynamics equations can be derived, for high symmetry crystals (the typical case considered in most textbooks), without evoking any of the two above physical principles.
Investigating Patterns: Symmetry and Tessellations
NSDL National Science Digital Library
This website provides 30 suggested activities in Symmetry and Tessellations using resources available across the World Wide Web. The author, Jill Britton, has complied this collection of links to coordinate with the chapters and activities from her publication, "Investigating Patterns: Symmetry and Tessellations" (Grades 5-8). The activities begin with "What is Mathematics?" and move on to cover topics such as Pythagoras´ observations of music, patterns on Ukrainian Easter eggs, and tessellating art. She provides a short comment on each of the websites and the links are arranged by activity topic. Links at the bottom of the website will take visitors to other collections of links relating to more pattern-related activities.
Dark energy from conformal symmetry breaking
F. Darabi
2013-06-18
The breakdown of conformal symmetry in a conformally invariant scalar-tensor gravitational model is revisited in the cosmological context. Although the old scenario of conformal symmetry breaking in cosmology containing scalar field has already been used in many earlier works, it seems that no special attention has been paid for the investigation on the possible connection between the breakdown of conformal symmetry and the existence of dark energy. In this paper, it is shown that the old scenario of conformal symmetry breaking in cosmology, if properly interpreted, not only has a potential ability to describe the origin of dark energy as a symmetry breaking effect, but also may resolve the coincidence problem.
General-Purpose Icosahedral Structure
NASA Technical Reports Server (NTRS)
Evans, J.
1984-01-01
Scheme based on geodesic sphere approximated by regular icosahedron. Structure rigid and lightweight. Allows access to all subsystems and equipment from outside. Regular icosahedron constructed from triangular panels. Five panels meeting at each corner all rigidly attached to fivesided adapter. Strengthened version useful on Earth for rapidly-erectable temporary shelters, industrial structures, or playground equipment.
Asymptotic symmetries in general relativity
NASA Astrophysics Data System (ADS)
Hogan, P. A.
1985-11-01
In the context of a recent reformulation of the theory of gravitational radiation from bounded sources in which both shearing and shear-free radiation is manifestly present, we derive the asymptotic symmetry group of the spacetime. The group we obtain contains the Bondi-Metzner-Sachs group as a subgroup. This observation is relevant to the problem of the mysterious role of shear-free radiation in the Bondi-Sachs approach to the theory of gravitational radiation from bounded sources.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Ba, Lucia; Bucataru, Ioan; Len, Manuel de; Salgado, Modesto; Vilario, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1? of a fiber bundle ? : E ? ?k where ?k is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Quantum restoration of broken symmetries
V. V. Belokurov; E. T. Shavgulidze
2013-03-14
A certain non-linear non-local substitution is shown to transform the action of the self-interacting quantum field to the free one. The functional integrals in both theories are equal to each other. However, the integrations are performed over different functional spaces. The classical action and the classical limit of the corresponding quantum theory turn out to be different. And the symmetry originally broken in the classical theory is restored in the classical limit of the quantum theory.
Gauge Symmetry and Neural Networks
Tetsuo Matsui
2001-12-26
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and resembles lattice gauge theory of high-energy physics. Time dependence of synapses describes the process of learning. The mean field theory predicts a new phase corresponding to confinement phase, in which brain loses ablility of learning and memory.
Algorithmic symmetry classification with invariance
Ian Lisle; S.-L. Tracy Huang
2010-01-01
Symmetry classification for a system of differential equations can be achieved algorithmically by applying a differential\\u000a reduction and completion algorithm to the infinitesimal determining equations of the system. The branches of the classification\\u000a should be invariant under the action of the equivalence group. We show that such invariance can be tested algorithmically\\u000a knowing only the determining equations of the equivalence
Clifford modules and symmetries of topological insulators
Gilles Abramovici; Pavel Kalugin
2011-05-17
We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of {\\em real} irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland-Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetries.
Symmetry measures of the electron density.
Casanova, David; Alemany, Pere; Alvarez, Santiago
2010-10-01
In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983
NASA Astrophysics Data System (ADS)
Leblanc, M.; Le Bail, A.; Audier, M.
1991-09-01
The structure of the tetragonal ?-Al 56(Cu, Zn) 11 Li 33 phase, expected as being related to the icosahedral T2-AL 6CuLi 3 quasicrystal and other periodic intermetallic Al-Li-(Cu-Zn-Mg) phases, has been determined by single crystal X-ray diffraction (P4 2/mmc, a = 14.05(3) , c = 83.14(6) , V = 16409(82) 3, Dx = 2.283, Dexp = 2.33, MoK?, ? = 0.71069 , ? = 3.4 mm -1, F(000) = 10606, R = 0.067, 1348 reflections). From the present crystallographic data, a structural description of the ? phase is made in terms of different arrangements of Friauf polyhedra, which form either partial or entire Samson polyhedra. These last are directly related to the Samson polyhedron defined in the BCC structure of R - Al 5CuLi 3.
Sato, K.; Kobayashi, Y.; Arinuma, K.; Kanazawa, I.; Tamura, R.; Shibuya, T.; Takeuchi, S. [National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565 (Japan); Department of Physics, Tokyo Gakugei University, 4-1-1 Koganei, Tokyo 184-8501 (Japan); Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8501 (Japan)
2004-09-01
Previously, we showed that the icosahedral quasicrystal Cd{sub 5.7}Yb possesses similar structural vacancies to those in its cubic 1/1-approximant Cd{sub 6}Yb by positron lifetime measurements [K. Sato, H. Uchiyama, K. Arinuma, I. Kanazawa, R. Tamura, T. Shibuya, and S. Takeuchi, Phys. Rev. B 66, 052201 (2002)]. In the present paper, the local chemical environment around the structural vacancies is specifically investigated by two-detector coincident Doppler broadening spectroscopy. Essentially the same annihilation sites with Cd-rich chemical environments are identified for the two phases. This strongly suggests that the quasicrystal is composed of the same cluster as the approximant. The difference in the structural vacancy density between the two phases is examined by positron diffusion experiments using a slow positron beam. The structural vacancy density in the quasicrystal is found to be 20% lower than that in the approximant.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the IsingIsing phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
NASA Astrophysics Data System (ADS)
He, Han-Xin
2009-08-01
The transverse symmetry transformations associated with the normal symmetry transformations are proposed to build the transverse constraints on the basic vertices in gauge theories. I show that, while the BRST symmetry in non-Abelian gauge theory QCD (Quantum Chromodynamics) leads to the Slavnov-Taylor identity for the quark-gluon vertex which constrains the longitudinal part of the vertex, the transverse symmetry transformation associated with the BRST symmetry enables to derive the transverse Slavnov-Taylor identity for the quark-gluon vertex, which constrains the transverse part of the quark-gluon vertex from the gauge symmetry of QCD.
Screw symmetry in columnar crystals
A. Mughal
2013-06-12
We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range 1 <= D/d <= 2.715 and also briefly discuss their helicity.
Pseudospin symmetry in nuclear physics
C. Bahri; J. P. Draayer; S. A. Moszkowski
1992-01-01
The origin and consequences of pseudospin symmetry in nuclear physics, which is exact for an oscillator potential with one-body orbit-orbit (ν{sub {ital l}{ital l}}) and spin-orbit (ν{sub {ital l}{ital s}}) interaction strengths in the ratio μ{ital ieq}2ν{sub {ital l}{ital l}}\\/ν{sub {ital l}{ital s}}=0.5, are considered. Specifically, the ν{sub {ital l}{ital s}}4ν{sub {ital l}{ital l}} condition is consistent with relativistic mean-field
Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
2011-01-01
Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry. PMID:21958045
Symmetry and Dirac points in graphene spectrum
Gregory Berkolaiko; Andrew Comech
2015-04-23
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by $2\\pi/3$ and inversion, rotation by $2\\pi/3$ and horizontal reflection, inversion or reflection with weakly broken rotation symmetry, and the case where no Dirac points arise: rotation by $2\\pi/3$ and vertical reflection. All proofs are based on symmetry considerations and are elementary in nature. In particular, existence of degeneracies in the spectrum is proved by a transplantation argument (which is deduced from the (co)representation of the relevant symmetry group). The conical shape of the dispersion relation is obtained from its invariance under rotation by $2\\pi/3$. Persistence of conical points when the rotation symmetry is weakly broken is proved using a geometric phase in one case and parity of the eigenfunctions in the other.
Symmetry Energy of Dilute Warm Nuclear Matter
Natowitz, J. B.; Hagel, K.; Kowalski, S.; Qin, L.; Shlomo, S.; Wada, R. [Cyclotron Institute, Texas A and M University, College Station, Texas 77843-3366 (United States); Roepke, G. [Institut fuer Physik, Universitaet Rostock, Universitaetsplatz 3, D-18055 Rostock (Germany); Typel, S. [Excellence Cluster Universe, Technische Universitaet Muenchen, Boltzmannstrasse 2, D-85748 Garching (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung GmbH, Theorie, Planckstrasse 1, D-64291 Darmstadt (Germany); Blaschke, D. [Instytut Fizyki Teoretycznej, Uniwersytet Wroclawski, plac Maksa Borna 9, 50-204 Wroclaw (Poland); Bogoliubov Laboratory for Theoretical Physics, JINR Dubna, Joliot-Curie street 6, 141980 Dubna (Russian Federation); Bonasera, A. [Cyclotron Institute, Texas A and M University, College Station, Texas 77843-3366 (United States); Laboratori Nazionali del Sud-INFN, via Santa Sofia 64, 95123 Catania (Italy); Klaehn, T. [Instytut Fizyki Teoretycznej, Uniwersytet Wroclawski, plac Maksa Borna 9, 50-204 Wroclaw (Poland); Theory Group, Physics Division, Building 203, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439 (United States); Wolter, H. H. [Fakultaet fuer Physik, Universitaet Muenchen, Am Coulombwall 1, D-85748 Garching (Germany)
2010-05-21
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.
Symmetry energy of dilute warm nuclear matter.
Natowitz, J B; Rpke, G; Typel, S; Blaschke, D; Bonasera, A; Hagel, K; Klhn, T; Kowalski, S; Qin, L; Shlomo, S; Wada, R; Wolter, H H
2010-05-21
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density. PMID:20867023
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Symmetry energy of dilute warm nuclear matter
J. B. Natowitz; G. Ropke; S. Typel; D. Blaschke; A. Bonasera; K. Hagel; T. Klahn; S. Kowalski; L. Qin; S. Shlomo; R. Wada; H. H. Wolter
2010-02-25
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular by the appearance of bound states. A recently developed quantum statistical (QS) approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.
Superconductivity in crystals without symmetry centers
L. N. Bulaevskii; A. A. Guseinov; A. I. Rusinov
1976-01-01
We consider the effect of spin-orbit interaction on the paramagnetic properties of superconducting crystals having a lattice without symmetry center. Systems of this type include superconducting metals with polar-symmetry lattice VHf and VRu. Arguments are advanced favoring the assumption that there may be no symmetry center in a lattice of layered dichalcogenide metals with incommensurate charge-density wave or of intercalated
QCD, Symmetry Breaking and the Random Lattice
Saul D. Cohen
2006-02-15
According to the Nielsen-Ninomiya No-Go theorem, the doubling of fermions on the lattice cannot be suppressed in a chiral theory. Whereas Wilson and staggered fermions suppress doublers with explicit breaking of chiral symmetry, the random lattice does so by spontaneous chiral symmetry breaking even in the free theory. I present results for meson masses, the chiral condensate and fermionic eigenvalues from simulations of quenched QCD on random lattices in four dimensions, focusing on chiral symmetry breaking.
Rosenthal, Peter B.
2015-01-01
Elucidation of the structure of biological macromolecules and larger assemblies has been essential to understanding the roles they play in living processes. Methods for three-dimensional structure determination of biological assemblies from images recorded in the electron microscope were therefore a key development. In his paper published in Philosophical Transactions B in 1971, Crowther described new computational procedures applied to the first three-dimensional reconstruction of an icosahedral virus from images of virus particles preserved in negative stain. The method for determining the relative orientation of randomly oriented particles and combining their images for reconstruction exploited the high symmetry of the virus particle. Computational methods for image analysis have since been extended to include biological assemblies without symmetry. Further experimental advances, combined with image analysis, have led to the method of cryomicroscopy, which is now used by structural biologists to study the structure and dynamics of biological machines and assemblies in atomic detail. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750240
Radiation Symmetry of NIF Hohlraums
NASA Astrophysics Data System (ADS)
Jones, O. S.; Suter, L. J.; Pollaine, S. M.; Haan, S. W.
1997-11-01
We have used the three-dimensional, view-factor radiation transport code, Gertie (G. Zimmerman, D. Munroe, R. Kirkpatrick, and D. Bailey.), to analyze the symmetry of indirect drive ignition experiments on the National Ignition Facility (NIF). These calculations directly consider vacuum radiation only. Plasma effects enter indirectly through specification of the time-dependent albedos and effective dimensions of the hohlraum and capsule. These specifications come from seperate simulations with the radiation hydrodynamics code Lasnex. First, we examine the intrinsic azimuthal asymmetry of NIF's full 192 beam configuration using highly refined grids. Next, we quantify the sensitivity of the overall symmetry to systematic effects such as laser power imbalance and beam pointing errors. The power balance analysis includes the effects of correlations due to shared amplifiers among pairs of beam quads. Finally, we estimate the degree of radiation asymmetries that may exist during the NIF activation phase. The NIF activation plan (M. Lane, B. Van Wontergrun, LLNL, private communication, 1997.) will allow target physics experiments as banks of beams come online. This set of calculations provides an idea of the degree of asymmetry that will exist during various phases of NIF activation, and thus allows us to assess how we might best use these early experiments.