Evidence from electron micrographs that icosahedral quasicrystals are icosahedral twins of cubic crystals.

PubMed

Pauling, L

1990-10-01

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.

Molecular symmetry with quaternions.

PubMed

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.

3-dimensional indexation of the icosahedral diffraction pattern using the techniques of electron microscopy

NASA Astrophysics Data System (ADS)

Bourdillon, Antony

2012-11-01

The following facts about icosahedra need wider attention. 1) The golden section τ is as fundamental to the icosahedral structure (length /edge) as π is to the sphere (circumference /diameter). 2) The diffraction series are in restricted Fibonacci order because the ratio of adjacent terms fn/fn-1 does not vary, but is the constant τ. The series is therefore geometric. 3) Because of the tetragonal subgroup in the icosahedral point group symmetry, many axes in the icosahedral structure have identical orientation to axes in the face centered cubic matrix of Al6Mn [1] (e.g. [100] and [111]). On these bases, a three dimensional stereographic projection will be presented. 4) A quasi-Bragg law is derived that correctly represents the diffraction series in powers of τ [2]. Furthermore, by employing the normal conventions of electron microscopy, all diffraction patterns are completely indexed in three dimensions. These are the topic of this presentation. Significant consequences will be presented elsewhere: 1) The diffraction pattern intensities near all main axes are correctly simulated, and all atoms are located on a specimen image. 2) The quasi-Bragg law has a special metric. Atomic locations are consistently calculated for the first time. 3) Whereas the Bragg law transforms a crystal lattice in real space into a reciprocal lattice in diffraction space, the quasi-Bragg law transforms a geometric diffraction pattern into a hierarchic structure. 4) Hyperspatial indexation [3] is superceded. [1] Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 1984, 53, 1951-3. [2] Bourdillon, A. J., Nearly free electron band structures in a logarithmically periodic solid, Sol. State Comm. 2009, 149, 1221-1225. [3] Duneau, M., and Katz, A., Phys Rev Lett 54, 2688-2691

Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections

ERIC Educational Resources Information Center

Chen, Lan; Sun, Hongwei; Lai, Chengming

2015-01-01

There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…

Pseudo-icosahedral Cr 55 Al 232 - δ as a high-temperature protective material

DOE PAGES

Rosa, R.; Bhattacharya, S.; Pabla, J.; ...

2018-03-19

In this paper, we report here a course of basic research into the potential suitability of a pseudo-icosahedral Cr aluminide as a material for high temperature protective coatings. Cr 55Al 232-δ [δ = 2.70(6)] exhibits high hardness at room temperature as well as low thermal conductivity and excellent oxidation resistance at 973 K, with an oxidation rate comparable to those of softer, denser benchmark materials. Lastly, the origin of these promising properties can be traced to competing long-range and short-range symmetries within the pseudo-icosahedral crystal structure, suggesting new criteria for future materials research.

Pseudo-icosahedral Cr55Al232 -δ as a high-temperature protective material

NASA Astrophysics Data System (ADS)

Rosa, R.; Bhattacharya, S.; Pabla, J.; He, H.; Misuraca, J.; Nakajima, Y.; Bender, A. D.; Antonacci, A. K.; Adrip, W.; McNally, D. E.; Zebro, A.; Kamenov, P.; Geschwind, G.; Ghose, S.; Dooryhee, E.; Ibrahim, A.; Tritt, T. M.; Aronson, M. C.; Simonson, J. W.

2018-03-01

We report here a course of basic research into the potential suitability of a pseudo-icosahedral Cr aluminide as a material for high-temperature protective coatings. Cr55Al232 -δ [ δ =2.70 (6 ) ] exhibits high hardness at room temperature as well as low thermal conductivity and excellent oxidation resistance at 973 K, with an oxidation rate comparable to those of softer, denser benchmark materials. The origin of these promising properties can be traced to competing long-range and short-range symmetries within the pseudo-icosahedral crystal structure, suggesting new criteria for future materials research.

Pseudo-icosahedral Cr 55 Al 232 - δ as a high-temperature protective material

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosa, R.; Bhattacharya, S.; Pabla, J.

In this paper, we report here a course of basic research into the potential suitability of a pseudo-icosahedral Cr aluminide as a material for high temperature protective coatings. Cr 55Al 232-δ [δ = 2.70(6)] exhibits high hardness at room temperature as well as low thermal conductivity and excellent oxidation resistance at 973 K, with an oxidation rate comparable to those of softer, denser benchmark materials. Lastly, the origin of these promising properties can be traced to competing long-range and short-range symmetries within the pseudo-icosahedral crystal structure, suggesting new criteria for future materials research.

Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory.

PubMed

Bindi, Luca; Lin, Chaney; Ma, Chi; Steinhardt, Paul J

2016-12-08

We report the first occurrence of an icosahedral quasicrystal with composition Al 62.0(8) Cu 31.2(8) Fe 6.8(4) , outside the measured equilibrium stability field at standard pressure of the previously reported Al-Cu-Fe quasicrystal (Al x Cu y Fe z , with x between 61 and 64, y between 24 and 26, z between 12 and 13%). The new icosahedral mineral formed naturally and was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite that experienced shock metamorphism, local melting (with conditions exceeding 5 GPa and 1,200 °C in some locations), and rapid cooling, all of which likely resulted from impact-induced shock in space. This is the first example of a quasicrystal composition discovered in nature prior to being synthesized in the laboratory. The new composition was found in a grain that has a separate metal assemblage containing icosahedrite (Al 63 Cu 24 Fe 13 ), currently the only other known naturally occurring mineral with icosahedral symmetry (though the latter composition had already been observed in the laboratory prior to its discovery in nature). The chemistry of both the icosahedral phases was characterized by electron microprobe, and the rotational symmetry was confirmed by means of electron backscatter diffraction.

Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory

PubMed Central

Bindi, Luca; Lin, Chaney; Ma, Chi; Steinhardt, Paul J.

2016-01-01

We report the first occurrence of an icosahedral quasicrystal with composition Al62.0(8)Cu31.2(8)Fe6.8(4), outside the measured equilibrium stability field at standard pressure of the previously reported Al-Cu-Fe quasicrystal (AlxCuyFez, with x between 61 and 64, y between 24 and 26, z between 12 and 13%). The new icosahedral mineral formed naturally and was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite that experienced shock metamorphism, local melting (with conditions exceeding 5 GPa and 1,200 °C in some locations), and rapid cooling, all of which likely resulted from impact-induced shock in space. This is the first example of a quasicrystal composition discovered in nature prior to being synthesized in the laboratory. The new composition was found in a grain that has a separate metal assemblage containing icosahedrite (Al63Cu24Fe13), currently the only other known naturally occurring mineral with icosahedral symmetry (though the latter composition had already been observed in the laboratory prior to its discovery in nature). The chemistry of both the icosahedral phases was characterized by electron microprobe, and the rotational symmetry was confirmed by means of electron backscatter diffraction. PMID:27929519

Icosahedral plant viral nanoparticles - bioinspired synthesis of nanomaterials/nanostructures.

PubMed

Narayanan, Kannan Badri; Han, Sung Soo

2017-10-01

Viral nanotechnology utilizes virus nanoparticles (VNPs) and virus-like nanoparticles (VLPs) of plant viruses as highly versatile platforms for materials synthesis and molecular entrapment that can be used in the nanotechnological fields, such as in next-generation nanoelectronics, nanocatalysis, biosensing and optics, and biomedical applications, such as for targeting, therapeutic delivery, and non-invasive in vivo imaging with high specificity and selectivity. In particular, plant virus capsids provide biotemplates for the production of novel nanostructured materials with organic/inorganic moieties incorporated in a very precise and controlled manner. Interestingly, capsid proteins of spherical plant viruses can self-assemble into well-organized icosahedral three-dimensional (3D) nanoscale multivalent architectures with high monodispersity and structural symmetry. Using viral genetic and protein engineering of icosahedral viruses with a variety of sizes, the interior, exterior and the interfaces between coat protein (CP) subunits can be manipulated to fabricate materials with a wide range of desirable properties allowing for biomineralization, encapsulation, infusion, controlled self-assembly, and multivalent ligand display of nanoparticles or molecules for varied applications. In this review, we discuss the various functional nanomaterials/nanostructures developed using the VNPs and VLPs of different icosahedral plant viruses and their nano(bio)technological and nanomedical applications. Copyright © 2017 Elsevier B.V. All rights reserved.

Raman effect in icosahedral boron-rich solids

PubMed Central

Werheit, Helmut; Filipov, Volodymyr; Kuhlmann, Udo; Schwarz, Ulrich; Armbrüster, Marc; Leithe-Jasper, Andreas; Tanaka, Takaho; Higashi, Iwami; Lundström, Torsten; Gurin, Vladimir N; Korsukova, Maria M

2010-01-01

We present Raman spectra of numerous icosahedral boron-rich solids having the structure of α-rhombohedral, β-rhombohedral, α-tetragonal, β-tetragonal, YB66, orthorhombic or amorphous boron. The spectra were newly measured and, in some cases, compared with reported data and discussed. We emphasize the importance of a high signal-to-noise ratio in the Raman spectra for detecting weak effects evoked by the modification of compounds, accommodation of interstitial atoms and other structural defects. Vibrations of the icosahedra, occurring in all the spectra, are interpreted using the description of modes in α-rhombohedral boron by Beckel et al. The Raman spectrum of boron carbide is largely clarified. Relative intra- and inter-icosahedral bonding forces are estimated for the different structural groups and for vanadium-doped β-rhombohedral boron. The validity of Badger's rule is demonstrated for the force constants of inter-icosahedral B–B bonds, whereas the agreement is less satisfactory for the intra-icosahedral B–B bonds. PMID:27877328

Deconfined Quantum Critical Points: Symmetries and Dualities

DOE PAGES

Wang, Chong; Nahum, Adam; Metlitski, Max A.; ...

2017-09-22

The deconfined quantum critical point (QCP), separating the Néel and valence bond solid phases in a 2D antiferromagnet, was proposed as an example of (2+1)D criticality fundamentally different from standard Landau-Ginzburg-Wilson-Fisher criticality. In this work, we present multiple equivalent descriptions of deconfined QCPs, and use these to address the possibility of enlarged emergent symmetries in the low-energy limit. The easy-plane deconfined QCP, besides its previously discussed self-duality, is dual to N f=2 fermionic quantum electrodynamics, which has its own self-duality and hence may have an O(4)×ZT2 symmetry. We propose several dualities for the deconfined QCP with SU(2) spin symmetry whichmore » together make natural the emergence of a previously suggested SO(5) symmetry rotating the Néel and valence bond solid orders. These emergent symmetries are implemented anomalously. The associated infrared theories can also be viewed as surface descriptions of (3+1) D topological paramagnets, giving further insight into the dualities. We describe a number of numerical tests of these dualities. We also discuss the possibility of “pseudocritical” behavior for deconfined critical points, and the meaning of the dualities and emergent symmetries in such a scenario.« less

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Quantum transport through single and multilayer icosahedral fullerenes

NASA Astrophysics Data System (ADS)

Lovey, Daniel A.; Romero, Rodolfo H.

2013-10-01

We use a tight-binding Hamiltonian and Green functions methods to calculate the quantum transmission through single-wall fullerenes and bilayered and trilayered onions of icosahedral symmetry attached to metallic leads. The electronic structure of the onion-like fullerenes takes into account the curvature and finite size of the fullerenes layers as well as the strength of the intershell interactions depending on to the number of interacting atom pairs belonging to adjacent shells. Misalignment of the symmetry axes of the concentric iscosahedral shells produces breaking of the level degeneracies of the individual shells, giving rise some narrow quasi-continuum bands instead of the localized discrete peaks of the individual fullerenes. As a result, the transmission function for non symmetrical onions is rapidly varying functions of the Fermi energy. Furthermore, we found that most of the features of the transmission through the onions are due to the electronic structure of the outer shell with additional Fano-like antiresonances arising from coupling with or between the inner shells.

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

NASA Astrophysics Data System (ADS)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

The Emergence of Dirac points in Photonic Crystals with Mirror Symmetry

PubMed Central

He, Wen-Yu; Chan, C. T.

2015-01-01

We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states. PMID:25640993

Curating viscoelastic properties of icosahedral viruses, virus-based nanomaterials, and protein cages.

PubMed

Kant, Ravi; Rayaprolu, Vamseedhar; McDonald, Kaitlyn; Bothner, Brian

2018-06-01

The beauty, symmetry, and functionality of icosahedral virus capsids has attracted the attention of biologists, physicists, and mathematicians ever since they were first observed. Viruses and protein cages assemble into functional architectures in a range of sizes, shapes, and symmetries. To fulfill their biological roles, these structures must self-assemble, resist stress, and are often dynamic. The increasing use of icosahedral capsids and cages in materials science has driven the need to quantify them in terms of structural properties such as rigidity, stiffness, and viscoelasticity. In this study, we employed Quartz Crystal Microbalance with Dissipation technology (QCM-D) to characterize and compare the mechanical rigidity of different protein cages and viruses. We attempted to unveil the relationships between rigidity, radius, shell thickness, and triangulation number. We show that the rigidity and triangulation numbers are inversely related to each other and the comparison of rigidity and radius also follows the same trend. Our results suggest that subunit orientation, protein-protein interactions, and protein-nucleic acid interactions are important for the resistance to deformation of these complexes, however, the relationships are complex and need to be explored further. The QCM-D based viscoelastic measurements presented here help us elucidate these relationships and show the future prospect of this technique in the field of physical virology and nano-biotechnology.

Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.

Analysis of phases in the structure determination of an icosahedral virus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plevka, Pavel; Kaufmann, Bärbel; Rossmann, Michael G.

2012-03-15

The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to themore » 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.« less

Analysis of phases in the structure determination of an icosahedral virus

PubMed Central

Plevka, Pavel; Kaufmann, Bärbel; 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 π. 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

Modified Stereographic Projections of Point Groups and Diagrams of Their Irreducible Representations

NASA Astrophysics Data System (ADS)

Kettle, Sidney F. A.

1999-05-01

Modified versions of the stereographic projections of the point groups of classical crystallography are presented. They show the consequences of symmetry operations rather than emphasizing the existence of symmetry elements. These projections may be used to give pictures of the irreducible representations of point groups and several examples are given. Such pictures add physical reality to the irreducible representations and facilitate simple lecture demonstration of many important aspects and applications of group theory in chemistry.

Forging Unsupported Metal-Boryl Bonds with Icosahedral Carboranes.

PubMed

Saleh, Liban M A; Dziedzic, Rafal M; Khan, Saeed I; Spokoyny, Alexander M

2016-06-13

In contrast to the plethora of metal-catalyzed cross-coupling methods available for the installation of functional groups on aromatic hydrocarbons, a comparable variety of methods are currently not available for icosahedral carboranes, which are boron-rich three-dimensional aromatic analogues of aryl groups. Part of this is due to the limited understanding of the elementary steps for cross-coupling involving carboranes. Here, we report our efforts in isolating metal-boryl complexes to further our understanding of one of these elementary steps, oxidative addition. Structurally characterized examples of group 10 M-B bonds featuring icosahedral carboranes are completely unknown. Use of mercurocarboranes as a reagent to deliver M-B bonds saw divergent reactivity for platinum and palladium, with a Pt-B bond being isolated for the former, and a rare Pd-Hg bond being formed for the latter. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Au13(8e): A secondary block for describing a special group of liganded gold clusters containing icosahedral Au13 motifs

NASA Astrophysics Data System (ADS)

Xu, Wen Wu; Zeng, Xiao Cheng; Gao, Yi

2017-05-01

A grand unified model (GUM) has been proposed recently to understand structure anatomy and evolution of liganded gold clusters. In this work, besides the two types of elementary blocks (triangular Au3(2e) and tetrahedral Au4(2e)), we introduce a secondary block, namely, the icosahedral Au13 with 8e valence electrons, noted as Au13(8e). Using this secondary block, structural anatomy and evolution of a special group of liganded gold nanoclusters containing icosahedral Au13 motifs can be conveniently analyzed. In addition, a new ligand-protected cluster Au49(PR3)10(SR)15Cl2 is predicted to exhibit high chemical and thermal stability, suggesting likelihood of its synthesis in the laboratory.

Analysis of phases in the structure determination of an icosahedral virus.

PubMed

Plevka, Pavel; Kaufmann, Bärbel; Rossmann, Michael G

2011-06-01

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 π. 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. © 2011 International Union of Crystallography

Icosahedral quasicrystals of intermetallic compounds are icosahedral twins of cubic crystals of three kinds, consisting of large (about 5000 atoms) icosahedral complexes in either a cubic body-centered or a cubic face-centered arrangement or smaller (about 1350 atoms) icosahedral complexes in the β-tungsten arrangement

PubMed Central

Pauling, Linus

1989-01-01

The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals. The first kind, represented by Al13Cu4Fe3, contains two very large icosahedral complexes, each of about 4680 atoms, in the body-centered arrangement, with six smaller icosahedral complexes (104 atoms each) in the principal interstices. The second kind, represented by Al5Mn, contains four of the very large complexes in the face-centered arrangement (cubic close packing), with four of the smaller clusters in the interstices. The third kind, represented by Al6CuLi3, contains eight icosahedral complexes, each of about 1350 atoms, in the β-W arrangement. The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified. Images PMID:16594078

Structure of Lie point and variational symmetry algebras for a class of odes

NASA Astrophysics Data System (ADS)

Ndogmo, J. C.

2018-04-01

It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced by a point transformation to the trivial equation y(n)=0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the maximal dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.

Bell Inequalities and Group Symmetry

NASA Astrophysics Data System (ADS)

Bolonek-Lasoń, Katarzyna

2017-12-01

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.

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

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

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

Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Klink, William H.; Schweiger, Wolfgang

2018-03-01

This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

SASS: A symmetry adapted stochastic search algorithm exploiting site symmetry

NASA Astrophysics Data System (ADS)

Wheeler, Steven E.; Schleyer, Paul v. R.; Schaefer, Henry F.

2007-03-01

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.

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses.

PubMed

Schein, Stan; Gayed, James Maurice

2014-02-25

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry.

Cooperative Jahn-Teller phase transition of icosahedral molecular units

NASA Astrophysics Data System (ADS)

Nasrollahi, Seyed H.; Vvedensky, Dimitri D.

2017-02-01

Non-linear molecules undergo distortions when the orbital degeneracy of the highest occupied level is lifted by the Jahn-Teller effect. If such molecules or clusters of atoms are coupled to one another, the system may experience a cooperative Jahn-Teller effect (CJTE). In this paper, we describe a model of how the CJTE leads to the crystallization of the disordered phase. The model Hamiltonian is based on a normal mode decomposition of the clusters in order to maintain the symmetry labels. We take account of the electron-strain and the electron-phonon couplings and, by displacing the coordinates of the oscillators, obtain a term that explicitly couples the Jahn-Teller centers, enabling us to perform a mean-field analysis. The calculation of the free energy then becomes straightforward, and obtaining phase diagrams in various regimes follows from the minimization of this free energy. The results show that the character of the phase transition may change from strong to weak first order and even to second-order, depending on the coupling to the vibrational modes. Taken together, these results may serve as a paradigm for crystallization near the transition temperature, where the atoms tend to form clusters of icosahedral symmetry.

Renormalization group approach to symmetry protected topological phases

NASA Astrophysics Data System (ADS)

van Nieuwenburg, Evert P. L.; Schnyder, Andreas P.; Chen, Wei

2018-04-01

A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

NASA Astrophysics Data System (ADS)

Xiao, R. C.; Cheung, C. H.; Gong, P. L.; Lu, W. J.; Si, J. G.; Sun, Y. P.

2018-06-01

k paths exactly with symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe2 family materials also have the spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and method, we predict that PtSe2 family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe2 family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.

Pedagogical systematic derivation of Noether point symmetries in special relativistic field theories and extended gravity cosmology

NASA Astrophysics Data System (ADS)

Haas, Fernando

2016-11-01

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the invariance condition develops as a set of partial differential equations determining the symmetry transformation. The solution is provided in the case of real scalar, complex scalar, free electromagnetic, and charged electromagnetic fields. Besides the usual conservation laws, a less popular symmetry is analyzed: the symmetry associated with the linear superposition of solutions, whenever applicable. The role of gauge invariance is emphasized. The case of the charged scalar particle under external electromagnetic fields is considered, and the accompanying Noether point symmetries determined. Noether point symmetries for a dynamical system in extended gravity cosmology are also deduced.

Symmetries, chirp-free points, and bistability in dispersion-managed fiber lines.

PubMed

Turitsyn, S K; Nijhof, J H; Mezentsev, V K; Doran, N J

1999-12-15

We show from an elementary symmetry analysis that, in dispersion-compensated systems for which a lossless model is valid, nonlinearity requires a chirp-free point at the center of symmetry (if such exists) of the map for any kind of unique periodic solution. We also present an example of a more-complex map when the periodic solution is not unique.

Beta cell device using icosahedral boride compounds

DOEpatents

Aselage, Terrence L.; Emin, David

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 0.15icosahedral boride compound self-heals, resisting degradation from radiation damage.

The Symmetry Group of the Permutahedron

ERIC Educational Resources Information Center

Crisman, Karl-Dieter

2011-01-01

Although it can be visualized fairly easily and its symmetry group is easy to calculate, the permutahedron is a somewhat neglected combinatorial object. We propose it as a useful case study in abstract algebra. It supplies concrete examples of group actions, the difference between right and left actions, and how geometry and algebra can work…

Hopf bifurcation with dihedral group symmetry - Coupled nonlinear oscillators

NASA Technical Reports Server (NTRS)

Golubitsky, Martin; Stewart, Ian

1986-01-01

The theory of Hopf bifurcation with symmetry developed by Golubitsky and Stewart (1985) is applied to systems of ODEs having the symmetries of a regular polygon, that is, whose symmetry group is dihedral. The existence and stability of symmetry-breaking branches of periodic solutions are considered. In particular, these results are applied to a general system of n nonlinear oscillators coupled symmetrically in a ring, and the generic oscillation patterns are described. It is found that the symmetry can force some oscillators to have twice the frequency of others. The case of four oscillators has exceptional features.

Point interactions, metamaterials, and PT-symmetry

NASA Astrophysics Data System (ADS)

Mostafazadeh, Ali

2016-05-01

We express the boundary conditions for TE and TM waves at the interfaces of an infinite planar slab of homogeneous metamaterial as certain point interactions and use them to compute the transfer matrix of the system. This allows us to demonstrate the omnidirectional reflectionlessness of Veselago's slab for waves of arbitrary wavelength, reveal the translational and reflection symmetry of this slab, explore the laser threshold condition and coherent perfect absorption for active negative-index metamaterials, introduce a point interaction modeling phase-conjugation, determine the corresponding antilinear transfer matrix, and offer a simple proof of the equivalence of Veselago's slab with a pair of parallel phase-conjugating plates. We also study the connection between certain optical setups involving metamaterials and a class of PT-symmetric quantum systems defined on wedge-shape contours in the complex plane. This provides a physical interpretation for the latter.

Weyl semimetals in optical lattices: moving and merging of Weyl points, and hidden symmetry at Weyl points

PubMed Central

Hou, Jing-Min; Chen, Wei

2016-01-01

We propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points with opposite topological charges on the surface Brillouin zone is presented. By adjusting the parameters, the Weyl points can move in the Brillouin zone. Interestingly, for two pairs of Weyl points, as one pair of them meet and annihilate, the originial two Fermi arcs coneect into one. As the remaining Weyl points annihilate further, the Fermi arc vanishes and a gap is opened. Furthermore, we find that there always exists a hidden symmetry at Weyl points, regardless of anywhere they located in the Brillouin zone. The hidden symmetry has an antiunitary operator with its square being −1. PMID:27644114

Tropical cyclones over the North Indian Ocean: experiments with the high-resolution global icosahedral grid point model GME

NASA Astrophysics Data System (ADS)

Kumkar, Yogesh V.; Sen, P. N.; Chaudhari, Hemankumar S.; Oh, Jai-Ho

2018-02-01

In this paper, an attempt has been made to conduct a numerical experiment with the high-resolution global model GME to predict the tropical storms in the North Indian Ocean during the year 2007. Numerical integrations using the icosahedral hexagonal grid point global model GME were performed to study the evolution of tropical cyclones, viz., Akash, Gonu, Yemyin and Sidr over North Indian Ocean during 2007. It has been seen that the GME model forecast underestimates cyclone's intensity, but the model can capture the evolution of cyclone's intensity especially its weakening during landfall, which is primarily due to the cutoff of the water vapor supply in the boundary layer as cyclones approach the coastal region. A series of numerical simulation of tropical cyclones have been performed with GME to examine model capability in prediction of intensity and track of the cyclones. The model performance is evaluated by calculating the root mean square errors as cyclone track errors.

Diffuse Scattering in the Icosahedral AL-Li-Cu Quasicrystal

NASA Astrophysics Data System (ADS)

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

1995-12-01

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

Dynamic stabilities of icosahedral-like clusters and their ability to form quasicrystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liang, Xiaogang; Hamid, Ilyar; Duan, Haiming, E-mail: dhm@xju.edu.cn

2016-06-15

The dynamic stabilities of the icosahedral-like clusters containing up to 2200 atoms are investigated for 15 metal elements. The clusters originate from five different initial structures (icosahedron, truncated decahedron, octahedron, closed-shell fragment of an HCP structure, and non-closed-shell fragment of an HCP structure). The obtained order of the dynamic stabilities of the icosahedral-like clusters can be assigned to three groups, from stronger to weaker, according to the size ranges involved: (Zr, Al, Ti) > (Cu, Fe, Co, Ni, Mg, Ag) > (Pb, Au, Pd, Pt, Rh, Ir), which correspond to the predicted formation ability of the quasicrystals. The differences ofmore » the sequences can be explained by analyzing the parameters of the Gupta-type many-body inter-atomic potentials.« less

Icosahedral quasicrystalline (Ti₁.₆V₀.₄Ni)₁₀₀₋xScx alloys: Synthesis, structure and their application in Ni-MH batteries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Wen; State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, CAS, Changchun 130022, Jilin; Yi, Jianhong

2013-06-01

Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti₁.₆V₀.₄Ni)₁₀₀₋xScx (x=0.5–6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g⁻¹ can be delivered. With furthermore » increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g⁻¹, and the electrocatalytic activity improvement is highly demanded. - Graphical abstract: Quasicrystalline Ti–V–Ni–Sc hydrogen storage materials: Sc addition into Ti₁.₆V₀.₄Ni alloy forms the icosahedral phase (see picture). With optimal Sc dosage, the anodic cycling stability and self-discharge property are greatly enhanced. - Highlights: • Crystalline disallowed 5-fold symmetry is present in (Ti₁.₆V₀.₄Ni)₁₀₀₋xScx alloys. • Ti-based metastable quasicrystalline alloys can store hydrogen electrochemically. • A maximum discharge capacity of 270 mA h g⁻¹ can be delivered. • Advantageous cycle stability and self-discharge property benefit from Sc addition. • Ti and V dissolution is suppressed by an oxide layer resulting from Sc corrosion.« less

Icosahedral quasicrystalline (Ti1.6V0.4Ni)100-xScx alloys: Synthesis, structure and their application in Ni-MH batteries

NASA Astrophysics Data System (ADS)

Hu, Wen; Yi, Jianhong; Zheng, Biju; Wang, Limin

2013-06-01

Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti1.6V0.4Ni)100-xScx (x=0.5-6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g-1 can be delivered. With further increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g-1, and the electrocatalytic activity improvement is highly demanded.

Zitterbewegung and symmetry switching in Klein’s four-group

NASA Astrophysics Data System (ADS)

Chotorlishvili, L.; Zięba, P.; Tralle, I.; Ugulava, A.

2018-01-01

Zitterbewegung is the exotic phenomenon associated either with relativistic electron-positron rapid oscillation or to electron-hole transitions in narrow gap semiconductors. In the present work, we enlarge the concept of Zitterbewegung and show that trembling motion may occur due to dramatic changes in the symmetry of the system. In particular, we exploit a paradigmatic model of quantum chaos, the quantum mathematical pendulum (universal Hamiltonian). The symmetry group of this system is Klein’s four-group that possesses three invariant subgroups. The energy spectrum of the system parametrically depends on the height of the potential barrier, and contains degenerate and non-degenerate areas, corresponding to the different symmetry subgroups. Change in the height of the potential barrier switches the symmetry subgroup and leads to trembling motion. We analyzed mean square fluctuations of the velocity operator and observed that trembling is enhanced in highly excited states. We observed a link between the phenomena of trembling motion and the uncertainty relations of noncommutative operators of the system.

Lifetimes in Te 124 : Examining critical-point symmetry in the Te nuclei

DOE PAGES

Hicks, S. F.; Vanhoy, J. R.; Burkett, P. G.; ...

2017-03-27

The Doppler-shift attenuation method following inelastic neutron scattering was used to determine the lifetimes of nuclear levels to 3.3-MeV excitation in 124Te. Level energies and spins, γ -ray energies and branching ratios, and multipole-mixing ratios were deduced from measured γ-ray angular distributions at incident neutron energies of 2.40 and 3.30 MeV, γ-ray excitation functions, and γγ coincidence measurements. The newly obtained reduced transition probabilities and level energies for 124Te were compared to critical-point symmetry model predictions. The E(5) and β 4 potential critical-point symmetries were also investigated in 122Te and 126Te.

Synthesis of icosahedral gold nanocrystals: a thermal process strategy.

PubMed

Zhou, Min; Chen, Shenhao; Zhao, Shiyong

2006-03-16

We demonstrate a one-step thermal process route to the synthesis of icosahedral gold nanocrystals. By regulating the concentrations of poly(vinyl pyrrolidone) (PVP) and HAuCl4 or changing the temperature, we can readily access the shapes of icosahedral nanocrystals with good uniformity. These gold nanostructures, with unique geometrical shapes, might find use in areas that include photonics, optoelectronics, and optical sensing. We also observed that these gold nanocrystals have a strong tendency to be immobilized spontaneously on the glass substrate.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models.

PubMed

Antonov, N V; Gulitskiy, N M; Kostenko, M M; Malyshev, A V

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E∝k^{1-y} and the dispersion law ω∝k^{2-η}. The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Statistical symmetry restoration in fully developed turbulence: Renormalization group analysis of two models

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.

2018-03-01

In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.

Additivity of Feature-Based and Symmetry-Based Grouping Effects in Multiple Object Tracking

PubMed Central

Wang, Chundi; Zhang, Xuemin; Li, Yongna; Lyu, Chuang

2016-01-01

Multiple object tracking (MOT) is an attentional process wherein people track several moving targets among several distractors. Symmetry, an important indicator of regularity, is a general spatial pattern observed in natural and artificial scenes. According to the “laws of perceptual organization” proposed by Gestalt psychologists, regularity is a principle of perceptual grouping, such as similarity and closure. A great deal of research reported that feature-based similarity grouping (e.g., grouping based on color, size, or shape) among targets in MOT tasks can improve tracking performance. However, no additive feature-based grouping effects have been reported where the tracking objects had two or more features. “Additive effect” refers to a greater grouping effect produced by grouping based on multiple cues instead of one cue. Can spatial symmetry produce a similar grouping effect similar to that of feature similarity in MOT tasks? Are the grouping effects based on symmetry and feature similarity additive? This study includes four experiments to address these questions. The results of Experiments 1 and 2 demonstrated the automatic symmetry-based grouping effects. More importantly, an additive grouping effect of symmetry and feature similarity was observed in Experiments 3 and 4. Our findings indicate that symmetry can produce an enhanced grouping effect in MOT and facilitate the grouping effect based on color or shape similarity. The “where” and “what” pathways might have played an important role in the additive grouping effect. PMID:27199875

The symmetry of single-molecule conduction.

PubMed

Solomon, Gemma C; Gagliardi, Alessio; Pecchia, Alessandro; Frauenheim, Thomas; Di Carlo, Aldo; Reimers, Jeffrey R; Hush, Noel S

2006-11-14

We introduce the conductance point group which defines the symmetry of single-molecule conduction within the nonequilibrium Green's function formalism. It is shown, either rigorously or to within a very good approximation, to correspond to a molecular-conductance point group defined purely in terms of the properties of the conducting molecule. This enables single-molecule conductivity to be described in terms of key qualitative chemical descriptors that are independent of the nature of the molecule-conductor interfaces. We apply this to demonstrate how symmetry controls the conduction through 1,4-benzenedithiol chemisorbed to gold electrodes as an example system, listing also the molecular-conductance point groups for a range of molecules commonly used in molecular electronics research.

The Influence of Texture Symmetry in Marker Pointing:. Experimenting with Humans and Algorithms

NASA Astrophysics Data System (ADS)

Cardaci, M.; Tabacchi, M. E.

2012-12-01

Symmetry plays a fundamental role in aiding the visual system, to organize its environmental stimuli and to detect visual patterns of natural and artificial objects. Various kinds of symmetry exist, and we will discuss how internal symmetry due to textures influences the choice of direction in visual tasks. Two experiments are presented: the first, with human subjects, deals with the effect of textures on preferences for a pointing direction. The second emulates the performances obtained in the first through the use of an algorithm based on a physic metaphor. Results from both experiments are shown and comment.

Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Tsamparlis, M.; Mustafa, M. T.

2018-02-01

A complete classification of the Lie and Noether point symmetries for the Klein-Gordon and the wave equation in pp-wave spacetimes is obtained. The classification analysis is carried out by reducing the problem of the determination of the point symmetries to the problem of existence of conformal killing vectors on the pp-wave spacetimes. Employing the existing results for the isometry classes of the pp-wave spacetimes, the functional form of the potential is determined for which the Klein-Gordon equation admits point symmetries and Noetherian conservation law. Finally the Lie and Noether point symmetries of the wave equation are derived.

Soft materials design via self assembly of functionalized icosahedral particles

NASA Astrophysics Data System (ADS)

Muthukumar, Vidyalakshmi Chockalingam

In this work we simulate self assembly of icosahedral building blocks using a coarse grained model of the icosahedral capsid of virus 1m1c. With significant advancements in site-directed functionalization of these macromolecules [1], we propose possible application of such self-assembled materials for drug delivery. While there have been some reports on organization of viral particles in solution through functionalization, exploiting this behaviour for obtaining well-ordered stoichiometric structures has not yet been explored. Our work is in well agreement with the earlier simulation studies of icosahedral gold nanocrystals, giving chain like patterns [5] and also broadly in agreement with the wet lab works of Finn, M.G. et al., who have shown small predominantly chain-like aggregates with mannose-decorated Cowpea Mosaic Virus (CPMV) [22] and small two dimensional aggregates with oligonucleotide functionalization on the CPMV capsid [1]. To quantify the results of our Coarse Grained Molecular Dynamics Simulations I developed analysis routines in MATLAB using which we found the most preferable nearest neighbour distances (from the radial distribution function (RDF) calculations) for different lengths of the functional groups and under different implicit solvent conditions, and the most frequent coordination number for a virus particle (histogram plots further using the information from RDF). Visual inspection suggests that our results most likely span the low temperature limits explored in the works of Finn, M.G. et al., and show a good degree of agreement with the experimental results in [1] at an annealing temperature of 4°C. Our work also reveals the possibility of novel stoichiometric N-mer type aggregates which could be synthesized using these capsids with appropriate functionalization and solvent conditions.

Quasicrystals at extreme conditions: The role of pressure in stabilizing icosahedral Al 63Cu 24Fe 13 at high temperature

DOE PAGES

Stagno, Vincenzo; Bindi, Luca; Park, Changyong; ...

2015-11-20

Icosahedrite, the first natural quasicrystal with composition Al 63Cu 24Fe 13, was discovered in several grains of the Khatyrka meteorite, a unique CV3 carbonaceous chondrite. The presence in the meteorite fragments of icosahedrite strictly associated with high-pressure phases like ahrensite and stishovite indicates a formation conditions at high pressures and temperatures, likely during an impact-induced shock occurred in contact with the reducing solar nebula gas. In contrast, previous experimental studies on the stability of synthetic icosahedral AlCuFe, which were limited to ambient pressure, indicated incongruent melting at ~1123 K, while high-pressure experiments carried out at room temperature showed structural stabilitymore » up to about 35 GPa. These data are insufficient to experimentally constrain the formation and stability of icosahedrite under extreme conditions. Here we present the results of in situ high pressure experiments using diamond anvil cells of the compressional behavior of synthetic icosahedrite up to ~50 GPa at room temperature. Simultaneous high P-T experiments have been also carried out using both laser-heated diamond anvil cells combined with in situ synchrotron X-ray diffraction (at ~42 GPa) and multi-anvil apparatus (at 21 GPa) to investigate the structural evolution of icosahedral Al 63Cu 24Fe 13 and crystallization of possible coexisting phases. The results demonstrate that the quasiperiodic symmetry of icosahedrite is retained over the entire experimental pressure range explored. In addition, we show that pressure acts to stabilize the icosahedral symmetry at temperatures much higher than previously reported. Based on our experimental study, direct crystallization of Al-Cu-Fe quasicrystals from an unusual Al-Cu-rich melt would be possible but limited to a narrow temperature range beyond which crystalline phases would form, like those observed in the Khatyrka meteorite. Here, an alternative mechanism would consist in late

From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space.

PubMed

Turci, Francesco; Tarjus, Gilles; Royall, C Patrick

2017-05-26

Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass formers, to tile space. Local icosahedral order, however, is strongly frustrated in Euclidean space, which obscures any causal relationship with the observed dynamical slowdown. Here we relieve frustration in a model glass-forming liquid by curving three-dimensional space onto the surface of a 4-dimensional hypersphere. For sufficient curvature, frustration vanishes and the liquid "freezes" in a fully icosahedral structure via a sharp "transition." Frustration increases upon reducing the curvature, and the transition to the icosahedral state smoothens while glassy dynamics emerge. Decreasing the curvature leads to decoupling between dynamical and structural length scales and the decrease of kinetic fragility. This sheds light on the observed glass-forming behavior in Euclidean space.

Sheet-like assemblies of spherical particles with point-symmetrical patches.

PubMed

Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K

2012-04-14

We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.

Turbulent scaling laws as solutions of the multi-point correlation equation using statistical symmetries

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Rosteck, Andreas; Avsarkisov, Victor

2013-11-01

Text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Most important, theses new symmetries have important consequences for our understanding of turbulent scaling laws. The symmetries form the essential foundation to construct exact solutions to the infinite set of MPCE, which in turn are identified as classical and new turbulent scaling laws. Examples on various classical and new shear flow scaling laws including higher order moments will be presented. Even new scaling have been forecasted from these symmetries and in turn validated by DNS. Turbulence modellers have implicitly recognized at least one of the statistical symmetries as this is the basis for the usual log-law which has been employed for calibrating essentially all engineering turbulence models. An obvious conclusion is to generally make turbulence models consistent with the new statistical symmetries.

Group theoretical symmetries and generalized Bäcklund transformations for integrable systems

NASA Astrophysics Data System (ADS)

Haak, Guido

1994-05-01

A notion of symmetry for 1+1-dimensional integrable systems is presented which is consistent with their group theoretic description. It is shown how a group symmetry may be used together with a dynamical reduction to produce new generalizations of the Bäcklund transformation for the Korteweg-de Vries equation to its SL(n,C) generalization. An additional application to the relativistic invariance of the Leznov-Saveliev systems is given.

The Connection Between Local Icosahedral Order in Metallic Liquids and the Nucleation of Ordered Phases

NASA Technical Reports Server (NTRS)

Curreri, Peter A. (Technical Monitor); Kelton, K. F.; Gangopadhyay, A.; Lee, G. W.; Hyers, R. W.; Rathz, R. J.; Rogers, J.; Schenk, T.; Simonet, V.; Holland-Moritz, D.

2003-01-01

Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si, for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.

The Connection Between Local Icosahedral Order in Metallic Liquids and the Nucleation of Ordered Phases

NASA Technical Reports Server (NTRS)

Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.; Holland-Moritz, D.;

Symmetry and electronic structure of noble-metal nanoparticles and the role of relativity.

PubMed

Häkkinen, Hannu; Moseler, Michael; Kostko, Oleg; Morgner, Nina; Hoffmann, Margarita Astruc; von Issendorff, Bernd

2004-08-27

We present high resolution UV-photoelectron spectra of cold mass selected Cun-, Agn-, and Aun- with n=53-58. The observed electron density of states is not the expected simple electron shell structure, but is strongly influenced by electron-lattice interactions. Only Cu55- and Ag55- exhibit highly degenerate states. This is a direct consequence of their icosahedral symmetry, as is confirmed by density functional theory calculations. Neighboring sizes exhibit perturbed electronic structures, as they are formed by removal or addition of atoms to the icosahedron and therefore have lower symmetries. Gold clusters in the same size range show completely different spectra with almost no degeneracy, which indicates that they have structures of much lower symmetry. This behavior is related to strong relativistic bonding effects in gold, as demonstrated by ab initio calculations for Au55-.

Surveying the quantum group symmetries of integrable open spin chains

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Retore, Ana L.

2018-05-01

Using anisotropic R-matrices associated with affine Lie algebras g ˆ (specifically, A2n(2), A2n-1 (2) , Bn(1), Cn(1), Dn(1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of g ˆ . We show that these transfer matrices also have a duality symmetry (for the cases Cn(1) and Dn(1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n-1 (2) , Bn(1) and Dn(1)). A key simplification is achieved by working in a certain "unitary" gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.

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

NASA Technical Reports Server (NTRS)

Garg, Anupam; Levine, Dov

1988-01-01

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

The Connection Between Local Icosahedral Order in Metallic Liquids and the Nucleation Behavior of Ordered Phases

NASA Technical Reports Server (NTRS)

Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.

2003-01-01

Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si[3], for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.

Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gu Zhengcheng; Wen Xiaogang

2009-10-15

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors T{sub inv} plus the symmetry group G{sub sym} of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, asmore » illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (G{sub sym},T{sub inv}) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (G{sub sym},T{sub inv}) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.« less

Ermakov's Superintegrable Toy and Nonlocal Symmetries

NASA Astrophysics Data System (ADS)

Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

2005-11-01

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.

The analysis of crystallographic symmetry types in finite groups

NASA Astrophysics Data System (ADS)

Sani, Atikah Mohd; Sarmin, Nor Haniza; Adam, Nooraishikin; Zamri, Siti Norziahidayu Amzee

2014-06-01

Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.

Orientation relationship between the T structure and the icosahedral quasicrystal in the Zn-Mg-Al alloy system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kei, E-mail: k.n@aoni.waseda.jp; Watanabe, Junya; Koyama, Yasumasa, E-mail: ykoyama@waseda.jp

2016-08-26

To understand the crystallographic relation between the Bergman-type icosahedral quasicrystal and its approximant-T structure, we have investigated the crystallographic features of prepared Zn-Mg-Al alloy samples, mainly by transmission electron microscopy. It was found that there existed three kinds of regions: that is, C14-Laves, approximant-T, and icosahedral-quasicrystal regions, in Zn-Mg-Al alloy samples with the composition of Zn-36at.%Mg-9at.%Al. Among these regions, in particular, we tried to determine an orientation relationship between neighboring icosahedral-quasicrystal and approximant-T regions. Based on the determined relationship, for instance, four threefold rotatory-inversion axes in the T structure were found to be parallel to four of ten threefold rotatory-inversionmore » axes in the icosahedral quasicrystal. It was thus understood that the atomic arrangements of the Bergman-type icosahedral quasicrystal and its approximant-T structure are likely to resemble each other.« less

Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.

PubMed

Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R

2016-05-13

The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.

Mysteries of icosahedral quasicrystals: how are the atoms arranged?

PubMed

Ishimasa, Tsutomu

2016-07-01

Higher-dimensional structure analysis of quasicrystals is now possible. Yamada et al. [IUCrJ (2016), 3, 247-258] have solved the atomic structure of icosahedral ScZn7.33 including the characteristic imperfections.

Method of making an icosahedral boride structure

DOEpatents

Hersee, Stephen D.; Wang, Ronghua; Zubia, David; Aselage, Terrance L.; Emin, David

2005-01-11

A method for fabricating thin films of an icosahedral boride on a silicon carbide (SiC) substrate is provided. Preferably the icosahedral boride layer is comprised of either boron phosphide (B.sub.12 P.sub.2) or boron arsenide (B.sub.12 As.sub.2). The provided method achieves improved film crystallinity and lowered impurity concentrations. In one aspect, an epitaxially grown layer of B.sub.12 P.sub.2 with a base layer or substrate of SiC is provided. In another aspect, an epitaxially grown layer of B.sub.12 As.sub.2 with a base layer or substrate of SiC is provided. In yet another aspect, thin films of B.sub.12 P.sub.2 or B.sub.12 As.sub.2 are formed on SiC using CVD or other vapor deposition means. If CVD techniques are employed, preferably the deposition temperature is above 1050.degree. C., more preferably in the range of 1100.degree. C. to 1400.degree. C., and still more preferably approximately 1150.degree. C.

Theoretical and Numerical Modeling of faceted Ionic crystalline vesicles

NASA Astrophysics Data System (ADS)

Olvera de La Cruz, Monica

2007-03-01

Icosahedral shape is found in several natural structures including large viruses, large fullerenes and cationic-anionic vesicles. Faceting into icosahedral shape can occur in large crystalline membranes via elasticity theory. Icosahedral symmetry is found in small systems of particles with short-range interactions on a sphere. Dr G. Vernizzi and I show a novel electrostatic-driven mechanism of ionic crystalline shells faceting into icosahedral shapes even for systems with a small number of particles. Icosahedral shape is possible in cationic and anionic molecules adsorbed onto spherical interfaces, such as emulsions or other immiscible liquid droplets because the large concentration of charges at the interface can lead to ionic crystals on the curved interface. Such self-organized ionic structures favors the formation of flat surfaces. We find that these ionic crystalline shells can have lower energy when faceted into icosahedra along particular directions. Indeed, the ``ionic'' buckling is driven by preferred bending directions of the planar ionic structure, along which is more likely for the icosahedral shape to develop an edge. Since only certain orientations are allowed, rotational symmetry is broken. One can hope to exploit this mechanism to generate functional materials where, for instance, proteins with specific charge groups can orient at specific directions along an icosahedral cationic-anionic vesicle.

Metallic-covalent bonding conversion and thermoelectric properties of Al-based icosahedral quasicrystals and approximants.

PubMed

Takagiwa, Yoshiki; Kimura, Kaoru

2014-08-01

In this article, we review the characteristic features of icosahedral cluster solids, metallic-covalent bonding conversion (MCBC), and the thermoelectric properties of Al-based icosahedral quasicrystals and approximants. MCBC is clearly distinguishable from and closely related to the well-known metal-insulator transition. This unique bonding conversion has been experimentally verified in 1/1-AlReSi and 1/0-Al 12 Re approximants by the maximum entropy method and Rietveld refinement for powder x-ray diffraction data, and is caused by a central atom inside the icosahedral clusters. This helps to understand pseudogap formation in the vicinity of the Fermi energy and establish a guiding principle for tuning the thermoelectric properties. From the electron density distribution analysis, rigid heavy clusters weakly bonded with glue atoms are observed in the 1/1-AlReSi approximant crystal, whose physical properties are close to icosahedral Al-Pd-TM (TM: Re, Mn) quasicrystals. They are considered to be an intermediate state among the three typical solids: metals, covalently bonded networks (semiconductor), and molecular solids. Using the above picture and detailed effective mass analysis, we propose a guiding principle of weakly bonded rigid heavy clusters to increase the thermoelectric figure of merit ( ZT ) by optimizing the bond strengths of intra- and inter-icosahedral clusters. Through element substitutions that mainly weaken the inter-cluster bonds, a dramatic increase of ZT from less than 0.01 to 0.26 was achieved. To further increase ZT , materials should form a real gap to obtain a higher Seebeck coefficient.

Metal-organic framework materials based on icosahedral boranes and carboranes

DOEpatents

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.

Icosahedral quasicrystals as twins of cubic crystals containing large icosahedral clusters of atoms: The 1012-atom primitive cubic structure of Al(6)CuLi(3), the C-phase Al(37)Cu(3)Li(21)Mg(3), and GaMg(2)Zn(3).

PubMed

Pauling, L

1988-06-01

Single-grain precession x-ray diffraction photographs of Al(6)CuLi(3) have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 A, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the beta-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, Al(37)Cu(3)Li(21)Mg(3), and to GaMg(2)Zn(3). A theory of icosahedral quasicrystals and amorphous metals is described.

Quantum group symmetry of the quantum Hall effect on non-flat surfaces

NASA Astrophysics Data System (ADS)

Alimohammadi, M.; Shafei Deh Abad, A.

1996-02-01

After showing that the magnetic translation operators are not the symmetries of the quantum Hall effect (QHE) on non-flat surfaces, we show that another set of operators which leads to the quantum group symmetries for some of these surfaces exists. As a first example we show that the su(2) symmetry of the QHE on a sphere leads to 0305-4470/29/3/010/img6(2) algebra in the equator. We explain this result by a contraction of su(2). Second, with the help of the symmetry operators of QHE on the Poincaré upper half plane, we will show that the ground-state wavefunctions form a representation of the 0305-4470/29/3/010/img6(2) algebra.

Improved Statistics for Determining the Patterson Symmetry fromUnmerged Diffraction Intensities

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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 notmore » 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.« less

HCIV-1 and Other Tailless Icosahedral Internal Membrane-Containing Viruses of the Family Sphaerolipoviridae.

PubMed

Demina, Tatiana A; Pietilä, Maija K; Svirskaitė, Julija; Ravantti, Janne J; Atanasova, Nina S; Bamford, Dennis H; Oksanen, Hanna M

2017-02-18

Members of the virus family Sphaerolipoviridae include both archaeal viruses and bacteriophages that possess a tailless icosahedral capsid with an internal membrane. The genera Alpha- and Betasphaerolipovirus comprise viruses that infect halophilic euryarchaea, whereas viruses of thermophilic Thermus bacteria belong to the genus Gammasphaerolipovirus . Both sequence-based and structural clustering of the major capsid proteins and ATPases of sphaerolipoviruses yield three distinct clades corresponding to these three genera. Conserved virion architectural principles observed in sphaerolipoviruses suggest that these viruses belong to the PRD1-adenovirus structural lineage. Here we focus on archaeal alphasphaerolipoviruses and their related putative proviruses. The highest sequence similarities among alphasphaerolipoviruses are observed in the core structural elements of their virions: the two major capsid proteins, the major membrane protein, and a putative packaging ATPase. A recently described tailless icosahedral haloarchaeal virus, Haloarcula californiae icosahedral virus 1 (HCIV-1), has a double-stranded DNA genome and an internal membrane lining the capsid. HCIV-1 shares significant similarities with the other tailless icosahedral internal membrane-containing haloarchaeal viruses of the family Sphaerolipoviridae . The proposal to include a new virus species, Haloarcula virus HCIV1 , into the genus Alphasphaerolipovirus was submitted to the International Committee on Taxonomy of Viruses (ICTV) in 2016.

Gain-Sparsity and Symmetry-Forced Rigidity in the Plane.

PubMed

Jordán, Tibor; Kaszanitzky, Viktória E; Tanigawa, Shin-Ichi

We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2 k with odd k , unifying and extending previous work on this subject. We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit matrices of the symmetric frameworks are isomorphic to gain sparsity matroids defined on the quotient graph of the framework, whose edges are labeled by elements of the corresponding symmetry group. The proofs are based on new Henneberg type inductive constructions of the gain graphs that correspond to the bases of the matroids in question, which can also be seen as symmetry preserving graph operations in the original graph.

Icosahedral quasicrystals as twins of cubic crystals containing large icosahedral clusters of atoms: The 1012-atom primitive cubic structure of Al6CuLi3, the C-phase Al37Cu3Li21Mg3, and GaMg2Zn3

PubMed Central

Pauling, Linus

1988-01-01

Single-grain precession x-ray diffraction photographs of Al6CuLi3 have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 Å, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the β-W arrangement. In this compound two of the clusters consist of 104 atoms and six consist of 136 atoms, with 24 atoms shared. The same structure is assigned to the C-phase, Al37Cu3Li21Mg3, and to GaMg2Zn3. A theory of icosahedral quasicrystals and amorphous metals is described. PMID:16593929

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…

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2012-01-01

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gliga, Sebastian; Kákay, Attila; Heyderman, Laura J.

In this paper, we study degeneracy and entropy in the ground state of artificial square ice. In theoretical models, individual nanomagnets are typically treated as single spins with only two degrees of freedom, leading to a twofold degenerate ground state with intensive entropy and thus no zero-point entropy. Here, we show that the internal degrees of freedom of the nanostructures can result, through edge bending of the magnetization and breaking of local magnetic symmetry at the vertices, in a transition to a highly degenerate ground state with finite zero-point entropy, similar to that of the pyrochlore spin ices. Finally, wemore » find that these additional degrees of freedom have observable consequences in the resonant spectrum of the lattice, and predict the occurrence of edge “melting” above a critical temperature at which the magnetic symmetry is restored.« less

Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

DOE PAGES

Gliga, Sebastian; Kákay, Attila; Heyderman, Laura J.; ...

2015-08-26

In this paper, we study degeneracy and entropy in the ground state of artificial square ice. In theoretical models, individual nanomagnets are typically treated as single spins with only two degrees of freedom, leading to a twofold degenerate ground state with intensive entropy and thus no zero-point entropy. Here, we show that the internal degrees of freedom of the nanostructures can result, through edge bending of the magnetization and breaking of local magnetic symmetry at the vertices, in a transition to a highly degenerate ground state with finite zero-point entropy, similar to that of the pyrochlore spin ices. Finally, wemore » find that these additional degrees of freedom have observable consequences in the resonant spectrum of the lattice, and predict the occurrence of edge “melting” above a critical temperature at which the magnetic symmetry is restored.« less

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

PubMed

Wang, Juven C; Gu, Zheng-Cheng; Wen, Xiao-Gang

2015-01-23

The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs. We find new examples of mixed gauge-gravity actions for U(1) SPTs in (4+1)D via the gravitational Chern-Simons term. Field theory representations of SPT invariants not only serve as tools for classifying SPTs, but also guide us in designing physical probes for them. In addition, our field theory representations are independently powerful for studying group cohomology within the mathematical context.

Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry.

PubMed

Miller, Jacob; Miyake, Akimasa

2018-04-27

An emerging insight is that ground states of symmetry-protected topological orders (SPTOs) possess latent computational complexity in terms of their many-body entanglement. By introducing a fractional symmetry of SPTO, which requires the invariance under 3-colorable symmetries of a lattice, we prove that every renormalization fixed-point state of 2D (Z_{2})^{m} SPTO with fractional symmetry can be utilized for universal quantum computation using only Pauli measurements, as long as it belongs to a nontrivial 2D SPTO phase. Our infinite family of fixed-point states may serve as a base model to demonstrate the idea of a "quantum computational phase" of matter, whose states share universal computational complexity ubiquitously.

Symmetry Analysis of Gauge-Invariant Field Equations via a Generalized Harrison-Estabrook Formalism.

NASA Astrophysics Data System (ADS)

Papachristou, Costas J.

The Harrison-Estabrook formalism for the study of invariance groups of partial differential equations is generalized and extended to equations that define, through their solutions, sections on vector bundles of various kinds. Applications include the Dirac, Yang-Mills, and self-dual Yang-Mills (SDYM) equations. The latter case exhibits interesting connections between the internal symmetries of SDYM and the existence of integrability characteristics such as a linear ("inverse scattering") system and Backlund transformations (BT's). By "verticalizing" the generators of coordinate point transformations of SDYM, nine nonlocal, generalized (as opposed to local, point) symmetries are constructed. The observation is made that the prolongations of these symmetries are parametric BT's for SDYM. It is thus concluded that the entire point group of SDYM contributes, upon verticalization, BT's to the system.

Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses

PubMed Central

Schein, Stan; Gayed, James Maurice

2014-01-01

The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry––tetrahedral, octahedral, and icosahedral––are the 5 Platonic polyhedra, the 13 Archimedean polyhedra––including the truncated icosahedron or soccer ball––and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, “Goldberg polyhedra,” which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a “Goldberg triangle.” We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler’s rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry. PMID:24516137

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.

Hardness and Elastic Modulus on Six-Fold Symmetry Gold Nanoparticles

PubMed Central

Ramos, Manuel; Ortiz-Jordan, Luis; Hurtado-Macias, Abel; Flores, Sergio; Elizalde-Galindo, José T.; Rocha, Carmen; Torres, Brenda; Zarei-Chaleshtori, Maryam; Chianelli, Russell R.

2013-01-01

The chemical synthesis of gold nanoparticles (NP) by using gold (III) chloride trihydrate (HAuCl∙3H2O) and sodium citrate as a reducing agent in aqueous conditions at 100 °C is presented here. Gold nanoparticles areformed by a galvanic replacement mechanism as described by Lee and Messiel. Morphology of gold-NP was analyzed by way of high-resolution transmission electron microscopy; results indicate a six-fold icosahedral symmetry with an average size distribution of 22 nm. In order to understand the mechanical behaviors, like hardness and elastic moduli, gold-NP were subjected to nanoindentation measurements—obtaining a hardness value of 1.72 GPa and elastic modulus of 100 GPa in a 3–5 nm of displacement at the nanoparticle’s surface. PMID:28809302

Applying Symmetries of Common Objects to Help Students Understand Stereoselectivity for Apparently Symmetric Substrates

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…

Theory of morphological transformation of viral capsid shell during the maturation process in the HK97 bacteriophage and similar viruses

NASA Astrophysics Data System (ADS)

Konevtsova, O. V.; Lorman, V. L.; Rochal, S. B.

2016-05-01

We consider the symmetry and physical origin of collective displacement modes playing a crucial role in the morphological transformation during the maturation of the HK97 bacteriophage and similar viruses. It is shown that the experimentally observed hexamer deformation and pentamer twist in the HK97 procapsid correspond to the simplest irreducible shear strain mode of a spherical shell. We also show that the icosahedral faceting of the bacteriophage capsid shell is driven by the simplest irreducible radial displacement field. The shear field has the rotational icosahedral symmetry group I while the radial field has the full icosahedral symmetry Ih. This difference makes their actions independent. The radial field sign discriminates between the icosahedral and the dodecahedral shapes of the faceted capsid shell, thus making the approach relevant not only for the HK97-like viruses but also for the parvovirus family. In the frame of the Landau-Ginzburg formalism we propose a simple phenomenological model valid for the first reversible step of the HK97 maturation process. The calculated phase diagram illustrates the discontinuous character of the virus shape transformation. The characteristics of the virus shell faceting and expansion obtained in the in vitro and in vivo experiments are related to the decrease in the capsid shell thickness and to the increase of the internal capsid pressure.

A new approach to determining symmetry groups of filtration properties of porous media in nonlinear filtration laws

NASA Astrophysics Data System (ADS)

Maksimov, V. M.; Dmitriev, N. M.; Dmitriev, M. N.

2017-04-01

Theoretical analysis of filtration properties of porous media for orthotropic and monoclinic symmetry groups has been carried out. It is shown how it is possible to establish a type of symmetry with the help of special laboratory investigations and to distinguish groups with orthotropic and monoclinic symmetry. It is established that the criterion for solving this problem is the use of nonlinear Darcy law at high flow velocities, where the effects of asymmetry of filtration properties manifest themselves upon a change in the flow direction.

Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carbone, Lisa; Murray, Scott H.; Sati, Hisham

For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(ℤ) on K∖G. We give explicit results for the action of the discrete U-duality groups SL{sub 2}(ℤ) and E{sub 7}(ℤ) on the scalar cosets SO(2)∖SL{sub 2}(ℝ) and [SU(8)/( ± Id)]∖E{sub 7(+7)}(ℝ) for type IIB supergravity in ten dimensions andmore » 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.« less

Statistical symmetries of the Lundgren-Monin-Novikov hierarchy.

PubMed

Wacławczyk, Marta; Staffolani, Nicola; Oberlack, Martin; Rosteck, Andreas; Wilczek, Michael; Friedrich, Rudolf

2014-07-01

It was shown by Oberlack and Rosteck [Discr. Cont. Dyn. Sys. S, 3, 451 2010] that the infinite set of multipoint correlation (MPC) equations of turbulence admits a considerable extended set of Lie point symmetries compared to the Galilean group, which is implied by the original set of equations of fluid mechanics. Specifically, a new scaling group and an infinite set of translational groups of all multipoint correlation tensors have been discovered. These new statistical groups have important consequences for our understanding of turbulent scaling laws as they are essential ingredients of, e.g., the logarithmic law of the wall and other scaling laws, which in turn are exact solutions of the MPC equations. In this paper we first show that the infinite set of translational groups of all multipoint correlation tensors corresponds to an infinite dimensional set of translations under which the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDF) are left invariant. Second, we derive a symmetry for the LMN hierarchy which is analogous to the scaling group of the MPC equations. Most importantly, we show that this symmetry is a measure of the intermittency of the velocity signal and the transformed functions represent PDFs of an intermittent (i.e., turbulent or nonturbulent) flow. Interesting enough, the positivity of the PDF puts a constraint on the group parameters of both shape and intermittency symmetry, leading to two conclusions. First, the latter symmetries may no longer be Lie group as under certain conditions group properties are violated, but still they are symmetries of the LMN equations. Second, as the latter two symmetries in its MPC versions are ingredients of many scaling laws such as the log law, the above constraints implicitly put weak conditions on the scaling parameter such as von Karman constant κ as they are functions of the group parameters. Finally, let us note that these kind of statistical symmetries are

Near-horizon BMS symmetries as fluid symmetries

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2017-10-01

The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat gravity. Recently, Donnay et al. have derived an analogous symmetry group acting on black hole event horizons. For a certain choice of boundary conditions, it is a semidirect product of Diff( S 2), the smooth diffeomorphisms of the twosphere, acting on C ∞( S 2), the smooth functions on the two-sphere. We observe that the same group appears in fluid dynamics as symmetries of the compressible Euler equations. We relate these two realizations of Diff( S 2) ⋉ C ∞( S 2) using the black hole membrane paradigm. We show that the Lie-Poisson brackets of membrane paradigm fluid charges reproduce the near-horizon BMS algebra. The perspective presented here may be useful for understanding the BMS algebra at null infinity.

Archaeal Haloarcula californiae Icosahedral Virus 1 Highlights Conserved Elements in Icosahedral Membrane-Containing DNA Viruses from Extreme Environments.

PubMed

Demina, Tatiana A; Pietilä, Maija K; Svirskaitė, Julija; Ravantti, Janne J; Atanasova, Nina S; Bamford, Dennis H; Oksanen, Hanna M

2016-07-19

Despite their high genomic diversity, all known viruses are structurally constrained to a limited number of virion morphotypes. One morphotype of viruses infecting bacteria, archaea, and eukaryotes is the tailless icosahedral morphotype with an internal membrane. Although it is considered an abundant morphotype in extreme environments, only seven such archaeal viruses are known. Here, we introduce Haloarcula californiae icosahedral virus 1 (HCIV-1), a halophilic euryarchaeal virus originating from salt crystals. HCIV-1 also retains its infectivity under low-salinity conditions, showing that it is able to adapt to environmental changes. The release of progeny virions resulting from cell lysis was evidenced by reduced cellular oxygen consumption, leakage of intracellular ATP, and binding of an indicator ion to ruptured cell membranes. The virion contains at least 12 different protein species, lipids selectively acquired from the host cell membrane, and a 31,314-bp-long linear double-stranded DNA (dsDNA). The overall genome organization and sequence show high similarity to the genomes of archaeal viruses in the Sphaerolipoviridae family. Phylogenetic analysis based on the major conserved components needed for virion assembly-the major capsid proteins and the packaging ATPase-placed HCIV-1 along with the alphasphaerolipoviruses in a distinct, well-supported clade. On the basis of its virion morphology and sequence similarities, most notably, those of its core virion components, we propose that HCIV-1 is a member of the PRD1-adenovirus structure-based lineage together with other sphaerolipoviruses. This addition to the lineage reinforces the notion of the ancient evolutionary links observed between the viruses and further highlights the limits of the choices found in nature for formation of a virion. Under conditions of extreme salinity, the majority of the organisms present are archaea, which encounter substantial selective pressure, being constantly attacked by

Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.

PubMed

Charbonneau, Patrick; Yaida, Sho

2017-05-26

The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon-the Gardner transition-has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, d_{u}=6. Here, we obtain evidence for the existence of these transitions in dpoint is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.

Observation of valleylike edge states of sound at a momentum away from the high-symmetry points

NASA Astrophysics Data System (ADS)

Xia, Bai-Zhan; Zheng, Sheng-Jie; Liu, Ting-Ting; Jiao, Jun-Rui; Chen, Ning; Dai, Hong-Qing; Yu, De-Jie; Liu, Jian

2018-04-01

In condensed matter physics, topologically protected edge transportation has drawn extensive attention over recent years. Thus far, the topological valley edge states have been produced near the Dirac cones fixed at the high-symmetry points of the Brillouin zone. In this paper, we demonstrate a unique valleylike phononic crystal (PnC) with the position-varying Dirac cones at the high-symmetry lines of the Brillouin zone boundary. The emergence of such Dirac cones, characterized by the vortex structure in a momentum space, is attributed to the unavoidable band crossing protected by the mirror symmetry. The Dirac cones can be unbuckled and a complete band gap can be induced through breaking the mirror symmetry. Interestingly, by simply rotating the square columns, we realize the valleylike vortex states and the band inversion effect which leads to the valley Hall phase transition. Along the valleylike PnC interfaces separating two distinct acoustic valley Hall phases, the valleylike protected edge transport of sound in domain walls is observed in both the simulations and the experiments. These results are promising for the exploration of alternative topological phenomena in the valleylike PnCs beyond the graphenelike lattice.

Structure-based engineering of an icosahedral virus for nanomedicine and nanotechnology.

PubMed

Steinmetz, N F; Lin, T; Lomonossoff, G P; Johnson, J E

2009-01-01

A quintessential tenet of nanotechnology is the self-assembly of nanometer-sized components into devices. Biological macromolecular systems such as viral particles were found to be suitable building blocks for nanotechnology for several reasons: viral capsids are extremely robust and can be produced in large quantities with ease, the particles self-assemble into monodisperse particles with a high degree of symmetry and polyvalency, they have the propensity to form arrays, and they offer programmability through genetic and chemical engineering. Here, we review the recent advances in engineering the icosahedral plant virus Cowpea mosaic virus (CPMV) for applications in nano-medicine and -technology. In the first part, we will discuss how the combined knowledge of the structure of CPMV at atomic resolution and the use of chimeric virus technology led to the generation of CPMV particles with short antigenic peptides for potential use as vaccine candidates. The second part focuses on the chemical addressability of CPMV. Strategies to chemically attach functional molecules at designed positions on the exterior surface of the viral particle are described. Biochemical conjugation methods led to the fabrication of electronically conducting CPMV particles and networks. In addition, functional proteins for targeted delivery to mammalian cells were successfully attached to CPMV. In the third part, we focus on the utilization of CPMV as a building block for the generation of 2D and 3D arrays. Overall, the potential applications of viral nanobuilding blocks are manifold and range from nanoelectronics to biomedical applications.

Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns

NASA Astrophysics Data System (ADS)

Kiselev, Alexei D.; Chigrinov, Vladimir G.

2014-10-01

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled.

Prediction of molecular crystal structures by a crystallographic QM/MM model with full space-group symmetry.

PubMed

Mörschel, Philipp; Schmidt, Martin U

2015-01-01

A crystallographic quantum-mechanical/molecular-mechanical model (c-QM/MM model) with full space-group symmetry has been developed for molecular crystals. The lattice energy was calculated by quantum-mechanical methods for short-range interactions and force-field methods for long-range interactions. The quantum-mechanical calculations covered the interactions within the molecule and the interactions of a reference molecule with each of the surrounding 12-15 molecules. The interactions with all other molecules were treated by force-field methods. In each optimization step the energies in the QM and MM shells were calculated separately as single-point energies; after adding both energy contributions, the crystal structure (including the lattice parameters) was optimized accordingly. The space-group symmetry was maintained throughout. Crystal structures with more than one molecule per asymmetric unit, e.g. structures with Z' = 2, hydrates and solvates, have been optimized as well. Test calculations with different quantum-mechanical methods on nine small organic molecules revealed that the density functional theory methods with dispersion correction using the B97-D functional with 6-31G* basis set in combination with the DREIDING force field reproduced the experimental crystal structures with good accuracy. Subsequently the c-QM/MM method was applied to nine compounds from the CCDC blind tests resulting in good energy rankings and excellent geometric accuracies.

Symmetry and equivalence restrictions in electronic structure calculations

NASA Technical Reports Server (NTRS)

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

1988-01-01

A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2017-03-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2013-06-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested

Validation of missed space-group symmetry in X-ray powder diffraction structures with dispersion-corrected density functional theory.

PubMed

Hempler, Daniela; Schmidt, Martin U; van de Streek, Jacco

2017-08-01

More than 600 molecular crystal structures with correct, incorrect and uncertain space-group symmetry were energy-minimized with dispersion-corrected density functional theory (DFT-D, PBE-D3). For the purpose of determining the correct space-group symmetry the required tolerance on the atomic coordinates of all non-H atoms is established to be 0.2 Å. For 98.5% of 200 molecular crystal structures published with missed symmetry, the correct space group is identified; there are no false positives. Very small, very symmetrical molecules can end up in artificially high space groups upon energy minimization, although this is easily detected through visual inspection. If the space group of a crystal structure determined from powder diffraction data is ambiguous, energy minimization with DFT-D provides a fast and reliable method to select the correct space group.

Controlling the Growth of Au on Icosahedral Seeds of Pd by Manipulating the Reduction Kinetics

DOE PAGES

Lv, Tian; Yang, Xuan; Zheng, Yiqun; ...

2016-03-29

This article reports a systematic study of how Au atoms nucleate and grow on Pd icosahedral seeds with a multiply twinned structure. By manipulating the reduction kinetics, we obtained Pd–Au bimetallic nanocrystals with two distinct shapes and structures. Specifically, Pd@Au core–shell icosahedra were formed when a relatively fast reduction rate was used for the HAuCl 4 precursor. At a slow reduction rate, in contrast, the nucleation and growth of Au atoms were mainly confined to one of the vertices of a Pd icosahedral seed, resulting in the formation of a Au icosahedron by sharing five adjacent faces with the Pdmore » seed. The same growth pattern was observed for Pd icosahedral seeds with both sizes of 32 and 20 nm. Also, we have also investigated the effects of other kinetic parameters, including the concentration of reducing agent and reaction temperature, on the growth pathway undertaken by the Au atoms. In conclusion, we believe that the mechanistic insights obtained from this study can be extended to other systems, including the involvement of different metals and/or seeds with different morphologies.« less

Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

PubMed Central

Wang, Gang wei; Xu, Tian zhou; Feng, Tao

2014-01-01

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided. PMID:24523885

Additional evidence from x-ray powder diffraction patterns that icosahedral quasi-crystals of intermetallic compounds are twinned cubic crystals

PubMed Central

Pauling, Linus

1988-01-01

Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, “noise”) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals. PMID:16593948

Itinerant ferromagnetism in fermionic systems with SP (2 N) symmetry

NASA Astrophysics Data System (ADS)

Yang, Wang; Wu, Congjun

The Ginzburg-Landau free energy of systems with SP (2 N) symmetry describes a second order phase transition on the mean field level, since the Casimir invariants of the SP (2 N) group can be only of even order combinations of the generators of the SP (2 N) group. This is in contrast with systems having the SU (N) symmetry, where the allowance of cubic term generally makes the phase transition into first order. In this work, we consider the Hertz-Millis type itinerant ferromagnetism in an interacting fermionic system with SP (2 N) symmetry, where the ferromagnetic orders are enriched by the multi-component nature of the system. The quantum criticality is discussed near the second order phase transition point.

Cooperative Formation of Icosahedral Proline Clusters from Dimers

NASA Astrophysics Data System (ADS)

Jacobs, Alexander D.; Jovan Jose, K. V.; Horness, Rachel; Raghavachari, Krishnan; Thielges, Megan C.; Clemmer, David E.

2018-01-01

Ion mobility spectrometry-mass spectrometry and Fourier transform infrared spectroscopy (FTIR) techniques were combined with quantum chemical calculations to examine the origin of icosahedral clusters of the amino acid proline. When enantiopure proline solutions are electrosprayed (using nanospray) from 100 mM ammonium acetate, only three peaks are observed in the mass spectrum across a concentration range of five orders of magnitude: a monomer [Pro+H]+ species, favored from 0.001 to 0.01 mM proline concentrations; a dimer [2Pro+H]+ species, the most abundant species for proline concentrations above 0.01 mM; and, the dimer and dodecamer [12Pro+2H]2+ for 1.0 mM and more concentrated proline solutions. Electrospraying racemic D/ L-proline solutions from 100 mM ammonium acetate leads to a monomer at low proline concentrations (0.001 to 0.1 mM), and a dimer at higher concentrations (>0.09 mM), as well as a very small population of 8 to 15 Pro clusters that comprise <0.1% of the total ion signals even at the highest proline concentration. Solution FTIR studies show unique features that increase in intensity in the enantiopure proline solutions, consistent with clustering, presumably from the icosahedral geometry in bulk solution. When normalized for the total proline, these results are indicative of a cooperative formation of the enantiopure 12Pro species from 2Pro. [Figure not available: see fulltext.

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

NASA Astrophysics Data System (ADS)

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

2008-03-01

A new type of ultra-high resolution atmospheric global circulation model is developed. The new model is designed to perform "cloud resolving simulations" by directly calculating deep convection and meso-scale circulations, which play key roles not only in the tropical circulations but in the global circulations of the atmosphere. Since cores of deep convection have a few km in horizontal size, they have not directly been resolved by existing atmospheric general circulation models (AGCMs). In order to drastically enhance horizontal resolution, a new framework of a global atmospheric model is required; we adopted nonhydrostatic governing equations and icosahedral grids to the new model, and call it Nonhydrostatic ICosahedral Atmospheric Model (NICAM). In this article, we review governing equations and numerical techniques employed, and present the results from the unique 3.5-km mesh global experiments—with O(10 9) computational nodes—using realistic topography and land/ocean surface thermal forcing. The results show realistic behaviors of multi-scale convective systems in the tropics, which have not been captured by AGCMs. We also argue future perspective of the roles of the new model in the next generation atmospheric sciences.

Simulations of polymorphic icosahedral shells assembling around many cargo molecules

NASA Astrophysics Data System (ADS)

Mohajerani, Farzaneh; Perlmutter, Jason; Hagan, Michael

Bacterial microcompartments (BMCs) are large icosahedral shells that sequester the enzymes and reactants responsible for particular metabolic pathways in bacteria. Although different BMCs vary in size and encapsulate different cargoes, they are constructed from similar pentameric and hexameric shell proteins. Despite recent groundbreaking experiments which visualized the formation of individual BMCs, the detailed assembly pathways and the factors which control shell size remain unclear. In this talk, we describe theoretical and computational models that describe the dynamical encapsulation of hundreds of cargo molecules by self-assembling icosahedral shells. We present phase diagrams and analysis of dynamical simulation trajectories showing how the thermodynamics, assembly pathways, and emergent structures depend on the interactions among shell proteins and cargo molecules. Our model suggests a mechanism for controlling insertion of the 12 pentamers required for a closed shell topology, and the relationship between assembly pathway and BMC size polydispersity. In addition to elucidating how native BMCs assemble,our results establish principles for reengineering BMCs or viral capsids as customizable nanoreactors that can assemble around a programmable set of enzymes and reactants. Supported by NIH R01GM108021 and Brandeis MRSEC DMR-1420382.

Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

PubMed

Nascimento, Daniel R; DePrince, A Eugene

2018-05-08

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

Relative Critical Points

NASA Astrophysics Data System (ADS)

Lewis, Debra

2013-05-01

Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic, Poisson, or variational - generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (co)adjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems - the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids - and generalizations of these systems.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

How does symmetry impact the flexibility of proteins?

PubMed

Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter

2014-02-13

It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures-and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body-bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body-bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains.

How does symmetry impact the flexibility of proteins?

PubMed Central

Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter

2014-01-01

It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures—and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body–bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body–bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains. PMID:24379431

Analysis of pulsed-neutron powder diffraction patterns of the icosahedral quasicrystals Pd3Siu and AlCuLiMg (three alloys) as twinned cubic crystals with large units.

PubMed Central

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

Analysis of pulsed-neutron powder diffraction patterns of the icosahedral quasicrystals Pd3Siu and AlCuLiMg (three alloys) as twinned cubic crystals with large units.

PubMed

Pauling, L

1991-08-01

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.

On the kinetic and equilibrium shapes of icosahedral Al 71Pd 19Mn 10 quasicrystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Senabulya, Nancy; Xiao, Xianghui; Han, Insung

The dynamics of growth and relaxation of icosahedral single quasicrystals in a liquid phase were investigated using in situ synchrotron-based X-ray tomography. Here, our 4D studies (i.e., space- and time-resolved) provide direct evidence that indicates the growth process of an Al 71Pd 19Mn 10 quasicrystal is governed predominantly by bulk transport rather than attachment kinetics. This work is in agreement with theoretical predictions, which show that the pentagonal dodecahedron is not the minimum energy structure in Al-Pd-Mn icosahedral quasicrystals, but merely a growth shape characterized by non-zero anisotropic velocity. This transient shape transforms into a truncated dodecahedral Archimedian polyhedron oncemore » equilibrium has been attained.« less

On the kinetic and equilibrium shapes of icosahedral Al 71Pd 19Mn 10 quasicrystals

DOE PAGES

Senabulya, Nancy; Xiao, Xianghui; Han, Insung; ...

2018-03-06

The dynamics of growth and relaxation of icosahedral single quasicrystals in a liquid phase were investigated using in situ synchrotron-based X-ray tomography. Here, our 4D studies (i.e., space- and time-resolved) provide direct evidence that indicates the growth process of an Al 71Pd 19Mn 10 quasicrystal is governed predominantly by bulk transport rather than attachment kinetics. This work is in agreement with theoretical predictions, which show that the pentagonal dodecahedron is not the minimum energy structure in Al-Pd-Mn icosahedral quasicrystals, but merely a growth shape characterized by non-zero anisotropic velocity. This transient shape transforms into a truncated dodecahedral Archimedian polyhedron oncemore » equilibrium has been attained.« less

Determination of Patterson group symmetry from sparse multi-crystal data sets in the presence of an indexing ambiguity.

PubMed

Gildea, Richard J; Winter, Graeme

2018-05-01

Combining X-ray diffraction data from multiple samples requires determination of the symmetry and resolution of any indexing ambiguity. For the partial data sets typical of in situ room-temperature experiments, determination of the correct symmetry is often not straightforward. The potential for indexing ambiguity in polar space groups is also an issue, although methods to resolve this are available if the true symmetry is known. Here, a method is presented to simultaneously resolve the determination of the Patterson symmetry and the indexing ambiguity for partial data sets. open access.

Unified structure theory of icosahedral quasicrystals: Evidence from neutron powder diffraction patterns that AlCrFeMnSi, AlCuLiMg, and TiNiFeSi icosahedral quasicrystals are twins of cubic crystals containing about 820 or 1012 atoms in a primitive unit cube

PubMed Central

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

High-resolution electron microscopy observation of a new crystalline approximant W' of Mg-Zn-Y icosahedral quasicrystal

PubMed

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.

Present knowledge of electronic properties and charge transport of icosahedral boron-rich solids

NASA Astrophysics Data System (ADS)

Werheit, Helmut

2009-06-01

B12 icosahedra or related structure elements determine the different modifications of elementary boron and numerous boron-rich compounds from α-rhombohedral boron with 12 to YB66 type with about 1584 atoms per unit cell. Typical are well-defined high density intrinsic defects: Jahn-Teller distorted icosahedra, vacancies, incomplete occupancies, statistical occupancies and antisite defects. The correlation between intrinsic point defects and electron deficiencies solves the discrepancy between theoretically predicted metal and experimentally proved semiconducting character. The electron deficiencies generate split-off valence states, which are decisive for the electronic transport, a superposition of band-type and hopping-type conduction. Their share depends on actual conditions like temperature or pre-excitation. The theoretical model of bipolaron hopping is incompatible with numerous experiments. Technical application of the typically p-type icosahedral boron-rich solids requires suitable n-type counterparts; doping and other possibilities are discussed.

Structural symmetry and protein function.

PubMed

Goodsell, D S; Olson, A J

2000-01-01

The majority of soluble and membrane-bound proteins in modern cells are symmetrical oligomeric complexes with two or more subunits. The evolutionary selection of symmetrical oligomeric complexes is driven by functional, genetic, and physicochemical needs. Large proteins are selected for specific morphological functions, such as formation of rings, containers, and filaments, and for cooperative functions, such as allosteric regulation and multivalent binding. Large proteins are also more stable against denaturation and have a reduced surface area exposed to solvent when compared with many individual, smaller proteins. Large proteins are constructed as oligomers for reasons of error control in synthesis, coding efficiency, and regulation of assembly. Symmetrical oligomers are favored because of stability and finite control of assembly. Several functions limit symmetry, such as interaction with DNA or membranes, and directional motion. Symmetry is broken or modified in many forms: quasisymmetry, in which identical subunits adopt similar but different conformations; pleomorphism, in which identical subunits form different complexes; pseudosymmetry, in which different molecules form approximately symmetrical complexes; and symmetry mismatch, in which oligomers of different symmetries interact along their respective symmetry axes. Asymmetry is also observed at several levels. Nearly all complexes show local asymmetry at the level of side chain conformation. Several complexes have reciprocating mechanisms in which the complex is asymmetric, but, over time, all subunits cycle through the same set of conformations. Global asymmetry is only rarely observed. Evolution of oligomeric complexes may favor the formation of dimers over complexes with higher cyclic symmetry, through a mechanism of prepositioned pairs of interacting residues. However, examples have been found for all of the crystallographic point groups, demonstrating that functional need can drive the evolution of

A Vertically Flow-Following, Icosahedral Grid Model for Medium-Range and Seasonal Prediction. Part 1: Model Description

NASA Technical Reports Server (NTRS)

Bleck, Rainer; Bao, Jian-Wen; Benjamin, Stanley G.; Brown, John M.; Fiorino, Michael; Henderson, Thomas B.; Lee, Jin-Luen; MacDonald, Alexander E.; Madden, Paul; Middlecoff, Jacques;

Isolation and Characterization of Metallosphaera turreted icosahedral virus (MTIV), a founding member of a new family of archaeal viruses.

PubMed

Wagner, Cassia; Reddy, Vijay; Asturias, Francisco; Khoshouei, Maryam; Johnson, John E; Manrique, Pilar; Munson-McGee, Jacob; Baumeister, Wolfgang; Lawrence, C Martin; Young, Mark J

2017-08-02

Our understanding of archaeal virus diversity and structure is just beginning to emerge. Here we describe a new archaeal virus, tentatively named Metallosphaera turreted icosahedral virus (MTIV), that was isolated from an acidic hot spring in Yellowstone National Park, USA. Two strains of the virus were identified and found to replicate in an archaeal host species closely related to Metallosphaera yellowstonensis Each strain encodes for a 9.8-9.9 kb, linear dsDNA genome with large inverted terminal repeats. Each genome encodes for 21 ORFs. Between the strains the ORFs display high homology, but they are quite distinct from other known viral genes. The 70-nm diameter virion is built upon on a T=28 icosahedral lattice. Both single particle cryo-electron microscopy and cryo-tomography reconstructions reveal an unusual structure that has 42 turret-like projections: 12 from each of the 5-fold axes and 30 hexameric units positioned on icosahedral 2-fold axes. Both the virion structural properties and genome content support MTIV as the founding member of a new family of archaeal viruses. Importance: Many archaeal viruses are quite different than viruses infecting bacteria and eukaryotes. Initial characterization of MTIV reveals a virus distinct from other known bacterial, eukaryotic, and archaeal viruses; this finding suggests that viruses infecting Archaea are still an understudied group of viruses. As the first known virus infecting the Metallosphaera , MTIV provides a new system for exploring archaeal virology by examining host-virus interactions and the unique features of MTIV structure-function relationships. These studies will likely expand our understanding of virus ecology and evolution. Copyright © 2017 American Society for Microbiology.

Asymptotic symmetries on Killing horizons

NASA Astrophysics Data System (ADS)

Koga, Jun-Ichirou

2001-12-01

We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.

Theory of phase diagrams described by thermodynamic potentials with T d symmetry

NASA Astrophysics Data System (ADS)

Mukovnin, A. A.; Talanov, V. M.

2014-09-01

Phase diagrams of crystals induced by irreducible representations with symmetry group ( T d ) are constructed within the phenomenological theory of second-order phase transitions. A model of the Landau thermodynamic potential is studied, state equations of all symmetry-conditioned phases are obtained, and general conditions for their thermodynamic stability are formulated. Equations for the boundaries of phase areas and lines of phase transitions are obtained for the fourth order of expansion of the potential via components of the order parameter. Some types of the collapse of the multicritical point of the phase diagram for the eighth order of potential expansion are studied using computer calculations. The possible existence of phase diagrams that contain one or more triple points and areas of existence of three and four phases is shown for the first time for the potentials with the above symmetry. Examples are given of crystals that undergo phase transitions in the considered symmetry of the order parameter.

Enhanced Facial Symmetry Assessment in Orthodontists

PubMed Central

Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.

2013-01-01

Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342

Group Theoretical Route to Deterministic Weyl Points in Chiral Photonic Lattices.

PubMed

Saba, Matthias; Hamm, Joachim M; Baumberg, Jeremy J; Hess, Ortwin

2017-12-01

Topological phases derived from point degeneracies in photonic band structures show intriguing and unique behavior. Previously identified band degeneracies are based on accidental degeneracies and subject to engineering on a case-by-case basis. Here we show that deterministic pseudo Weyl points with nontrivial topology and hyperconic dispersion exist at the Brillouin zone center of chiral cubic symmetries. This conceivably allows realization of topologically protected frequency isolated surface bands in 3D and n=0 properties as demonstrated for a nanoplasmonic system and a photonic crystal.

Group Theoretical Route to Deterministic Weyl Points in Chiral Photonic Lattices

NASA Astrophysics Data System (ADS)

Saba, Matthias; Hamm, Joachim M.; Baumberg, Jeremy J.; Hess, Ortwin

2017-12-01

Topological phases derived from point degeneracies in photonic band structures show intriguing and unique behavior. Previously identified band degeneracies are based on accidental degeneracies and subject to engineering on a case-by-case basis. Here we show that deterministic pseudo Weyl points with nontrivial topology and hyperconic dispersion exist at the Brillouin zone center of chiral cubic symmetries. This conceivably allows realization of topologically protected frequency isolated surface bands in 3D and n =0 properties as demonstrated for a nanoplasmonic system and a photonic crystal.

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

NASA Astrophysics Data System (ADS)

Xiong, Charles Zhaoxi; Alexandradinata, A.

2018-03-01

It is demonstrated that fermionic/bosonic symmetry-protected topological (SPT) phases across different dimensions and symmetry classes can be organized using geometric constructions that increase dimensions and symmetry-reduction maps that change symmetry groups. Specifically, it is shown that the interacting classifications of SPT phases with and without glide symmetry fit into a short exact sequence, so that the classification with glide is constrained to be a direct sum of cyclic groups of order 2 or 4. Applied to fermionic SPT phases in the Wigner-Dyson class AII, this implies that the complete interacting classification in the presence of glide is Z4⊕Z2⊕Z2 in three dimensions. In particular, the hourglass-fermion phase recently realized in the band insulator KHgSb must be robust to interactions. Generalizations to spatiotemporal glide symmetries are discussed.

Identification, display, and use of symmetry elements in atomic and electronic structure models.

PubMed

Khosrovani, N; Kung, P W; Freeman, C M; Gorman, A M; Kölmel, C M; Levine, S M; Newsam, J M

1999-01-01

Crystallographic symmetry plays an important role in structure determination from diffraction or scattering data, in spectroscopy and in simulations. It is convenient and insightful to integrate the display and use of such symmetry data with data analysis and modeling methods. We outline the integration of a suite of crystallographic algorithms, closely coupled with interactive graphical displays. These include techniques for identifying the unit cell of a solid, for automatically determining space and point group symmetries, for generalized displays of symmetry elements overlaid on structural models, and for construction, editing, and transformation of models subject to symmetry constraints. In addition, electron densities derived from periodic density functional calculations can be symmetrized and displayed with the corresponding symmetry elements. Applications of these various capabilities in crystallographic research are illustrated by topical examples.

Symmetry-breaking oscillations in membrane optomechanics

NASA Astrophysics Data System (ADS)

Wurl, C.; Alvermann, A.; Fehske, H.

2016-12-01

We study the classical dynamics of a membrane inside a cavity in the situation where this optomechanical system possesses a reflection symmetry. Symmetry breaking occurs through supercritical and subcritical pitchfork bifurcations of the static fixed-point solutions. Both bifurcations can be observed through variation of the laser-cavity detuning, which gives rise to a boomerang-like fixed-point pattern with hysteresis. The symmetry-breaking fixed points evolve into self-sustained oscillations when the laser intensity is increased. In addition to the analysis of the accompanying Hopf bifurcations we describe these oscillations at finite amplitudes with an ansatz that fully accounts for the frequency shift relative to the natural membrane frequency. We complete our study by following the route to chaos for the membrane dynamics.

ISO(4,1) symmetry in the EFT of inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Creminelli, Paolo; Emami, Razieh; Simonović, Marko

In DBI inflation the cubic action is a particular linear combination of the two, otherwise independent, cubic operators π-dot {sup 3} and π-dot (∂{sub i}π){sup 2}. We show that in the Effective Field Theory (EFT) of inflation this is a consequence of an approximate 5D Poincar and apos;e symmetry, ISO(4,1), non-linearly realized by the Goldstone π. This symmetry uniquely fixes, at lowest order in derivatives, all correlation functions in terms of the speed of sound c{sub s}. In the limit c{sub s} → 1, the ISO(4,1) symmetry reduces to the Galilean symmetry acting on π. On the other hand, wemore » point out that the non-linear realization of SO(4,2), the isometry group of 5D AdS space, does not fix the cubic action in terms of c{sub s}.« less

Symmetries of relativistic world lines

NASA Astrophysics Data System (ADS)

Koch, Benjamin; Muñoz, Enrique; Reyes, Ignacio A.

2017-10-01

Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a fundamental symmetry, which is present for any Lagrangian term that involves x˙2. As a basic model that incorporates the fundamental symmetries of quantum gravity and string theory, we consider the Lagrangian action of the relativistic point particle. A path integral quantization for this seemingly simple system has long presented notorious problems. Here we show that those problems are overcome by taking into account the additional symmetry, leading directly to the exact Klein-Gordon propagator.

Structure of epsilon15 bacteriophage reveals genome organization and DNA packaging/injection apparatus

NASA Astrophysics Data System (ADS)

Jiang, Wen; Chang, Juan; Jakana, Joanita; Weigele, Peter; King, Jonathan; Chiu, Wah

2006-02-01

The critical viral components for packaging DNA, recognizing and binding to host cells, and injecting the condensed DNA into the host are organized at a single vertex of many icosahedral viruses. These component structures do not share icosahedral symmetry and cannot be resolved using a conventional icosahedral averaging method. Here we report the structure of the entire infectious Salmonella bacteriophage epsilon15 (ref. 1) determined from single-particle cryo-electron microscopy, without icosahedral averaging. This structure displays not only the icosahedral shell of 60 hexamers and 11 pentamers, but also the non-icosahedral components at one pentameric vertex. The densities at this vertex can be identified as the 12-subunit portal complex sandwiched between an internal cylindrical core and an external tail hub connecting to six projecting trimeric tailspikes. The viral genome is packed as coaxial coils in at least three outer layers with ~90 terminal nucleotides extending through the protein core and the portal complex and poised for injection. The shell protein from icosahedral reconstruction at higher resolution exhibits a similar fold to that of other double-stranded DNA viruses including herpesvirus, suggesting a common ancestor among these diverse viruses. The image reconstruction approach should be applicable to studying other biological nanomachines with components of mixed symmetries.

Functional renormalization group approach to electronic structure calculations for systems without translational symmetry

NASA Astrophysics Data System (ADS)

Seiler, Christian; Evers, Ferdinand

2016-10-01

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.

Scale-chiral symmetry, ω meson, and dense baryonic matter

NASA Astrophysics Data System (ADS)

Ma, Yong-Liang; Rho, Mannque

2018-05-01

It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension (|γG2| ) of the gluon field strength tensor squared (G2 ) that represents the quantum trace anomaly should be 1.0 ≲|γG2|≲3.5 . The magnitude of |γG2| estimated here will be useful for studying hadron and nuclear physics based on the scale-chiral effective theory. More significantly, that the dilaton limit fixed point can be arrived at with γG2≠0 at some high density signals that scale symmetry can arise in dense medium as an "emergent" symmetry.

Hyperbolic-symmetry vector fields.

PubMed

Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2015-12-14

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

AFLOW-SYM: platform for the complete, automatic and self-consistent symmetry analysis of crystals.

PubMed

Hicks, David; Oses, Corey; Gossett, Eric; Gomez, Geena; Taylor, Richard H; Toher, Cormac; Mehl, Michael J; Levy, Ohad; Curtarolo, Stefano

2018-05-01

Determination of the symmetry profile of structures is a persistent challenge in materials science. Results often vary amongst standard packages, hindering autonomous materials development by requiring continuous user attention and educated guesses. This article presents a robust procedure for evaluating the complete suite of symmetry properties, featuring various representations for the point, factor and space groups, site symmetries and Wyckoff positions. The protocol determines a system-specific mapping tolerance that yields symmetry operations entirely commensurate with fundamental crystallographic principles. The self-consistent tolerance characterizes the effective spatial resolution of the reported atomic positions. The approach is compared with the most used programs and is successfully validated against the space-group information provided for over 54 000 entries in the Inorganic Crystal Structure Database (ICSD). Subsequently, a complete symmetry analysis is applied to all 1.7+ million entries of the AFLOW data repository. The AFLOW-SYM package has been implemented in, and made available for, public use through the automated ab initio framework AFLOW.

Magnetism in icosahedral quasicrystals: current status and open questions

DOE PAGES

Goldman, Alan I.

2014-07-02

Progress in our understanding of the magnetic properties of R-containing icosahedral quasicrystals (R = rare earth element) from over 20 years of experimental effort is reviewed. This includes the much studied R-Mg-Zn and R-Mg-Cd ternary systems, as well as several magnetic quasicrystals that have been discovered and investigated more recently including Sc-Fe-Zn, R-Ag-In, Yb-Au-Al, the recently synthesized R-Cd binary quasicrystals, and their periodic approximants. In many ways, the magnetic properties among these quasicrystals are very similar. However, differences are observed that suggest new experiments and promising directions for future research.

Terahertz emission from the intrinsic Josephson junctions of high-symmetry thermally-managed Bi2Sr2CaCu2O8+δ microstrip antennas

NASA Astrophysics Data System (ADS)

Klemm, Richard A.; Davis, Andrew E.; Wang, Qing X.; Yamamoto, Takashi; Cerkoney, Daniel P.; Reid, Candy; Koopman, Maximiliaan L.; Minami, Hidetoshi; Kashiwagi, Takanari; Rain, Joseph R.; Doty, Constance M.; Sedlack, Michael A.; Morales, Manuel A.; Watanabe, Chiharu; Tsujimoto, Manabu; Delfanazari, Kaveh; Kadowaki, Kazuo

2017-12-01

We show for high-symmetry disk, square, or equilateral triangular thin microstrip antennas of any composition respectively obeying C ∞v , C 4v , and C 3v point group symmetries, that the transverse magnetic electromagnetic cavity mode wave functions are restricted in form to those that are one-dimensional representations of those point groups. Plots of the common nodal points of the ten lowest-energy non-radiating two-dimensional representations of each of these three symmetries are presented. For comparison with symmetry-broken disk intrinsic Josephson junction microstrip antennas constructed from the highly anisotropic layered superconductor Bi2Sr2CaCu2O8+δ (BSCCO), we present plots of the ten lowest frequency orthonormal wave functions and of their emission power angular distributions. These results are compared with previous results for square and equilateral triangular thin microstrip antennas.

Notation Confusion of Symmetry Species for Molecules with Several Large-Amplitude Internal Motions

NASA Astrophysics Data System (ADS)

Groner, P.

2011-06-01

The Mulliken convention has become the standard notation for symmetry species (irreducible representations) of point groups for quasi-rigid molecules. No such convention exists for symmetry species of symmetry groups for semi-rigid or non-rigid molecules with large amplitude internal motions (LAMs). As a result, we have a situation where we create notations in a do-it-yourself fashion or adopt them from the literature, sometimes even without proper reference to its derivation or to the character table on which it is based. This may be just a nuisance for those who are comfortable enough with group theory and molecular symmetry groups to figure "it" out, but it represents a real problem for everybody else. The notation confusion is illustrated with examples from the literature (both old and new) on molecules with two or more LAMs. Most authors use the notation introduced by Myers and Wilson for molecules such as acetone or propane. No universal notation is in use for molecules with two methyl groups but lower overall symmetry. For example, the notation G_1_8 is used for one of these groups. As it turns out, different people use the same notation for different groups. This presentation is an attempt to bring some light into the dark and to combat confusion with a call for an anti-confusion convention. R. S. Mulliken, Phys. Rev. 43, 279 (1933). R. J. Myers, E. B. Wilson, J. Chem. Phys. 33, 186 (1960).

Symmetry-protected topological insulator and its symmetry-enriched topologically ordered boundary

NASA Astrophysics Data System (ADS)

Wang, Juven; Wen, Xiao-Gang; Witten, Edward

We propose a mechanism for achieving symmetry-enriched topologically ordered boundaries for symmetry-protected topological states, including those of topological insulators. Several different boundary phases and their phase transitions are considered, including confined phases, deconfined phases, symmetry-breaking, gapped and gapless phases. National Science Foundation PHY-1606531, Corning Glass Works Foundation Fellowship, NSF Grant DMR- 1506475 and NSFC 11274192, the BMO Financial Group and the John Templeton Foundation No. 39901.

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

DOE PAGES

Cvetič, Mirjam; Grassi, Antonella; Poretschkin, Maximilian

2017-06-30

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairsmore » for symmetric examples with Z 2 and Z 3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.« less

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cvetič, Mirjam; Grassi, Antonella; Poretschkin, Maximilian

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairsmore » for symmetric examples with Z 2 and Z 3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.« less

Generalized global symmetries

DOE PAGES

Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan; ...

2015-02-26

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 havemore » ’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. In conclusion, our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.« less

Diphosphine-protected ultrasmall gold nanoclusters: opened icosahedral Au 13 and heart-shaped Au 8 clusters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Shan-Shan; Feng, Lei; Senanayake, Ravithree D.

Two ultrasmall gold clusters, Au 13 and Au 8 , were identified as a distorted I h icosahedral Au 13 and edge-shared “core + 4 exo ” structure Au 8 S 2 cores, respectively. They showed interesting luminescence and electrochemical properties.

Diphosphine-protected ultrasmall gold nanoclusters: opened icosahedral Au 13 and heart-shaped Au 8 clusters

DOE PAGES

Zhang, Shan-Shan; Feng, Lei; Senanayake, Ravithree D.; ...

2018-01-01

Two ultrasmall gold clusters, Au 13 and Au 8 , were identified as a distorted I h icosahedral Au 13 and edge-shared “core + 4 exo ” structure Au 8 S 2 cores, respectively. They showed interesting luminescence and electrochemical properties.

Band warping, band non-parabolicity, and Dirac points in electronic and lattice structures

NASA Astrophysics Data System (ADS)

Resca, Lorenzo; Mecholsky, Nicholas A.; Pegg, Ian L.

2017-10-01

We illustrate at a fundamental level the physical and mathematical origins of band warping and band non-parabolicity in electronic and vibrational structures. We point out a robust presence of pairs of topologically induced Dirac points in a primitive-rectangular lattice using a p-type tight-binding approximation. We analyze two-dimensional primitive-rectangular and square Bravais lattices with implications that are expected to generalize to more complex structures. Band warping is shown to arise at the onset of a singular transition to a crystal lattice with a larger symmetry group, which allows the possibility of irreducible representations of higher dimensions, hence band degeneracy, at special symmetry points in reciprocal space. Band warping is incompatible with a multi-dimensional Taylor series expansion, whereas band non-parabolicities are associated with multi-dimensional Taylor series expansions to all orders. Still band non-parabolicities may merge into band warping at the onset of a larger symmetry group. Remarkably, while still maintaining a clear connection with that merging, band non-parabolicities may produce pairs of conical intersections at relatively low-symmetry points. Apparently, such conical intersections are robustly maintained by global topology requirements, rather than any local symmetry protection. For two p-type tight-binding bands, we find such pairs of conical intersections drifting along the edges of restricted Brillouin zones of primitive-rectangular Bravais lattices as lattice constants vary relatively to each other, until these conical intersections merge into degenerate warped bands at high-symmetry points at the onset of a square lattice. The conical intersections that we found appear to have similar topological characteristics as Dirac points extensively studied in graphene and other topological insulators, even though our conical intersections have none of the symmetry complexity and protection afforded by the latter more

On the symmetries of integrability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellon, M.; Maillard, J.M.; Viallet, C.

1992-06-01

In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

Integrability from point symmetries in a family of cosmological Horndeski Lagrangians

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos

2017-07-01

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

Studies of inactivation mechanism of non-enveloped icosahedral virus by a visible ultrashort pulsed laser

PubMed Central

2014-01-01

Background Low-power ultrashort pulsed (USP) lasers operating at wavelengths of 425 nm and near infrared region have been shown to effectively inactivate viruses such as human immunodeficiency virus (HIV), M13 bacteriophage, and murine cytomegalovirus (MCMV). It was shown previously that non-enveloped, helical viruses such as M13 bacteriophage, were inactivated by a USP laser through an impulsive stimulated Raman scattering (ISRS) process. Recently, enveloped virus like MCMV has been shown to be inactivated by a USP laser via protein aggregation induced by an ISRS process. However, the inactivation mechanism for a clinically important class of viruses – non-enveloped, icosahedral viruses remains unknown. Results and discussions We have ruled out the following four possible inactivation mechanisms for non-enveloped, icosahedral viruses, namely, (1) inactivation due to ultraviolet C (UVC) photons produced by non-linear optical process of the intense, fundamental laser beam at 425 nm; (2) inactivation caused by thermal heating generated by the direct laser absorption/heating of the virion; (3) inactivation resulting from a one-photon absorption process via chromophores such as porphyrin molecules, or indicator dyes, potentially producing reactive oxygen or other species; (4) inactivation by the USP lasers in which the extremely intense laser pulse produces shock wave-like vibrations upon impact with the viral particle. We present data which support that the inactivation mechanism for non-enveloped, icosahedral viruses is the impulsive stimulated Raman scattering process. Real-time PCR experiments show that, within the amplicon size of 273 bp tested, there is no damage on the genome of MNV-1 caused by the USP laser irradiation. Conclusion We conclude that our model non-enveloped virus, MNV-1, is inactivated by the ISRS process. These studies provide fundamental knowledge on photon-virus interactions on femtosecond time scales. From the analysis of the transmission

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…

Generic first-order phase transitions between isotropic and orientational phases with polyhedral symmetries

NASA Astrophysics Data System (ADS)

Liu, Ke; Greitemann, Jonas; Pollet, Lode

2018-01-01

Polyhedral nematics are examples of exotic orientational phases that possess a complex internal symmetry, representing highly nontrivial ways of rotational symmetry breaking, and are subject to current experimental pursuits in colloidal and molecular systems. The classification of these phases has been known for a long time; however, their transitions to the disordered isotropic liquid phase remain largely unexplored, except for a few symmetries. In this work, we utilize a recently introduced non-Abelian gauge theory to explore the nature of the underlying nematic-isotropic transition for all three-dimensional polyhedral nematics. The gauge theory can readily be applied to nematic phases with an arbitrary point-group symmetry, including those where traditional Landau methods and the associated lattice models may become too involved to implement owing to a prohibitive order-parameter tensor of high rank or (the absence of) mirror symmetries. By means of exhaustive Monte Carlo simulations, we find that the nematic-isotropic transition is generically first-order for all polyhedral symmetries. Moreover, we show that this universal result is fully consistent with our expectation from a renormalization group approach, as well as with other lattice models for symmetries already studied in the literature. We argue that extreme fine tuning is required to promote those transitions to second-order ones. We also comment on the nature of phase transitions breaking the O(3 ) symmetry in general cases.

Laughlin states on the Poincaré half-plane and their quantum group symmetry

NASA Astrophysics Data System (ADS)

Alimohammadi, M.; Mohseni Sadjadi, H.

1996-09-01

We find the Laughlin states of the electrons on the Poincaré half-plane in different representations. In each case we show that a quantum group 0305-4470/29/17/025/img5 symmetry exists such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the fractional quantum Hall effect.

Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry

PubMed Central

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

Studies of Inactivation Mechanism of non-enveloped icosahedral viruses by a visible ultrashort pulsed laser

USDA-ARS?s Scientific Manuscript database

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...

Structure of the orthorhombic form of Mn(2)Al(7), Fe(2)Al(7), and (Mn(0.7)Fe(0.3))(2)Al(7) that by twinning produces grains with decagonal point-group symmetry.

PubMed

Pauling, L

1988-04-01

Analysis of electron diffraction photographs of grains of Mn(2)Al(7), Fe(2)Al(7), and (Mn(0.7)Fe(0.3))(2)Al(7) leads to the conclusion that they are 5-fold twins of a 1664-atom orthorhombic crystal with a = 32.86 A, b = 31.23 A, and c = 24.80 A and with 16 icosahedral clusters of 104 atoms in positions shifted by small amounts from those of the cubic beta-tungsten structure.

Spectroscopic criteria for identification of nuclear tetrahedral and octahedral symmetries: Illustration on a rare earth nucleus

NASA Astrophysics Data System (ADS)

Dudek, J.; Curien, D.; Dedes, I.; Mazurek, K.; Tagami, S.; Shimizu, Y. R.; Bhattacharjee, T.

2018-02-01

We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a rare earth nucleus 152Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach, and general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well-defined spins. In the exact-symmetry limit those bands involve no E 2 transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers, and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape isomers and, possibly, new waiting point nuclei—impacting the nucleosynthesis processes in astrophysics—and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

NASA Astrophysics Data System (ADS)

Chiu, Ching-Kai; Schnyder, Andreas P.

2014-11-01

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov-de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror Z2 numbers and topological crystalline nodal superconductors with mirror winding numbers.

Quantum group symmetries and completeness for \\boldsymbol {A}_{\\boldsymbol {2n}}^{\\boldsymbol{(2)}} open spin chains

NASA Astrophysics Data System (ADS)

Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang

2017-07-01

We argue that the Hamiltonians for A(2)2n open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries Uq(Bn) and Uq(Cn) , respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

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.

Structure of the orthorhombic form of Mn2Al7, Fe2Al7, and (Mn0.7Fe0.3)2Al7 that by twinning produces grains with decagonal point-group symmetry

PubMed Central

Pauling, Linus

1988-01-01

Analysis of electron diffraction photographs of grains of Mn2Al7, Fe2Al7, and (Mn0.7Fe0.3)2Al7 leads to the conclusion that they are 5-fold twins of a 1664-atom orthorhombic crystal with a = 32.86 Å, b = 31.23 Å, and c = 24.80 Å and with 16 icosahedral clusters of 104 atoms in positions shifted by small amounts from those of the cubic β-tungsten structure. PMID:16593921

Renormalization group naturalness of GUT Higgs potentials

NASA Astrophysics Data System (ADS)

Allanach, B. C.; Amelino-Camelia, G.; Philipsen, O.; Pisanti, O.; Rosa, L.

1999-01-01

We analyze the symmetry-breaking patterns of grand unified theories from the point of view of a recently proposed criterion of renormalization-group naturalness. We perform the analysis on simple non-SUSY SU(5) and SO(10) and SUSY SU(5) GUTs. We find that the naturalness criterion can favor spontaneous symmetry breaking in the direction of the smallest of the maximal little groups. Some differences between theories with and without supersymmetry are also emphasized.

Allosteric Control of Icosahedral Capsid Assembly

PubMed Central

Lazaro, Guillermo R.

2017-01-01

During the lifecycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that, above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly, and thus should be accounted for in models that are used to estimate interaction parameters from experimental data. PMID:27117092

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

Compatible orders and fermion-induced emergent symmetry in Dirac systems

NASA Astrophysics Data System (ADS)

Janssen, Lukas; Herbut, Igor F.; Scherer, Michael M.

2018-01-01

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with O (N1) and O (N2) symmetries, respectively. Using ɛ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent O (N1+N2) symmetry for arbitrary values of N1 and N2 and fermion flavor numbers Nf as long as the corresponding representation of the Clifford algebra exists. Small O (N ) -breaking perturbations near the chiral O (N ) fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic O (N ) fixed point, which is stable only when N <3 . As a by-product, we obtain predictions for the critical behavior of the chiral O (N ) universality classes for arbitrary N and fermion flavor number Nf. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.

Structural evolutions and hereditary characteristics of icosahedral nano-clusters formed in Mg70Zn30 alloys during rapid solidification processes

NASA Astrophysics Data System (ADS)

Liang, Yong-Chao; Liu, Rang-Su; Xie, Quan; Tian, Ze-An; Mo, Yun-Fei; Zhang, Hai-Tao; Liu, Hai-Rong; Hou, Zhao-Yang; Zhou, Li-Li; Peng, Ping

2017-02-01

To investigate the structural evolution and hereditary mechanism of icosahedral nano-clusters formed during rapid solidification, a molecular dynamics (MD) simulation study has been performed for a system consisting of 107 atoms of liquid Mg70Zn30 alloy. Adopting Honeycutt-Anderson (HA) bond-type index method and cluster type index method (CTIM-3) to analyse the microstructures in the system it is found that for all the nano-clusters including 2~8 icosahedral clusters in the system, there are 62 kinds of geometrical structures, and those can be classified, by the configurations of the central atoms of basic clusters they contained, into four types: chain-like, triangle-tailed, quadrilateral-tailed and pyramidal-tailed. The evolution of icosahedral nano-clusters can be conducted by perfect heredity and replacement heredity, and the perfect heredity emerges when temperature is slightly less than Tm then increase rapidly and far exceeds the replacement heredity at Tg; while for the replacement heredity, there are three major modes: replaced by triangle (3-atoms), quadrangle (4-atoms) and pentagonal pyramid (6-atoms), rather than by single atom step by step during rapid solidification processes.

A fast point-cloud computing method based on spatial symmetry of Fresnel field

NASA Astrophysics Data System (ADS)

Wang, Xiangxiang; Zhang, Kai; Shen, Chuan; Zhu, Wenliang; Wei, Sui

2017-10-01

Aiming at the great challenge for Computer Generated Hologram (CGH) duo to the production of high spatial-bandwidth product (SBP) is required in the real-time holographic video display systems. The paper is based on point-cloud method and it takes advantage of the propagating reversibility of Fresnel diffraction in the propagating direction and the fringe pattern of a point source, known as Gabor zone plate has spatial symmetry, so it can be used as a basis for fast calculation of diffraction field in CGH. A fast Fresnel CGH method based on the novel look-up table (N-LUT) method is proposed, the principle fringe patterns (PFPs) at the virtual plane is pre-calculated by the acceleration algorithm and be stored. Secondly, the Fresnel diffraction fringe pattern at dummy plane can be obtained. Finally, the Fresnel propagation from dummy plan to hologram plane. The simulation experiments and optical experiments based on Liquid Crystal On Silicon (LCOS) is setup to demonstrate the validity of the proposed method under the premise of ensuring the quality of 3D reconstruction the method proposed in the paper can be applied to shorten the computational time and improve computational efficiency.

First-Order Interfacial Transformations with a Critical Point: Breaking the Symmetry at a Symmetric Tilt Grain Boundary

NASA Astrophysics Data System (ADS)

Yang, Shengfeng; Zhou, Naixie; Zheng, Hui; Ong, Shyue Ping; Luo, Jian

2018-02-01

First-order interfacial phaselike transformations that break the mirror symmetry of the symmetric ∑5 (210 ) tilt grain boundary (GB) are discovered by combining a modified genetic algorithm with hybrid Monte Carlo and molecular dynamics simulations. Density functional theory calculations confirm this prediction. This first-order coupled structural and adsorption transformation, which produces two variants of asymmetric bilayers, vanishes at an interfacial critical point. A GB complexion (phase) diagram is constructed via semigrand canonical ensemble atomistic simulations for the first time.

Spatially-protected Topology and Group Cohomology in Band Insulators

NASA Astrophysics Data System (ADS)

Alexandradinata, A.

This thesis investigates band topologies which rely fundamentally on spatial symmetries. A basic geometric property that distinguishes spatial symmetry regards their transformation of the spatial origin. Point groups consist of spatial transformations that preserve the spatial origin, while un-split extensions of the point groups by spatial translations are referred to as nonsymmorphic space groups. The first part of the thesis addresses topological phases with discretely-robust surface properties: we introduce theories for the Cnv point groups, as well as certain nonsymmorphic groups that involve glide reflections. These band insulators admit a powerful characterization through the geometry of quasimomentum space; parallel transport in this space is represented by the Wilson loop. The non-symmorphic topology we study is naturally described by a further extension of the nonsymmorphic space group by quasimomentum translations (the Wilson loop), thus placing real and quasimomentum space on equal footing -- here, we introduce the language of group cohomology into the theory of band insulators. The second part of the thesis addresses topological phases without surface properties -- their only known physical consequences are discrete signatures in parallel transport. We provide two such case studies with spatial-inversion and discrete-rotational symmetries respectively. One lesson learned here regards the choice of parameter loops in which we carry out transport -- the loop must be chosen to exploit the symmetry that protects the topology. While straight loops are popular for their connection with the geometric theory of polarization, we show that bent loops also have utility in topological band theory.

Optimal fold symmetry of LH2 rings on a photosynthetic membrane

PubMed Central

Cleary, Liam; Chen, Hang; Chuang, Chern; Silbey, Robert J.; Cao, Jianshu

2013-01-01

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order. PMID:23650366

Optimal fold symmetry of LH2 rings on a photosynthetic membrane.

PubMed

Cleary, Liam; Chen, Hang; Chuang, Chern; Silbey, Robert J; Cao, Jianshu

2013-05-21

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.

Many-molecule encapsulation by an icosahedral shell

PubMed Central

Perlmutter, Jason D; Mohajerani, Farzaneh; Hagan, Michael F

2016-01-01

We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants. DOI: http://dx.doi.org/10.7554/eLife.14078.001 PMID:27166515

Gauging Spatial Symmetries and the Classification of Topological Crystalline Phases

NASA Astrophysics Data System (ADS)

Thorngren, Ryan; Else, Dominic V.

2018-01-01

We put the theory of interacting topological crystalline phases on a systematic footing. These are topological phases protected by space-group symmetries. Our central tool is an elucidation of what it means to "gauge" such symmetries. We introduce the notion of a crystalline topological liquid and argue that most (and perhaps all) phases of interest are likely to satisfy this criterion. We prove a crystalline equivalence principle, which states that in Euclidean space, crystalline topological liquids with symmetry group G are in one-to-one correspondence with topological phases protected by the same symmetry G , but acting internally, where if an element of G is orientation reversing, it is realized as an antiunitary symmetry in the internal symmetry group. As an example, we explicitly compute, using group cohomology, a partial classification of bosonic symmetry-protected topological phases protected by crystalline symmetries in (3 +1 ) dimensions for 227 of the 230 space groups. For the 65 space groups not containing orientation-reversing elements (Sohncke groups), there are no cobordism invariants that may contribute phases beyond group cohomology, so we conjecture that our classification is complete.

Exploiting Symmetry on Parallel Architectures.

NASA Astrophysics Data System (ADS)

Stiller, Lewis Benjamin

1995-01-01

This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.

Universality of modular symmetries in two-dimensional magnetotransport

NASA Astrophysics Data System (ADS)

Olsen, K. S.; Limseth, H. S.; Lütken, C. A.

2018-01-01

We analyze experimental quantum Hall data from a wide range of different materials, including semiconducting heterojunctions, thin films, surface layers, graphene, mercury telluride, bismuth antimonide, and black phosphorus. The fact that these materials have little in common, except that charge transport is effectively two-dimensional, shows how robust and universal the quantum Hall phenomenon is. The scaling and fixed point data we analyzed appear to show that magnetotransport in two dimensions is governed by a small number of universality classes that are classified by modular symmetries, which are infinite discrete symmetries not previously seen in nature. The Hall plateaux are (infrared) stable fixed points of the scaling-flow, and quantum critical points (where the wave function is delocalized) are unstable fixed points of scaling. Modular symmetries are so rigid that they in some cases fix the global geometry of the scaling flow, and therefore predict the exact location of quantum critical points, as well as the shape of flow lines anywhere in the phase diagram. We show that most available experimental quantum Hall scaling data are in good agreement with these predictions.

Magnetic Resonance Characterization of Defects in Icosahedral and Cubic Boron Arsenide Bulk Crystals

NASA Astrophysics Data System (ADS)

Glaser, E. R.; Freitas, J. A., Jr.; Cress, C. D.; Perkins, F. K.; Prokes, S. M.; Ruppalt, L. B.; Culbertson, J. C.; Whiteley, C.; Edgar, J. H.; Tian, F.; Ren, Z.; Kim, J.; Shi, L.; Naval Research Lab Team; Kansas State U. Team; U. Houston Team; U. Texas Team

Low-temperature electron spin resonance (ESR) at 9.5 GHz and optically-detected magnetic resonance (ODMR) at 24 GHz were employed to investigate point defects in icosahedral and cubic Boron Arsenide bulk crystals. These semiconductors are of interest for use in high radiation and/or high temperature environments. ESR of the (001) B12As2 (Eg = 3.47 eV) mm-size platelets revealed two distinct features of unknown origin. The first signal is characterized by Zeeman splitting g-values of g|| = 2.017, g⊥ = 2.0183 while the second with g|| = 2.0182, g⊥ = 1.9997. Most notably, the second signal was also observed from ODMR on the broad 2.4 eV ``yellow/green'' photoluminescence band previously reported for these crystals and suggests its direct involvement in this likely defect-related radiative recombination process. Preliminary ESR obtained for the 100-300 micron-size cubic BAs crystals revealed a signal with g-value of 2.018 (very similar to that found for the B12As2 crystals) and broad FWHM value of 182 G. Possible origins of these defects will be discussed.

Quantifying wall turbulence via a symmetry approach: A Lie group theory

NASA Astrophysics Data System (ADS)

She, Zhen-Su; Chen, Xi; Hussain, Fazle

2017-11-01

We present a symmetry-based approach which yields analytic expressions for the mean velocity and kinetic energy profiles from a Lie-group analysis. After verifying the dilation-group invariance of the Reynolds averaged Navier-Stokes equation in the presence of a wall, we select a stress and energy length function as similarity variables which are assumed to have a simple dilation-invariant form. Three kinds of (local) invariant forms of the length functions are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall. The mean velocity profile is then predicted using the mean momentum equation, which yields, in particular, analytic expressions for the (universal) wall function and separate wake functions for pipe and channel - which are validated by data from direct numerical simulations (DNS). Future applications to a variety of wall flows such as flows around flat plate or airfoil, in a Rayleigh-Benard cell or Taylor-Couette system, etc., are discussed, for which the dilation group invariance is valid in the wall-normal direction.

Chemical potential and reaction electronic flux in symmetry controlled reactions.

PubMed

Vogt-Geisse, Stefan; Toro-Labbé, Alejandro

2016-07-15

In symmetry controlled reactions, orbital degeneracies among orbitals of different symmetries can occur along a reaction coordinate. In such case Koopmans' theorem and the finite difference approximation provide a chemical potential profile with nondifferentiable points. This results in an ill-defined reaction electronic flux (REF) profile, since it is defined as the derivative of the chemical potential with respect to the reaction coordinate. To overcome this deficiency, we propose a new way for the calculation of the chemical potential based on a many orbital approach, suitable for reactions in which symmetry is preserved. This new approach gives rise to a new descriptor: symmetry adapted chemical potential (SA-CP), which is the chemical potential corresponding to a given irreducible representation of a symmetry group. A corresponding symmetry adapted reaction electronic flux (SA-REF) is also obtained. Using this approach smooth chemical potential profiles and well defined REFs are achieved. An application of SA-CP and SA-REF is presented by studying the Cs enol-keto tautomerization of thioformic acid. Two SA-REFs are obtained, JA'(ξ) and JA'' (ξ). It is found that the tautomerization proceeds via an in-plane delocalized 3-center 4-electron O-H-S hypervalent bond which is predicted to exist only in the transition state (TS) region. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Communication: Photoionization of degenerate orbitals for randomly oriented molecules: The effect of time-reversal symmetry on recoil-ion momentum angular distributions

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-Ichi

2018-04-01

The photoelectron asymmetry parameter β, which characterizes the direction of electrons ejected from a randomly oriented molecular ensemble by linearly polarized light, is investigated for degenerate orbitals. We show that β is totally symmetric under the symmetry operation of the point group of a molecule, and it has mixed properties under time reversal. Therefore, all degenerate molecular orbitals, except for the case of degeneracy due to time reversal, have the same β (Wigner-Eckart theorem). The exceptions are e-type complex orbitals of the Cn, Sn, Cnh, T, and Th point groups, and calculations on boric acid (C3h symmetry) are performed as an example. However, including those point groups, all degenerate orbitals have the same β if those orbitals are real. We discuss the implications of this operator formalism for molecular alignment and photoelectron circular dichroism.

Mime therapy improves facial symmetry in people with long-term facial nerve paresis: a randomised controlled trial.

PubMed

Beurskens, Carien H G; Heymans, Peter G

2006-01-01

What is the effect of mime therapy on facial symmetry and severity of paresis in people with facial nerve paresis? Randomised controlled trial. 50 people recruited from the Outpatient department of two metropolitan hospitals with facial nerve paresis for more than nine months. The experimental group received three months of mime therapy consisting of massage, relaxation, inhibition of synkinesis, and co-ordination and emotional expression exercises. The control group was placed on a waiting list. Assessments were made on admission to the trial and three months later by a measurer blinded to group allocation. Facial symmetry was measured using the Sunnybrook Facial Grading System. Severity of paresis was measured using the House-Brackmann Facial Grading System. After three months of mime therapy, the experimental group had improved their facial symmetry by 20.4 points (95% CI 10.4 to 30.4) on the Sunnybrook Facial Grading System compared with the control group. In addition, the experimental group had reduced the severity of their paresis by 0.6 grade (95% CI 0.1 to 1.1) on the House-Brackmann Facial Grading System compared with the control group. These effects were independent of age, sex, and duration of paresis. Mime therapy improves facial symmetry and reduces the severity of paresis in people with facial nerve paresis.

Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev—Petviashvili Equation

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Chen, Yong; Ma, Zheng-Yi

2016-08-01

A generalized Kadomtsev—Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev—Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev—Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005

A molecular symmetry analysis of the electronic states and transition dipole moments for molecules with two torsional degrees of freedom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Obaid, R.; Applied Chemistry Department, Palestine Polytechnic University, Hebron, Palestine; Leibscher, M., E-mail: monika.leibscher@itp.uni-hannover.de

2015-02-14

We present a molecular symmetry analysis of electronic states and transition dipole moments for molecules which undergo large amplitude intramolecular torsions. The method is based on the correlation between the point group of the molecule at highly symmetric configurations and the molecular symmetry group. As an example, we determine the global irreducible representations of the electronic states and transition dipole moments for the quinodimethane derivative 2-[4-(cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1, 3-dioxole for which two torsional degrees of freedom can be activated upon photo-excitation and construct the resulting symmetry adapted transition dipole functions.

Group-theoretical analysis of two-dimensional hexagonal materials

NASA Astrophysics Data System (ADS)

Minami, Susumu; Sugita, Itaru; Tomita, Ryosuke; Oshima, Hiroyuki; Saito, Mineo

2017-10-01

Two-dimensional hexagonal materials such as graphene and silicene have highly symmetric crystal structures and Dirac cones at the K point, which induce novel electronic properties. In this report, we calculate their electronic structures by using density functional theory and analyze their band structures on the basis of the group theory. Dirac cones frequently appear when the symmetry at the K point is high; thus, two-dimensional irreducible representations are included. We discuss the relationship between symmetry and the appearance of the Dirac cone.

Symmetry investigations on the incompressible stationary axisymmetric Euler equations with swirl

NASA Astrophysics Data System (ADS)

Frewer, M.; Oberlack, M.; Guenther, S.

2007-08-01

We discuss the incompressible stationary axisymmetric Euler equations with swirl, for which we derive via a scalar stream function an equivalent representation, the Bragg-Hawthorne equation [Bragg, S.L., Hawthorne, W.R., 1950. Some exact solutions of the flow through annular cascade actuator discs. J. Aero. Sci. 17, 243]. Despite this obvious equivalence, we will show that under a local Lie point symmetry analysis the Bragg-Hawthorne equation exposes itself as not being fully equivalent to the original Euler equations. This is reflected in the way that it possesses additional symmetries not being admitted by its counterpart. In other words, a symmetry of the Bragg-Hawthorne equation is in general not a symmetry of the Euler equations. Not the differential Euler equations but rather a set of integro-differential equations attains full equivalence to the Bragg-Hawthorne equation. For these intermediate Euler equations, it is interesting to note that local symmetries of the Bragg-Hawthorne equation transform to local as well as to nonlocal symmetries. This behaviour, on the one hand, is in accordance with Zawistowski's result [Zawistowski, Z.J., 2001. Symmetries of integro-differential equations. Rep. Math. Phys. 48, 269; Zawistowski, Z.J., 2004. General criterion of invariance for integro-differential equations. Rep. Math. Phys. 54, 341] that it is possible for integro-differential equations to admit local Lie point symmetries. On the other hand, with this transformation process we collect symmetries which cannot be obtained when carrying out a usual local Lie point symmetry analysis. Finally, the symmetry classification of the Bragg-Hawthorne equation is used to find analytical solutions for the phenomenon of vortex breakdown.

Perception of Mirror Symmetry in Autism Spectrum Disorders

ERIC Educational Resources Information Center

Falter, Christine M.; Bailey, Anthony J.

2012-01-01

Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…

Essays on symmetry

NASA Astrophysics Data System (ADS)

Ismael, Jenann Tareq

1997-04-01

Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.

Is the standard model saved asymptotically by conformal symmetry?

NASA Astrophysics Data System (ADS)

Gorsky, A.; Mironov, A.; Morozov, A.; Tomaras, T. N.

2015-03-01

It is pointed out that the top-quark and Higgs masses and the Higgs VEV with great accuracy satisfy the relations 4 m {/H 2} = 2 m {/T 2} = v 2, which are very special and reminiscent of analogous ones at Argyres-Douglas points with enhanced conformal symmetry. Furthermore, the RG evolution of the corresponding Higgs self-interaction and Yukawa couplings λ(0) = 1/8 and y(0) = 1 leads to the free-field stable point in the pure scalar sector at the Planck scale, also suggesting enhanced conformal symmetry. Thus, it is conceivable that the Standard Model is the low-energy limit of a distinct special theory with (super?) conformal symmetry at the Planck scale. In the context of such a "scenario," one may further speculate that the Higgs particle is the Goldstone boson of (partly) spontaneously broken conformal symmetry. This would simultaneously resolve the hierarchy and Landau pole problems in the scalar sector and would provide a nearly flat potential with two almost degenerate minima at the electroweak and Planck scales.

Natural electroweak breaking from a mirror symmetry.

PubMed

Chacko, Z; Goh, Hock-Seng; Harnik, Roni

2006-06-16

We present "twin Higgs models," simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.

Analytical and computational modeling of early penetration of non-enveloped icosahedral viruses into cells.

PubMed

Katzengold, Rona; Zaharov, Evgeniya; Gefen, Amit

2016-07-27

As obligate intracellular parasites, all viruses penetrate target cells to initiate replication and infection. This study introduces two approaches for evaluating the contact loads applied to a cell during early penetration of non-enveloped icosahedral viruses. The first approach is analytical modeling which is based on Hertz's theory for the contact of two elastic bodies; here we model the virus capsid as a triangle and the cell as an order-of-magnitude larger sphere. The second approach is finite element modeling, where we simulate three types of viruses: adeno-, papilloma- and polio- viruses, each interacting with a cell section. We find that the peak contact pressures and forces generated at the initial virus-cell contact depend on the virus geometry - that is both size and shape. With respect to shape, we show that the icosahedral virus shape induces greater peak pressures compared to a spherical virus shape. With respect to size, it is shown that the larger the virus is the greater are the contact loads in the attacked cell. Utilization of our modeling can be substantially useful not only for basic science studies, but also in other, more applied fields, such as in the field of gene therapy, or in `phage' virus studies.

Towards a realistic model of Higgsless electroweak symmetry breaking.

PubMed

Csáki, Csaba; Grojean, Christophe; Pilo, Luigi; Terning, John

2004-03-12

We present a 5D gauge theory in warped space based on a bulk SU(2)L x SU(2)R x U(1)(B-L) gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resemble that in the standard model (SM). To leading order in the warp factor the rho parameter and the coupling of the Z (S parameter) are as in the SM, while corrections are expected at the level of a percent. From the anti-de Sitter (AdS) conformal field theory point of view the model presented here can be viewed as the AdS dual of a (walking) technicolorlike theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W, Z, and gamma resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles.

Extended symmetry analysis of generalized Burgers equations

NASA Astrophysics Data System (ADS)

Pocheketa, Oleksandr A.; Popovych, Roman O.

2017-10-01

Using enhanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form ut + uux + f(t, x)uxx = 0. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, hidden symmetries, conservation laws, potential admissible transformations, and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry

NASA Astrophysics Data System (ADS)

Mambrini, Matthieu; Orús, Román; Poilblanc, Didier

2016-11-01

We elaborate a simple classification scheme of all rank-5 SU(2) spin rotational symmetric tensors according to (i) the onsite physical spin S , (ii) the local Hilbert space V⊗4 of the four virtual (composite) spins attached to each site, and (iii) the irreducible representations of the C4 v point group of the square lattice. We apply our scheme to draw a complete list of all SU(2)-symmetric translationally and rotationally invariant projected entangled pair states (PEPS) with bond dimension D ≤6 . All known SU(2)-symmetric PEPS on the square lattice are recovered and simple generalizations are provided in some cases. More generally, to each of our symmetry class can be associated a (D -1 )-dimensional manifold of spin liquids (potentially) preserving lattice symmetries and defined in terms of D -independent tensors of a given bond dimension D . In addition, generic (low-dimensional) families of PEPS explicitly breaking either (i) particular point-group lattice symmetries (lattice nematics) or (ii) time-reversal symmetry (chiral spin liquids) or (iii) SU(2) spin rotation symmetry down to U(1 ) (spin nematics or Néel antiferromagnets) can also be constructed. We apply this framework to search for new topological chiral spin liquids characterized by well-defined chiral edge modes, as revealed by their entanglement spectrum. In particular, we show how the symmetrization of a double-layer PEPS leads to a chiral topological state with a gapless edge described by a SU (2) 2 Wess-Zumino-Witten model.

Spacetime symmetries and topology in bimetric relativity

NASA Astrophysics Data System (ADS)

Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard

2018-04-01

We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

Symmetry in polarimetric remote sensing

NASA Technical Reports Server (NTRS)

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

1993-01-01

Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Spinor Structure and Internal Symmetries

NASA Astrophysics Data System (ADS)

Varlamov, V. V.

2015-10-01

Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

NASA Astrophysics Data System (ADS)

Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo

2017-06-01

This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009

Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

NASA Astrophysics Data System (ADS)

Hou, Jing-Min

2013-09-01

We study a two-dimensional fermionic square lattice, which supports the existence of a two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2π-flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2π-flux topological semimetal are protected by two distinct novel hidden symmetries, which both correspond to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry.

Multicritical points for spin-glass models on hierarchical lattices.

PubMed

Ohzeki, Masayuki; Nishimori, Hidetoshi; Berker, A Nihat

2008-06-01

The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry, and the replica method. We find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data. We propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one. This improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data.

The Crystallographic Structure of Panicum Mosaic Virus (PMV)

PubMed Central

Makino, Debora L.; Larson, Steven B.; McPherson, Alexander

2012-01-01

The structure of Panicum Mosaic Virus (PMV) was determined by X-ray diffraction analysis to 2.9 Å resolution. The crystals were of pseudo symmetry F23; the true crystallographic unit cell was of space group P21 with a=411.7 Å, b=403.9 Å and c=412.5 Å, with β=89.7°. The asymmetric unit was two entire T=3 virus particles, or 360 protein subunits. The structure was solved by conventional molecular replacement from two distant homologues, Cocksfoot Mottle Virus (CfMV) and Tobacco Necrosis Virus (TNV), of ~20% sequence identity followed by phase extension. The model was initially refined with exact icosahedral constraints and then with icosahedral restraints. The virus has Ca++ ions octahedrally coordinated by six aspartic acid residues on quasi threefold axes, which is completely different than for either CfMV or TNV. Amino terminal residues 1–53, 1–49 and 1-21 of the A, B and C subunits, respectively, and the four C-terminal residues (239-242) are not visible in electron density maps. The additional ordered residues of the C chain form a prominent “arm” that intertwines with symmetry equivalent “arms” at icosahedral threefold axes, as was seen in both CfMV and TNV. A 17 nucleotide hairpin segment of genomic RNA is icosahedrally ordered and bound at 60 equivalent sites at quasi twofold A–B subunit interfaces at the interior surface of the capsid. This segment of RNA may serve as a conformational switch for coat protein subunits, as has been proposed for similar RNA segments in other viruses. PMID:23123270

Allosteric effects in bacteriophage HK97 procapsids revealed directly from covariance analysis of cryo EM data.

PubMed

Xu, Nan; Veesler, David; Doerschuk, Peter C; Johnson, John E

2018-05-01

The information content of cryo EM data sets exceeds that of the electron scattering potential (cryo EM) density initially derived for structure determination. Previously we demonstrated the power of data variance analysis for characterizing regions of cryo EM density that displayed functionally important variance anomalies associated with maturation cleavage events in Nudaurelia Omega Capensis Virus and the presence or absence of a maturation protease in bacteriophage HK97 procapsids. Here we extend the analysis in two ways. First, instead of imposing icosahedral symmetry on every particle in the data set during the variance analysis, we only assume that the data set as a whole has icosahedral symmetry. This change removes artifacts of high variance along icosahedral symmetry axes, but retains all of the features previously reported in the HK97 data set. Second we present a covariance analysis that reveals correlations in structural dynamics (variance) between the interior of the HK97 procapsid with the protease and regions of the exterior (not seen in the absence of the protease). The latter analysis corresponds well with hydrogen deuterium exchange studies previously published that reveal the same correlation. Copyright © 2018 Elsevier Inc. All rights reserved.

Flat connections in open string mirror symmetry

NASA Astrophysics Data System (ADS)

Alim, Murad; Hecht, Michael; Jockers, Hans; Mayr, Peter; Mertens, Adrian; Soroush, Masoud

2012-06-01

We study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use flatness and integrability conditions to define distinguished flat coordinates and the superpotential function at an arbitrary point in the open-closed deformation space. Integrability conditions are given for concrete deformation spaces with several closed and open string deformations. We study explicit examples for expansions around different limit points, including orbifold Gromov-Witten invariants, and brane configurations with several brane moduli. In particular, the latter case covers stacks of parallel branes with non-Abelian symmetry.

Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation

NASA Astrophysics Data System (ADS)

Wu, Jian-Wen; Lou, Sen-Yue; Yu, Jun

2017-05-01

The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University

Fluctuations and symmetry energy in nuclear fragmentation dynamics.

PubMed

Colonna, M

2013-01-25

Within a dynamical description of nuclear fragmentation, based on the liquid-gas phase transition scenario, we explore the relation between neutron-proton density fluctuations and nuclear symmetry energy. We show that, along the fragmentation path, isovector fluctuations follow the evolution of the local density and approach an equilibrium value connected to the local symmetry energy. Higher-density regions are characterized by smaller average asymmetry and narrower isotopic distributions. This dynamical analysis points out that fragment final state isospin fluctuations can probe the symmetry energy of the density domains from which fragments originate.

Bilateral coordination and gait symmetry after body-weight supported treadmill training for persons with chronic stroke.

PubMed

Combs, Stephanie A; Dugan, Eric L; Ozimek, Elicia N; Curtis, Amy B

2013-04-01

Locomotor interventions are commonly assessed using functional outcomes, but these outcomes provide limited information about changes toward recovery or compensatory mechanisms. The study purposes were to examine changes in gait symmetry and bilateral coordination following body-weight supported treadmill training in individuals with chronic hemiparesis due to stroke and to compare findings to participants without disability. Nineteen participants with stroke (>6 months) who ambulated between 0.4 and 0.8 m/s and 22 participants without disability were enrolled in this repeated-measures study. The stroke group completed 24 intervention sessions over 8 weeks with 20 minutes of walking/session. The non-disabled group served as a comparison for describing changes in symmetry and coordination. Bilateral 3-dimensional motion analysis and gait speed were assessed across 3 time points (pre-test, immediate post-test, and 6-month retention). Continuous relative phase was used to evaluate bilateral coordination (thigh-thigh, shank-shank, foot-foot) and gait symmetry was assessed with spatiotemporal ratios (step length, swing time, stance time). Significant improvements in continuous relative phase (shank-shank and foot-foot couplings) were found at post-test and retention for the stroke group. Significant differences in spatiotemporal symmetry ratios were not found over time. Compared to the non-disabled group, changes in bilateral coordination moved in the direction of normal recovery. Most measures of continuous relative phase were more responsive to change after training than the spatiotemporal ratios. After body-weight supported treadmill training, the stroke group made improvements toward recovery of normal bilateral coordination. Bilateral coordination and gait symmetry measures may assess different aspects of gait. Copyright © 2013 Elsevier Ltd. All rights reserved.

Higgsless approach to electroweak symmetry breaking

NASA Astrophysics Data System (ADS)

Grojean, Christophe

2007-11-01

Higgsless models are an attempt to achieve a breaking of the electroweak symmetry via boundary conditions at the end-points of a fifth dimension compactified on an interval, as an alternative to the usual Higgs mechanism. There is no physical Higgs scalar in the spectrum and the perturbative unitarity violation scale is delayed via the exchange of massive spin-1 KK resonances. The correct mass spectrum is reproduced in a model in warped space, which inherits a custodial symmetry from a left-right gauge symmetry in the bulk. Phenomenological challenges as well as collider signatures are presented. From the AdS/CFT perspective, this model appears as a weakly coupled dual to walking technicolour models. To cite this article: C. Grojean, C. R. Physique 8 (2007).

Symmetry of priapulids (Priapulida). 1. Symmetry of adults.

PubMed

Adrianov, A V; Malakhov, V V

2001-02-01

Priapulids possess a radial symmetry that is remarkably reflected in both external morphology and internal anatomy. It results in the appearance of 25-radial (a number divisible by five) symmetry summarized as a combination of nonaradial, octaradial, and octaradial (9+8+8) symmetries of scalids. The radial symmetry is a secondary appearance considered as an evolutionary adaptation to a lifestyle within the three-dimensional environment of bottom sediment. The eight anteriormost, or primary, scalids retain their particular position because of their innervation directly from the circumpharyngeal brain. As a result of a combination of the octaradial symmetry of primary scalids, pentaradial symmetry of teeth, and the 25-radial symmetry of scalids, the initial bilateral symmetry remains characterized by the single sagittal plane. Copyright 2001 Wiley-Liss, Inc.

Black Hole Thermodynamics and Lorentz Symmetry

NASA Astrophysics Data System (ADS)

Jacobson, Ted; Wall, Aron C.

2010-08-01

Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.

BOOK REVIEW: Symmetry Breaking

NASA Astrophysics Data System (ADS)

Ryder, L. H.

2005-11-01

One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would

Appearance of singularities of optical fields under torsion of crystals containing threefold symmetry axes.

PubMed

Skab, Ihor; Vasylkiv, Yurij; Zapeka, Bohdan; Savaryn, Viktoriya; Vlokh, Rostyslav

2011-07-01

We present an analysis of the effect of torsion stresses on the spatial distribution of optical birefringence in crystals of different point symmetry groups. The symmetry requirements needed so that the optical beam carries dislocations of the phase front are evaluated for the case when the crystals are twisted and the beam closely corresponds to a plane wave. It is shown that the torsion stresses can produce screw-edge, pure screw, or pure edge dislocations of the phase front in the crystals belonging to cubic and trigonal systems. The conditions for appearance of canonical and noncanonical vortices in the conditions of crystal torsion are analyzed. © 2011 Optical Society of America

Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.

PubMed

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. Copyright 2001 Wiley-Liss, Inc.

Classification of symmetry-protected phases for interacting fermions in two dimensions

NASA Astrophysics Data System (ADS)

Cheng, Meng; Bi, Zhen; You, Yi-Zhuang; Gu, Zheng-Cheng

2018-05-01

Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H3( G ,U (1 ) ) . Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H1(G ,Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G ×Z2f is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.

Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths.

PubMed

Ledermann, Alexandra; Cademartiri, Ludovico; Hermatschweiler, Martin; Toninelli, Costanza; Ozin, Geoffrey A; Wiersma, Diederik S; Wegener, Martin; von Freymann, Georg

2006-12-01

Quasicrystals are a class of lattices characterized by a lack of translational symmetry. Nevertheless, the points of the lattice are deterministically arranged, obeying rotational symmetry. Thus, we expect properties that are different from both crystals and glasses. Indeed, naturally occurring electronic quasicrystals (for example, AlPdMn metal alloys) show peculiar electronic, vibrational and physico-chemical properties. Regarding artificial quasicrystals for electromagnetic waves, three-dimensional (3D) structures have recently been realized at GHz frequencies and 2D structures have been reported for the near-infrared region. Here, we report on the first fabrication and characterization of 3D quasicrystals for infrared frequencies. Using direct laser writing combined with a silicon inversion procedure, we achieve high-quality silicon inverse icosahedral structures. Both polymeric and silicon quasicrystals are characterized by means of electron microscopy and visible-light Laue diffraction. The diffraction patterns of structures with a local five-fold real-space symmetry axis reveal a ten-fold symmetry as required by theory for 3D structures.

Patterns of symmetry breaking in chiral QCD

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Konishi, Kenichi; Shifman, Mikhail

2018-05-01

We consider S U (N ) Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid ψ χ η model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bifermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e. also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain) and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.

Biofeedback to Promote Movement Symmetry After Total Knee Arthroplasty: A Feasibility Study

PubMed Central

ZENI, JOSEPH; ABUJABER, SUMAYAH; FLOWERS, PORTIA; POZZI, FEDERICO; SNYDER-MACKLER, LYNN

2014-01-01

STUDY DESIGN Prospective analysis of a longitudinal cohort with an embedded comparison group at a single time point. OBJECTIVES To determine the feasibility and effectiveness of an outpatient rehabilitation protocol that includes movement symmetry biofeedback on functional and biomechanical outcomes after total knee arthroplasty (TKA). BACKGROUND TKA reduces pain and improves functional ability, but many patients experience strength deficits and movement abnormalities in the operated limb, despite outpatient rehabilitation. These asymmetries increase load on the nonoperated limb, and greater asymmetry is related to worse functional outcomes. METHODS Biomechanical and functional metrics were assessed 2 to 3 weeks prior to TKA, at discharge from outpatient physical therapy, and 6 months after TKA in 11 patients (9 men, 2 women; mean ± SD age, 61.4 ± 5.8 years; body mass index, 33.1 ± 5.4 kg/m2) who received 6 to 8 weeks of outpatient physical therapy that included specialized symmetry training. Six-month outcomes were compared to a control group, matched by age, body mass index, and sex (9 men, 2 women; mean ± SD age, 61.8 ± 5 years; body mass index, 34.3 ± 5.1 kg/m2), that did not receive specialized symmetry retraining. RESULTS Of the 11 patients who received added symmetry training, 9 demonstrated clinically meaningful improvements that exceeded the minimal detectable change for all performance-based functional tests at 6 months post-TKA compared to pre-TKA. Six months after TKA, when walking, patients who underwent symmetry retraining had greater knee extension during midstance and had mean sagittal knee moments that were more symmetrical, biphasic, and more representative of normal knee kinetics compared to patients who did not undergo symmetry training. No patients experienced adverse events as the result of the protocol. CONCLUSION Adding symmetry retraining to postoperative protocols is clinically viable, safe, and may have additional benefits compared

Spin-1 Dirac-Weyl fermions protected by bipartite symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Zeren; School of Physics, Peking University, Beijing 100871; Liu, Zhirong, E-mail: LiuZhiRong@pku.edu.cn

2015-12-07

We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K′ in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T{sub 3}, an extensivelymore » studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K′.« less

Dynamic generation of light states with discrete symmetries

NASA Astrophysics Data System (ADS)

Cordero, S.; Nahmad-Achar, E.; Castaños, O.; López-Peña, R.

2018-01-01

A dynamic procedure is established within the generalized Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group Cn. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, |ψ〉 M1,and |ψ〉 M 2, is considered. It can be generated by the proper selection of the time of flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order n =| M1-M2| .

Hawking radiation by Kerr black holes and conformal symmetry.

PubMed

Agullo, Ivan; Navarro-Salas, José; Olmo, Gonzalo J; Parker, Leonard

2010-11-19

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.

Influence of inter-item symmetry in visual search.

PubMed

Roggeveen, Alexa B; Kingstone, Alan; Enns, James T

2004-01-01

Does visual search involve a serial inspection of individual items (Feature Integration Theory) or are items grouped and segregated prior to their consideration as a possible target (Attentional Engagement Theory)? For search items defined by motion and shape there is strong support for prior grouping (Kingstone and Bischof, 1999). The present study tested for grouping based on inter-item shape symmetry. Results showed that target-distractor symmetry strongly influenced search whereas distractor-distractor symmetry influenced search more weakly. This indicates that static shapes are evaluated for similarity to one another prior to their explicit identification as 'target' or 'distractor'. Possible reasons for the unequal contributions of target-distractor and distractor-distractor relations are discussed.

Symmetry breaking in the opinion dynamics of a multi-group project organization

NASA Astrophysics Data System (ADS)

Zhu, Zhen-Tao; Zhou, Jing; Li, Ping; Chen, Xing-Guang

2012-10-01

A bounded confidence model of opinion dynamics in multi-group projects is presented in which each group's opinion evolution is driven by two types of forces: (i) the group's cohesive force which tends to restore the opinion back towards the initial status because of its company culture; and (ii) nonlinear coupling forces with other groups which attempt to bring opinions closer due to collaboration willingness. Bifurcation analysis for the case of a two-group project shows a cusp catastrophe phenomenon and three distinctive evolutionary regimes, i.e., a deadlock regime, a convergence regime, and a bifurcation regime in opinion dynamics. The critical value of initial discord between the two groups is derived to discriminate which regime the opinion evolution belongs to. In the case of a three-group project with a symmetric social network, both bifurcation analysis and simulation results demonstrate that if each pair has a high initial discord, instead of symmetrically converging to consensus with the increase of coupling scale as expected by Gabbay's result (Physica A 378 (2007) p. 125 Fig. 5), project organization (PO) may be split into two distinct clusters because of the symmetry breaking phenomenon caused by pitchfork bifurcations, which urges that apart from divergence in participants' interests, nonlinear interaction can also make conflict inevitable in the PO. The effects of two asymmetric level parameters are tested in order to explore the ways of inducing dominant opinion in the whole PO. It is found that the strong influence imposed by a leader group with firm faith on the flexible and open minded follower groups can promote the formation of a positive dominant opinion in the PO.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Symmetry-enforced stability of interacting Weyl and Dirac semimetals

NASA Astrophysics Data System (ADS)

Carlström, Johan; Bergholtz, Emil J.

2018-04-01

The nodal and effectively relativistic dispersion featuring in a range of novel materials including two-dimensional graphene and three-dimensional Dirac and Weyl semimetals has attracted enormous interest during the past decade. Here, by studying the structure and symmetry of the diagrammatic expansion, we show that these nodal touching points are in fact perturbatively stable to all orders with respect to generic two-body interactions. For effective low-energy theories relevant for single and multilayer graphene, type-I and type-II Weyl and Dirac semimetals, as well as Weyl points with higher topological charge, this stability is shown to be a direct consequence of a spatial symmetry that anticommutes with the effective Hamiltonian while leaving the interaction invariant. A more refined argument is applied to the honeycomb lattice model of graphene showing that its Dirac points are also perturbatively stable to all orders. We also give examples of nodal Hamiltonians that acquire a gap from interactions as a consequence of symmetries different from those of Weyl and Dirac materials.

Symmetries in N-body problem

NASA Astrophysics Data System (ADS)

Xia, Zhihong

2008-09-01

The purpose of this note is to introduce some of the basic techniques in group theory to the study the symmetries of the Newtonian n-body problem. The main tool is the representations of finite groups.

Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice

NASA Astrophysics Data System (ADS)

Hou, Jing-Min

2014-03-01

We study a two-dimensional fermionic square lattice, which supports the existence of two-dimensional Weyl semimetal, quantum anomalous Hall effect, and 2 π -flux topological semimetal in different parameter ranges. We show that the band degenerate points of the two-dimensional Weyl semimetal and 2 π -flux topological semimetal are protected by two distinct novel hidden symmetries, which both corresponds to antiunitary composite operations. When these hidden symmetries are broken, a gap opens between the conduction and valence bands, turning the system into a insulator. With appropriate parameters, a quantum anomalous Hall effect emerges. The degenerate point at the boundary between the quantum anomalous Hall insulator and trivial band insulator is also protected by the hidden symmetry. [PRL 111, 130403(2013)] This work was supported by the National Natural Science Foundation of China under Grants No. 11004028 and No. 11274061.

Graph fibrations and symmetries of network dynamics

NASA Astrophysics Data System (ADS)

Nijholt, Eddie; Rink, Bob; Sanders, Jan

2016-11-01

Dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking. A methodology for classifying patterns of synchrony in networks was developed by Golubitsky and Stewart. They showed that the robustly synchronous dynamics of a network is determined by its quotient networks. This result was recently reformulated by DeVille and Lerman, who pointed out that the reduction from a network to a quotient is an example of a graph fibration. The current paper exploits this observation and demonstrates the importance of self-fibrations of network graphs. Self-fibrations give rise to symmetries in the dynamics of a network. We show that every network admits a lift with a semigroup or semigroupoid of self-fibrations. The resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking. Also, when the network has a trivial symmetry groupoid, then every robust synchrony in the lift is determined by symmetry. We finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks.

Floquet topological phases with symmetry in all dimensions

NASA Astrophysics Data System (ADS)

Roy, Rahul; Harper, Fenner

2017-05-01

Dynamical systems may host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and identify several distinct classes of evolution that host dynamical order. Using ideas from group cohomology, we construct a set of interacting Floquet drives that generate dynamical symmetry-protected topological order for each nontrivial cohomology class in every dimension, illustrating our construction with explicit two-dimensional examples. We also identify a set of symmetry-protected Floquet drives that lie outside of the group cohomology construction, and a further class of symmetry-respecting topological drives which host chiral edge modes. We use these special drives to define a notion of phase (stable to a class of local perturbations in the bulk) and the concepts of relative and absolute topological order, which can be applied to many different classes of unitary evolutions. These include fully many-body localized unitary evolutions and time crystals.

Conditions for observing emergent SU(4) symmetry in a double quantum dot

NASA Astrophysics Data System (ADS)

Nishikawa, Yunori; Curtin, Oliver J.; Hewson, Alex C.; Crow, Daniel J. G.; Bauer, Johannes

2016-06-01

We analyze conditions for the observation of a low-energy SU(4) fixed point in capacitively coupled quantum dots. One problem, due to dots with different couplings to their baths, has been considered by L. Tosi, P. Roura-Bas, and A. A. Aligia, J. Phys.: Condens. Matter 27, 335601 (2015), 10.1088/0953-8984/27/33/335601. They showed how symmetry can be effectively restored via the adjustment of individual gates voltages, but they make the assumption of infinite on-dot and interdot interaction strengths. A related problem is the difference in the magnitudes between the on-dot and interdot strengths for capacitively coupled quantum dots. Here we examine both factors, based on a two-site Anderson model, using the numerical renormalization group to calculate the local spectral densities on the dots and the renormalized parameters that specify the low-energy fixed point. Our results support the conclusions of Tosi et al. that low-energy SU(4) symmetry can be restored, but asymptotically achieved only if the interdot interaction U12 is greater than or of the order of the bandwidth of the coupled conduction bath D , which might be difficult to achieve experimentally. By comparing the SU(4) Kondo results for a total dot occupation ntot=1 and 2, we conclude that the temperature dependence of the conductance is largely determined by the constraints of the Friedel sum rule rather than the SU(4) symmetry and suggest that an initial increase of the conductance with temperature is a distinguishing characteristic feature of an ntot=1 universal SU(4) fixed point.

Molecular Symmetry in Ab Initio Calculations

NASA Astrophysics Data System (ADS)

Madhavan, P. V.; Written, J. L.

1987-05-01

A scheme is presented for the construction of the Fock matrix in LCAO-SCF calculations and for the transformation of basis integrals to LCAO-MO integrals that can utilize several symmetry unique lists of integrals corresponding to different symmetry groups. The algorithm is fully compatible with vector processing machines and is especially suited for parallel processing machines.

Symmetry tuning for DIME Campaign

NASA Astrophysics Data System (ADS)

Krasheninnikova, Natalia; Schmitt, Mark; Tregillis, Ian; Bradley, P.; Cobble, J.; Kyrala, G.; Murphy, T.; Obrey, K.; Hsu, S.; Shah, R.; Batha, S.; Craxton, S.; McKenty, P.

2012-10-01

Defect Induced Mix Experiment (DIME) investigates the effects of 4 pi as well as surface feature-driven mix on the directly driven ICF capsule implosion. To minimize the effects of the laser-drive asymmetry, beam pointings, pulse shape, and the energy distribution between the lasers need to be optimized for a particular capsule and shot energy. In support of the DIME experimental campaigns on OMEGA and NIF, symmetry tuning was performed with the rad-hydro code HYDRA. To assess the impact on the symmetry, synthetic radiographs and self-emission images were examined and compared with the experimental results from OMEGA and NIF shots. The dynamics of the capsules imploded under polar direct drive conditions were compared with symmetrically driven ones and the effects of cross-beam transfer and the laser imprinting on the symmetry were also investigated. Work performed by Los Alamos National Laboratory under contract DE-AC52-06NA25396 for the National Nuclear Security Administration of the U.S. Department of Energy.

Flavor physics without flavor symmetries

NASA Astrophysics Data System (ADS)

Buchmuller, Wilfried; Patel, Ketan M.

2018-04-01

We quantitatively analyze a quark-lepton flavor model derived from a six-dimensional supersymmetric theory with S O (10 )×U (1 ) gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk 16 -plets charged under the U (1 ) provide the three quark-lepton generations whereas two uncharged 10 -plets yield two Higgs doublets. At the orbifold fixed points mass matrices are generated with rank one or two. Moreover, the zero modes mix with heavy vectorlike split multiplets. The model possesses no flavor symmetries. Nevertheless, there exist a number of relations between Yukawa couplings, remnants of the underlying grand unified theory symmetry and the wave function profiles of the zero modes, which lead to a prediction of the light neutrino mass scale, mν 1˜10-3 eV and heavy Majorana neutrino masses in the range from 1 012 to 1 014 GeV . The model successfully includes thermal leptogenesis.

Symmetry breaking in occupation number based slave-particle methods

NASA Astrophysics Data System (ADS)

Georgescu, Alexandru B.; Ismail-Beigi, Sohrab

2017-10-01

We describe a theoretical approach to finding spontaneously symmetry-broken electronic phases due to strong electronic interactions when using recently developed slave-particle (slave-boson) approaches based on occupation numbers. We describe why, to date, spontaneous symmetry breaking has proven difficult to achieve in such approaches. We then provide a total energy based approach for introducing auxiliary symmetry-breaking fields into the solution of the slave-particle problem that leads to lowered total energies for symmetry-broken phases. We point out that not all slave-particle approaches yield energy lowering: the slave-particle model being used must explicitly describe the degrees of freedom that break symmetry. Finally, our total energy approach permits us to greatly simplify the formalism used to achieve a self-consistent solution between spinon and slave modes while increasing the numerical stability and greatly speeding up the calculations.

Nonsymmorphic cubic Dirac point and crossed nodal rings across the ferroelectric phase transition in LiOsO3

NASA Astrophysics Data System (ADS)

Yu, Wing Chi; Zhou, Xiaoting; Chuang, Feng-Chuan; Yang, Shengyuan A.; Lin, Hsin; Bansil, Arun

2018-05-01

Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point—a fourfold-degenerate band-crossing point with cubic dispersion in a plane and a linear dispersion in the third direction—can be stabilized through the presence of a nonsymmorphic glide mirror symmetry in the space group of the crystal. Notably, the cubic Dirac point in our case appears on a threefold axis, even though it has been believed previously that such a point can only appear on a sixfold axis. We show that a cubic Dirac point involving a threefold axis can be realized close to the Fermi level in the nonferroelectric phase of LiOsO3. Upon lowering temperature, LiOsO3 has been shown experimentally to undergo a structural phase transition from the nonferroelectric phase to the ferroelectric phase with spontaneously broken inversion symmetry. Remarkably, we find that the broken symmetry transforms the cubic Dirac point into three mutually crossed nodal rings. There also exist several linear Dirac points in the low-energy band structure of LiOsO3, each of which is transformed into a single nodal ring across the phase transition.

Some Quantum Symmetries and Their Breaking II

NASA Astrophysics Data System (ADS)

Selesnick, S. A.

2013-04-01

We consider symmetry breaking in the context of vector bundle theory, which arises quite naturally not only when attempting to "gauge" symmetry groups, but also as a means of localizing those global symmetry breaking effects known as spontaneous. We review such spontaneous symmetry breaking first for a simplified version of the Goldstone scenario for the case of global symmetries, and then in a localized form which is applied to a derivation of some of the phenomena associated with superconduction in both its forms, type I and type II. We then extend these procedures to effect the Higgs mechanism of electroweak theory, and finally we describe an extension to the flavor symmetries of the lightest quarks, including a brief discussion of CP-violation in the neutral kaon system. A largely self-contained primer of vector bundle theory is provided in Sect. 4, which supplies most of the results required thereafter.

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE PAGES

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen; ...

2017-03-27

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

The phase transitions between Z n × Z n bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n × Z n. We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transitionmore » and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.« less

A topological approach unveils system invariances and broken symmetries in the brain.

PubMed

Tozzi, Arturo; Peters, James F

2016-05-01

Symmetries are widespread invariances underscoring countless systems, including the brain. A symmetry break occurs when the symmetry is present at one level of observation but is hidden at another level. In such a general framework, a concept from algebraic topology, namely, the Borsuk-Ulam theorem (BUT), comes into play and sheds new light on the general mechanisms of nervous symmetries. The BUT tells us that we can find, on an n-dimensional sphere, a pair of opposite points that have the same encoding on an n - 1 sphere. This mapping makes it possible to describe both antipodal points with a single real-valued vector on a lower dimensional sphere. Here we argue that this topological approach is useful for the evaluation of hidden nervous symmetries. This means that symmetries can be found when evaluating the brain in a proper dimension, although they disappear (are hidden or broken) when we evaluate the same brain only one dimension lower. In conclusion, we provide a topological methodology for the evaluation of the most general features of brain activity, i.e., the symmetries, cast in a physical/biological fashion that has the potential to be operationalized. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen Xie; Liu Zhengxin; Wen Xiaogang

2011-12-15

Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z{sub 2} symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related tomore » a nontrivial 3-cocycle of the Z{sub 2} group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if Z{sub 2} symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite Z{sub 2} symmetry-protected topological order.« less

Comment on 'Supersymmetry, PT-symmetry and spectral bifurcation'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagchi, B., E-mail: bbagchi123@rediffmail.com; Quesne, C., E-mail: cquesne@ulb.ac.be

2011-02-15

We demonstrate that the recent paper by Abhinav and Panigrahi entitled 'Supersymmetry, PT-symmetry and spectral bifurcation' [K. Abhinav, P.K. Panigrahi, Ann. Phys. 325 (2010) 1198], which considers two different types of superpotentials for the PT-symmetric complexified Scarf II potential, fails to take into account the invariance under the exchange of its coupling parameters. As a result, they miss the important point that for unbroken PT-symmetry this potential indeed has two series of real energy eigenvalues, to which one can associate two different superpotentials. This fact was first pointed out by the present authors during the study of complex potentials havingmore » a complex sl(2) potential algebra.« less

Human Odometry Verifies the Symmetry Perspective on Bipedal Gaits

ERIC Educational Resources Information Center

Turvey, M. T.; Harrison, Steven J.; Frank, Till D.; Carello, Claudia

2012-01-01

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias "cells") required to model them. Primary gaits are characterized by dihedral symmetry, whereas secondary gaits are characterized by a lower, cyclic symmetry. This fact was used in a test of human…

Conformal field theories from deformations of theories with Wn symmetry

NASA Astrophysics Data System (ADS)

Babaro, Juan Pablo; Giribet, Gaston; Ranjbar, Arash

2016-10-01

We construct a set of nonrational conformal field theories that consist of deformations of Toda field theory for s l (n ). In addition to preserving conformal invariance, the theories may still exhibit a remnant infinite-dimensional affine symmetry. The case n =3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N -point correlation functions on the Riemann sphere and show that these can be expressed in terms of s l (n ) Toda field theory ((N -2 )n +2 ) -point correlation functions.

Symmetry-guaranteed nodal-line semimetals in an fcc lattice

NASA Astrophysics Data System (ADS)

Kawakami, Takuto; Hu, Xiao

2017-12-01

We demonstrate theoretically that nodal-line semimetals (NLSs) can be realized in an fcc lattice with orbitals belonging to the same irreducible representation, such as {px,py,pz} or {dx y,dy z,dz x} orbitals on every lattice site. The three orbitals are divided into two subgroups in terms of the parity with respect to the mirror reflections on high-symmetry planes of the fcc lattice, which, with rotation symmetry, endows symmetry-guaranteed NL passing through W points in the Brillouin zone. Depending on the parameters, there also appears an accidental NL around the Γ point. We notice that the symmetry-guaranteed NL addressed in the present work can be found in band structures of elemental solids taking the fcc structure, such as Cu, Ag, Au, In, Ga, etc., as well as opal, which is an fcc photonic crystal of SiO2 spheres. Furthermore, we clarify that the fcc lattice of Si spheres exhibits a NL in a frequency band where no other photonic band exists, which provides a unique platform to realize topological NLSs under intensive search, and can be explored for achieving slow light.

Increased Sensitivity to Mirror Symmetry in Autism

PubMed Central

Perreault, Audrey; Gurnsey, Rick; Dawson, Michelle; Mottron, Laurent; Bertone, Armando

2011-01-01

Can autistic people see the forest for the trees? Ongoing uncertainty about the integrity and role of global processing in autism gives special importance to the question of how autistic individuals group local stimulus attributes into meaningful spatial patterns. We investigated visual grouping in autism by measuring sensitivity to mirror symmetry, a highly-salient perceptual image attribute preceding object recognition. Autistic and non-autistic individuals were asked to detect mirror symmetry oriented along vertical, oblique, and horizontal axes. Both groups performed best when the axis was vertical, but across all randomly-presented axis orientations, autistics were significantly more sensitive to symmetry than non-autistics. We suggest that under some circumstances, autistic individuals can take advantage of parallel access to local and global information. In other words, autistics may sometimes see the forest and the trees, and may therefore extract from noisy environments genuine regularities which elude non-autistic observers. PMID:21559337

Adding the Third Dimension to Virus Life Cycles: Three-Dimensional Reconstruction of Icosahedral Viruses from Cryo-Electron Micrographs

PubMed Central

Baker, T. S.; Olson, N. H.; Fuller, S. D.

1999-01-01

Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-Å) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical. PMID:10585969

Conformal and projective symmetries in Newtonian cosmology

NASA Astrophysics Data System (ADS)

Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2017-02-01

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schrödinger group or the Conformal Galilei Algebra.

Problems in understanding the structure and assembly of viruses

DOE Office of Scientific and Technical Information (OSTI.GOV)

King, J.

1997-12-01

Though viruses infect the cells of all groups of animals, plants, and microorganisms, their structures follow a limited number of general themes; spherical or cylindrical shells built of hundreds of repeated protein subunits enclosing a nucleic acid - DNA or RNA - genome. Since the 1960s it has been known that the protein shells of spherical viruses in fact conform to icosahedral symmetry or to subtle deviations from icosahedral symmetry. The construction of the shell lattices and the transformations they go through in the different stages of the viral life cycle are not fully understood. The shells contain the nucleicmore » in a highly condensed state, of unknown coiling/organization. Features of the well studied bacterial viruses will be reviewed, with examples from adenoviruses, herpesviruses, poliovirus, and HIV. The emergence of new viral disease has led to increased interest in the development of agents which interfere with virus reproduction at the level of the assembly or function of the organized particle. Recently computational approaches to the problem of virus assembly have made important contributions to clarifying shell assembly processes. 1 ref.« less

Z n clock models and chains of so(n)2 non-Abelian anyons: symmetries, integrable points and low energy properties

NASA Astrophysics Data System (ADS)

Finch, Peter E.; Flohr, Michael; Frahm, Holger

2018-02-01

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain {Z}n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n  =  3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.

Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal

NASA Astrophysics Data System (ADS)

Fan, C. Z.; Weber, Th.; Deloudi, S.; Steurer, W.

2011-07-01

In order to reveal its influence on quasicrystal structure analysis, multiple diffraction (MD) effects in an icosahedral Al-Cu-Fe quasicrystal have been investigated in-house on an Oxford Diffraction four-circle diffractometer equipped with an Onyx™ CCD area detector and MoKα radiation. For that purpose, an automated approach for Renninger scans (ψ-scans) has been developed. Two weak reflections were chosen as the main reflections (called P) in the present measurements. As is well known for periodic crystals, it is also observed for this quasicrystal that the intensity of the main reflection may significantly increase if the simultaneous (H) and the coupling (P-H) reflections are both strong, while there is no obvious MD effect if one of them is weak. The occurrence of MD events during ψ-scans has been studied based on an ideal structure model and the kinematical MD theory. The reliability of the approach is revealed by the good agreement between simulation and experiment. It shows that the multiple diffraction effect is quite significant.

Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus

NASA Astrophysics Data System (ADS)

Kim, Jimin; Baik, Seung Su; Jung, Sung Won; Sohn, Yeongsup; Ryu, Sae Hee; Choi, Hyoung Joon; Yang, Bohm-Jung; Kim, Keun Su

2017-12-01

We report the realization of novel symmetry-protected Dirac fermions in a surface-doped two-dimensional (2D) semiconductor, black phosphorus. The widely tunable band gap of black phosphorus by the surface Stark effect is employed to achieve a surprisingly large band inversion up to ˜0.6 eV . High-resolution angle-resolved photoemission spectra directly reveal the pair creation of Dirac points and their movement along the axis of the glide-mirror symmetry. Unlike graphene, the Dirac point of black phosphorus is stable, as protected by space-time inversion symmetry, even in the presence of spin-orbit coupling. Our results establish black phosphorus in the inverted regime as a simple model system of 2D symmetry-protected (topological) Dirac semimetals, offering an unprecedented opportunity for the discovery of 2D Weyl semimetals.

An empirical approach to symmetry and probability

NASA Astrophysics Data System (ADS)

North, Jill

We often rely on symmetries to infer outcomes' probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this question with an a priori indifference principle. Reasons to reject such a principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning generally. I argue that a priori symmetries need never constrain our probability attributions, even for initial credences.

Topological photonic crystal with ideal Weyl points

NASA Astrophysics Data System (ADS)

Wang, Luyang; Jian, Shao-Kai; Yao, Hong

Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on symmetry analysis, we show that a minimal number of symmetry-related Weyl points can be realized in time-reversal invariant photonic crystals. We propose to realize these ``ideal'' Weyl points in modified double-gyroid photonic crystals, which is confirmed by our first-principle photonic band-structure calculations. Photonic crystals with ideal Weyl points are qualitatively advantageous in applications such as angular and frequency selectivity, broadband invisibility cloaking, and broadband 3D-imaging.

Classification of Arnold-Beltrami flows and their hidden symmetries

NASA Astrophysics Data System (ADS)

Fré, P.; Sorin, A. S.

2015-07-01

In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ℳ3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★ g d, which can be solved by using time-honored harmonic analysis. Taking for ℳ3, a torus T 3 constructed as ℝ3/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ★ g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an

Abelian gauge symmetries in F-theory and dual theories

NASA Astrophysics Data System (ADS)

Song, Peng

In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by

Using Symmetry Group Correlation Tables to Explain why Erham (and Other Programs) cannot BE Used to Analyze Torsional Splittings of Some Molecules

NASA Astrophysics Data System (ADS)

Groner, Peter

2016-06-01

ERHAM has been used to analyze rotational spectra of many molecules with torsional splitting caused by one or two internal rotors. The gauche form of dimethyl ether-d1 whose equilibrium structure has C1 symmetry is an example of a molecule for which ERHAM could not model additional small splittings resolvable for many transitions, whereas the spectrum of the symmetric (anti, trans) form with a C{_s} equilibrium structure could be analyzed successfully with ERHAM. A more recent example where ERHAM failed is pinacolone CH_3-CO-C(CH_3)_3. In this case, the barriers to internal rotation of the methyl groups within the -C(CH_3)_3 unit are too high to produce observable internal rotation splittings, but the splittings due to the CH_3-CO methyl group could not be modeled correctly with ERHAM nor with any other available program (XIAM, BELGI-Cs, BELGI-C1, RAM36). In the paper, it was speculated that BELGI-Cs-2tops might be able to the job, but arguments against this possibility have also been put forward. The correlation between irreducible representations of groups and their subgroups according to Watson can be used not only to determine the total number of substates (components) to be expected but also to help decide which particular program has a chance for a successful analysis. As it turns out, the number of components of split lines depends on the molecular symmetry at equilibrium in relation to the highest possible symmetry for a given molecular symmetry group. Therefore, for pinacolone, the vibrational ground state is split into 10 torsional substates. P. Groner, J. Mol. Spectrosc. 278 (2012) 52-67. C. Richard et al. A&A 552 (2013), A117. Y. Zhao et al., J. Mol. Spectrosc. 318 (2015) 91-100, with references to all other programs mentioned in the abstract. J. K. G. Watson, Can. J. Physics 43 (1965) 1996-2007.

Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals

PubMed Central

Mei, Jun; Chen, Zeguo; Wu, Ying

2016-01-01

We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound. PMID:27587311

Higgsing the stringy higher spin symmetry

DOE PAGES

Gaberdiel, Matthias R.; Peng, Cheng; Zadeh, Ida G.

2015-10-01

It has recently been argued that the symmetric orbifold theory of T 4 is dual to string theory on AdS 3 × S 3 × T 4 at the tensionless point. At this point in moduli space, the theory possesses a very large symmetry algebra that includes, in particular, a W ∞ algebra capturing the gauge fields of a dual higher spin theory. Using conformal perturbation theory, we study the behaviour of the symmetry generators of the symmetric orbifold theory under the deformation that corresponds to switching on the string tension. We show that the generators fall nicely into Reggemore » trajectories, with the higher spin fields corresponding to the leading Regge trajectory. We also estimate the form of the Regge trajectories for large spin, and find evidence for the familiar logarithmic behaviour, thereby suggesting that the symmetric orbifold theory is dual to an AdS background with pure RR flux.« less

Nonlocal Symmetries and Interaction Solutions for Potential Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Ren, Bo; Yu, Jun; Liu, Xi-Zhong

2016-03-01

The nonlocal symmetry for the potential Kadomtsev-Petviashvili (pKP) equation is derived by the truncated Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable. Thanks to localization process, the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems. The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations. Based on the consistent tanh expansion method, a nonauto-Bäcklund transformation (BT) theorem of the pKP equation is constructed. We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem. Some special interaction solutions are investigated both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106, 11275129 and 11405110, the Natural Science Foundation of Zhejiang Province of China under Grant No. LQ13A050001

Broken chiral symmetry on a null plane

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2013-10-15

On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-planemore » description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.« less

Symmetries in Physics

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.

Symmetries in Physics

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.

Deconfined quantum critical point on the triangular lattice

NASA Astrophysics Data System (ADS)

Jian, Chao-Ming; Thomson, Alex; Rasmussen, Alex; Bi, Zhen; Xu, Cenke

2018-05-01

In this work we propose a theory for the deconfined quantum critical point (DQCP) for spin-1/2 systems on a triangular lattice, which is a direct unfine-tuned quantum phase transition between the standard "√{3 }×√{3 } " noncollinear antiferromagnetic order (or the so-called 120∘ state) and the "√{12 }×√{12 } " valence solid bond (VBS) order, both of which are very standard ordered phases often observed in numerical simulations. This transition is beyond the standard Landau-Ginzburg paradigm and is also fundamentally different from the original DQCP theory on the square lattice due to the very different structures of both the magnetic and VBS order on frustrated lattices. We first propose a topological term in the effective-field theory that captures the "intertwinement" between the √{3 }×√{3 } antiferromagnetic order and the √{12 }×√{12 } VBS order. Then using a controlled renormalization-group calculation, we demonstrate that an unfine-tuned direct continuous DQCP exists between the two ordered phases mentioned above. This DQCP is described by the Nf=4 quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/Z4 symmetry only at the critical point. The aforementioned topological term is also naturally derived from the Nf=4 QED. We also point out that physics around this DQCP is analogous to the boundary of a 3 d bosonic symmetry- protected topological state with only on-site symmetries.

Evaluation of Interocular Retinal Nerve Fiber Layer Thickness Symmetry as a Diagnostic Modality for Glaucoma.

PubMed

Hong, Seung Woo; Lee, Seung Bum; Jee, Dong-Hyun; Ahn, Myung Douk

2016-09-01

The purpose of study was to measure the diagnostic utility of interocular retinal nerve fiber layer (RNFL) symmetry and interocular RNFL thickness comparison. Both eyes of 103 normal subjects and 106 glaucoma patients (31 patients with early glaucoma and 75 patients with moderate to severe glaucoma) received comprehensive ophthalmologic evaluation including visual field testing and optic disc scanning using optical coherence tomography. RNFL thickness values for 256 measurement points were rearranged according to a new reference line connecting the optic disc center and the foveola. The interocular RNFL thickness symmetry value and absolute and fractional interocular difference in RNFL thickness were calculated and compared between groups. Area under the receiver operating characteristic curves (AUROCs) were calculated and compared. Among the parameters reflecting whole RNFL status, the corrected interocular RNFL thickness symmetry exhibited the largest AUROCs at all glaucoma stages. RNFL thickness and absolute and fractional interocular difference in RNFL thickness exhibited largest AUROC in the inferotemporal area, regardless of glaucoma stage. In the early glaucoma group, absolute and fractional interocular RNFL thickness differences in the temporal and superotemporal areas exhibited equal to or larger AUROCs than RNFL thickness. The AUROCs for RNFL thickness were greater than those for absolute and fractional interocular RNFL thickness differences in the moderate to severe glaucoma group except in the nasal and temporal area. The corrected interocular RNFL thickness symmetry value is an effective diagnostic tool for glaucoma. Interocular comparison of RNFL thickness has good diagnostic performance and gives information about the RNFL beyond just the RNFL thickness itself.

Fermion-induced quantum critical points.

PubMed

Li, Zi-Xiang; Jiang, Yi-Fan; Jian, Shao-Kai; Yao, Hong

2017-08-22

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

The priority of internal symmetries in particle physics

NASA Astrophysics Data System (ADS)

Kantorovich, Aharon

2003-12-01

In this paper, I try to decipher the role of internal symmetries in the ontological maze of particle physics. The relationship between internal symmetries and laws of nature is discussed within the framework of ;Platonic realism.; The notion of physical ;structure; is introduced as representing a deeper ontological layer behind the observable world. I argue that an internal symmetry is a structure encompassing laws of nature. The application of internal symmetry groups to particle physics came about in two revolutionary steps. The first was the introduction of the internal symmetries of hadrons in the early 1960s. These global and approximate symmetries served as means of bypassing the dynamics. I argue that the realist could interpret these symmetries as ontologically prior to the hadrons. The second step was the gauge revolution in the 1970s, where symmetries became local and exact and were integrated with the dynamics. I argue that the symmetries of the second generation are fundamental in the following two respects: (1) According to the so-called ;gauge argument,; gauge symmetry dictates the existence of gauge bosons, which determine the nature of the forces. This view, which has been recently criticized by some philosophers, is widely accepted in particle physics at least as a heuristic principle. (2) In view of grand unified theories, the new symmetries can be interpreted as ontologically prior to baryon matter.

Note on gauge and gravitational anomalies of discrete Z N symmetries

NASA Astrophysics Data System (ADS)

Byakti, Pritibhajan; Ghosh, Diptimoy; Sharma, Tarun

2018-01-01

In this note, we discuss the consistency conditions which a discrete Z N symmetry should satisfy in order that it is not violated by gauge and gravitational instantons. As examples, we enlist all the Z N ℛ-symmetries as well as non-ℛ Z N symmetries (N=2,3,4) in the minimally supersymmetric standard model (MSSM) that are free from gauge and gravitational anomalies. We show that there exists non-anomalous discrete symmetries that forbid Baryon number violation up to dimension 6 level (in superspace). We also observe that there exists no non-anomalous Z 3 ℛ-symmetry in the MSSM. Furthermore, we point out that in a theory with one Majorana spin 3/2 gravitino, a large class of Z 4 ℛ-symmetries are violated in the presence of Eguchi-Hanson (EH) gravitational instanton. This is also in general true for higher Z N ℛ-symmetries. We also notice that in 4 dimensional N=1 supergravity, the global U(1) ℛ-symmetry is always violated by the EH instanton irrespective of the matter content of the theory.

Mutual information and spontaneous symmetry breaking

NASA Astrophysics Data System (ADS)

Hamma, A.; Giampaolo, S. M.; Illuminati, F.

2016-01-01

We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g., at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly nontrivial. We prove this result in general, by considering the quantum mutual information based on the two-Rényi entanglement entropy and using a locality result stemming from quasiadiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum X Y model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.

Gauging hidden symmetries in two dimensions

NASA Astrophysics Data System (ADS)

Samtleben, Henning; Weidner, Martin

2007-08-01

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine fraktur e9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of fraktur e9. This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of fraktur e9.

Renormalization group fixed points of foliated gravity-matter systems

NASA Astrophysics Data System (ADS)

Biemans, Jorn; Platania, Alessia; Saueressig, Frank

2017-05-01

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.

Topological photonic crystal with equifrequency Weyl points

NASA Astrophysics Data System (ADS)

Wang, Luyang; Jian, Shao-Kai; Yao, Hong

2016-06-01

Weyl points in three-dimensional photonic crystals behave as monopoles of Berry flux in momentum space. Here, based on general symmetry analysis, we show that a minimal number of four symmetry-related (consequently equifrequency) Weyl points can be realized in time-reversal invariant photonic crystals. We further propose an experimentally feasible way to modify double-gyroid photonic crystals to realize four equifrequency Weyl points, which is explicitly confirmed by our first-principle photonic band-structure calculations. Remarkably, photonic crystals with equifrequency Weyl points are qualitatively advantageous in applications including angular selectivity, frequency selectivity, invisibility cloaking, and three-dimensional imaging.

Impact of a nonuniform charge distribution on virus assembly

NASA Astrophysics Data System (ADS)

Li, Siyu; Erdemci-Tandogan, Gonca; Wagner, Jef; van der Schoot, Paul; Zandi, Roya

2017-08-01

Many spherical viruses encapsulate their genomes in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genomes. We model the effect of the nonuniform icosahedral charge distribution from the protein shell instead using a mean-field theory. We find that this nonuniform charge distribution strongly affects the optimal genome length and that it can explain the experimentally observed phenomenon of overcharging of virus and viruslike particles.

Atomistic modeling of the low-frequency mechanical modes and Raman spectra of icosahedral virus capsids

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.

Scale-setting, flavor dependence, and chiral symmetry restoration

DOE PAGES

Binosi, D; Roberts, Craig D.; Rodriguez-Quintero, J.

2017-06-13

Here, we determine the flavor dependence of the renormalization-group-invariant running interaction through judicious use of both unquenched Dyson-Schwinger equation and lattice results for QCD’s gauge-sector two-point functions. An important step is the introduction of a physical scale setting procedure that enables a realistic expression of the effect of different numbers of active quark flavours on the interaction. Using this running interaction in concert with a well constrained class of dressed–gluon-quark vertices, we estimate the critical number of active lighter-quarks above which dynamical chiral symmetry breaking becomes impossible: n cr f ≈ 9; and hence in whose neighborhood QCD is plausiblymore » a conformal theory.« less

Approximate symmetries of Hamiltonians

NASA Astrophysics Data System (ADS)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

Deciphering the kinetic mechanism of spontaneous self-assembly of icosahedral capsids.

PubMed

Nguyen, Hung D; Reddy, Vijay S; Brooks, Charles L

2007-02-01

Self-assembly of viral proteins into icosahedral capsids is an interesting yet poorly understood phenomenon of which elucidation may aid the exploration of beneficial applications of capsids in materials science and medicine. Using molecular dynamics simulations of coarse-grained models for capsid proteins, we show that the competition between the formation of full capsids and nonidealized structures is strongly dependent upon the protein concentration and temperature, occurring kinetically as a cascade of elementary reactions in which free monomers are added to the growing oligomers on a downhill free-energy landscape. However, the insertion of the final subunits is the rate-limiting, energetically unfavorable step in viral capsid assembly. A phase diagram has been constructed to show the regions where capsids or nonidealized structures are stable at each concentration and temperature. We anticipate that our findings will provide guidance in identifying suitable conditions required for in vitro viral capsid assembly experiments.

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

ERIC Educational Resources Information Center

Fujita, Shinsaku

1986-01-01

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

Minimalist approach to the classification of symmetry protected topological phases

NASA Astrophysics Data System (ADS)

Xiong, Zhaoxi

A number of proposals with differing predictions (e.g. group cohomology, cobordisms, group supercohomology, spin cobordisms, etc.) have been made for the classification of symmetry protected topological (SPT) phases. Here we treat various proposals on equal footing and present rigorous, general results that are independent of which proposal is correct. We do so by formulating a minimalist Generalized Cohomology Hypothesis, which is satisfied by existing proposals and captures essential aspects of SPT classification. From this Hypothesis alone, formulas relating classifications in different dimensions and/or protected by different symmetry groups are derived. Our formalism is expected to work for fermionic as well as bosonic phases, Floquet as well as stationary phases, and spatial as well as on-site symmetries.

Baryon magnetic moments: Symmetries and relations

NASA Astrophysics Data System (ADS)

Parreño, Assumpta; Savage, Martin J.; Tiburzi, Brian C.; Wilhelm, Jonas; Chang, Emmanuel; Detmold, William; Orginos, Kostas

2018-03-01

Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled ∑0- ⋀ system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spinflavor symmetry in the large Nc limit of QCD is shared by the naïve constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggest further calculations that would shed light on the curious patterns of baryon magnetic moments.

Broken Symmetry

ScienceCinema

Englert, Francois

2018-05-24

- 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

Asymptotic symmetries and electromagnetic memory

NASA Astrophysics Data System (ADS)

Pasterski, Sabrina

2017-09-01

Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts — so called "memories". Namely, low frequency emissions in momentum space correspond to long time integrations of the corre-sponding radiation in position space. Memory effect observables constructed in this manner are non-vanishing in typical scattering processes, which has implications for the asymptotic symmetry group. Here we complete this triad for the case of large U(1) gauge symmetries at null infinity. In particular, we show that the previously studied electromagnetic memory effect, whereby the passage of electromagnetic radiation produces a net velocity kick for test charges in a distant detector, is the position space observable corresponding to th Weinberg soft photon pole in momentum space scattering amplitudes.

Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems

PubMed Central

Mohanasubha, R.; Chandrasekar, V. K.; Lakshmanan, M.

2016-01-01

In this work, we establish a connection between the extended Prelle–Singer procedure and other widely used analytical methods to identify integrable systems in the case of nth-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to the nth-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations. PMID:27436964

Interocular high-order corneal wavefront aberration symmetry

NASA Astrophysics Data System (ADS)

Lombardo, Marco; Lombardo, Giuseppe; Serrao, Sebastiano

2006-04-01

The interocular symmetry of the high-order corneal wavefront aberration (WA) in a population of myopic eyes was analyzed before and after photorefractive keratectomy (PRK). The preoperative and one-year postoperative corneal aberration data (from third to seventh Zernike orders) for 4- and 7-mm pupils from right and left eyes were averaged after correcting for the effects of enantiomorphism to test for mirror symmetry. Also, the mean corneal point-spread function (PSF) for right and left eyes was calculated. Preoperatively, a moderate and high degree of correlation in the high-order corneal WA between eyes was found for 4- and 7-mm pupils, respectively. Myopic PRK did not significantly change the interocular symmetry of corneal high-order aberrations. No discernible differences in the orientation PSF between eyes were observed one year after surgery in comparison with the preoperative state over the two analyzed pupils.

Symmetry breaking by bifundamentals

NASA Astrophysics Data System (ADS)

Schellekens, A. N.

2018-03-01

We derive all possible symmetry breaking patterns for all possible Higgs fields that can occur in intersecting brane models: bifundamentals and rank-2 tensors. This is a field-theoretic problem that was already partially solved in 1973 by Ling-Fong Li [1]. In that paper the solution was given for rank-2 tensors of orthogonal and unitary group, and U (N )×U (M ) and O (N )×O (M ) bifundamentals. We extend this first of all to symplectic groups. When formulated correctly, this turns out to be straightforward generalization of the previous results from real and complex numbers to quaternions. The extension to mixed bifundamentals is more challenging and interesting. The scalar potential has up to six real parameters. Its minima or saddle points are described by block-diagonal matrices built out of K blocks of size p ×q . Here p =q =1 for the solutions of Ling-Fong Li, and the number of possibilities for p ×q is equal to the number of real parameters in the potential, minus 1. The maximum block size is p ×q =2 ×4 . Different blocks cannot be combined, and the true minimum occurs for one choice of basic block, and for either K =1 or K maximal, depending on the parameter values.

Gravitation, Symmetry and Undergraduates

NASA Astrophysics Data System (ADS)

Jorgensen, Jamie

2001-04-01

This talk will discuss "Project Petrov" Which is designed to investigate gravitational fields with symmetry. Project Petrov represents a collaboration involving physicists, mathematicians as well as graduate and undergraduate math and physics students. An overview of Project Petrov will be given, with an emphasis on students' contributions, including software to classify and generate Lie algebras, to classify isometry groups, and to compute the isometry group of a given metric.

Symmetry enriched U(1) quantum spin liquids

NASA Astrophysics Data System (ADS)

Zou, Liujun; Wang, Chong; Senthil, T.

2018-05-01

We classify and characterize three-dimensional U (1 ) quantum spin liquids [deconfined U (1 ) gauge theories] with global symmetries. These spin liquids have an emergent gapless photon and emergent electric/magnetic excitations (which we assume are gapped). We first discuss in great detail the case with time-reversal and SO(3 ) spin rotational symmetries. We find there are 15 distinct such quantum spin liquids based on the properties of bulk excitations. We show how to interpret them as gauged symmetry-protected topological states (SPTs). Some of these states possess fractional response to an external SO (3 ) gauge field, due to which we dub them "fractional topological paramagnets." We identify 11 other anomalous states that can be grouped into three anomaly classes. The classification is further refined by weakly coupling these quantum spin liquids to bosonic symmetry protected topological (SPT) phases with the same symmetry. This refinement does not modify the bulk excitation structure but modifies universal surface properties. Taking this refinement into account, we find there are 168 distinct such U (1 ) quantum spin liquids. After this warm-up, we provide a general framework to classify symmetry enriched U (1 ) quantum spin liquids for a large class of symmetries. As a more complex example, we discuss U (1 ) quantum spin liquids with time-reversal and Z2 symmetries in detail. Based on the properties of the bulk excitations, we find there are 38 distinct such spin liquids that are anomaly-free. There are also 37 anomalous U (1 ) quantum spin liquids with this symmetry. Finally, we briefly discuss the classification of U (1 ) quantum spin liquids enriched by some other symmetries.

Consistency condition for inflation from (broken) conformal symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schalm, Koenraad; Aalst, Ted van der; Shiu, Gary, E-mail: kschalm@lorentz.leidenuniv.nl, E-mail: shiu@physics.wisc.edu, E-mail: vdaalst@lorentz.leidenuniv.nl

2013-03-01

We investigate the symmetry constraints on the bispectrum, i.e. the three-point correlation function of primordial density fluctuations, in slow-roll inflation. It follows from the defining property of slow-roll inflation that primordial correlation functions inherit most of their structure from weakly broken de Sitter symmetries. Using holographic techniques borrowed from the AdS/CFT correspondence, the symmetry constraints on the bispectrum can be mapped to a set of stress-tensor Ward identities in a weakly broken 2+1-dimensional Euclidean CFT. We construct the consistency condition from these Ward identities using conformal perturbation theory. This requires a second order Ward identity and the use of themore » evolution equation. Our result also illustrates a subtle difference between conformal perturbation theory and the slow-roll expansion.« less

Weak Lie symmetry and extended Lie algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goenner, Hubert

2013-04-15

The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).

Statistics of Point Vortex Turbulence in Non-neutral Flows and in Flows with Translational and Rotational Symmetries

NASA Astrophysics Data System (ADS)

Esler, J. G.

2017-12-01

A theory (Esler and Ashbee in J Fluid Mech 779:275-308, 2015) describing the statistics of N freely-evolving point vortices in a bounded two-dimensional domain is extended. First, the case of a non-neutral vortex gas is addressed, and it is shown that the density of states function can be identified with the probability density function of an infinite sum of independent non-central chi-squared random variables, the details of which depend only on the shape of the domain. Equations for the equilibrium energy spectrum and other statistical quantities follow, the validity of which are verified against direct numerical simulations of the equations of motion. Second, domains with additional conserved quantities associated with a symmetry (e.g., circle, periodic channel) are investigated, and it is shown that the treatment of the non-neutral case can be modified to account for the additional constraint.

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

PubMed

Stróż, Kazimierz

2011-09-01

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic

Al-centered icosahedral ordering in Cu46Zr46Al8 bulk metallic glass

NASA Astrophysics Data System (ADS)

Fang, H. Z.; Hui, X.; Chen, G. L.; Liu, Z. K.

2009-03-01

Icosahedral short-range order, of which Al atoms are caged in the center of icosahedra with Cu and Zr atoms being the vertices, has been evidenced in the Cu46Zr46Al8 glassy structure by ab initio molecular dynamics simulation. These Al-centered clusters distribute irregularly in the three-dimensional space and form a "backbone" structure of the Cu46Zr46Al8 glass alloy. It is suggested that this kind of local structural feature is attributed to the requirement of efficient dense packing and the chemical affinity between Zr-Zr, Zr-Al, and Cu-Zr atoms. Our calculated results are found to be in good agreement with the experimental data.

R parity violation from discrete R symmetries

DOE PAGES

Chen, Mu-Chun; Ratz, Michael; Takhistov, Volodymyr

2014-12-15

We consider supersymmetric extensions of the standard model in which the usual R or matter parity gets replaced by another R or non–R discrete symmetry that explains the observed longevity of the nucleon and solves the µ problem of MSSM. In order to identify suitable symmetries, we develop a novel method of deriving the maximal Z (R) N symmetry that satisfies a given set of constraints. We identify R parity violating (RPV) and conserving models that are consistent with precision gauge unification and also comment on their compatibility with a unified gauge symmetry such as the Pati–Salam group. Finally, wemore » provide a counter– example to the statement found in the recent literature that the lepton number violating RPV scenarios must have µ term and the bilinear κ L Hu operator of comparable magnitude.« less

Influence of leaching on surface composition, microstructure, and valence band of single grain icosahedral Al-Cu-Fe quasicrystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lowe, M.; McGrath, R.; Sharma, H. R.

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 bymore » x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe{sub 3}O{sub 4} rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.« less

Symmetry breaking patterns for inflation

NASA Astrophysics Data System (ADS)

Klein, Remko; Roest, Diederik; Stefanyszyn, David

2018-06-01

We study inflationary models where the kinetic sector of the theory has a non-linearly realised symmetry which is broken by the inflationary potential. We distinguish between kinetic symmetries which non-linearly realise an internal or space-time group, and which yield a flat or curved scalar manifold. This classification leads to well-known inflationary models such as monomial inflation and α-attractors, as well as a new model based on fixed couplings between a dilaton and many axions which non-linearly realises higher-dimensional conformal symmetries. In this model, inflation can be realised along the dilatonic direction, leading to a tensor-to-scalar ratio r ˜ 0 .01 and a spectral index n s ˜ 0 .975. We refer to the new model as ambient inflation since inflation proceeds along an isometry of an anti-de Sitter ambient space-time, which fully determines the kinetic sector.

Nanostructure symmetry: Relevance for physics and computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dupertuis, Marc-André; Oberli, D. Y.; Karlsson, K. F.

2014-03-31

We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.

Thirty-thousand-year-old distant relative of giant icosahedral DNA viruses with a pandoravirus morphology

PubMed Central

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

2014-01-01

The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine–thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine–cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590

Thirty-thousand-year-old distant relative of giant icosahedral DNA viruses with a pandoravirus morphology.

PubMed

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

2014-03-18

The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine-thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine-cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health.

The Eightfold Way: A Theory of Strong Interaction Symmetry

DOE R&D Accomplishments Database

Gell-Mann, M.

1961-03-15

A new model of the higher symmetry of elementary particles is introduced ln which the eight known baryons are treated as a supermultiplet, degenerate in the limit of unitary symmetry but split into isotopic spin multiplets by a symmetry-breaking term. The symmetry violation is ascribed phenomenologically to the mass differences. The baryons correspond to an eight-dimensional irreducible representation of the unitary group. The pion and K meson fit into a similar set of eight particles along with a predicted pseudoscalar meson X {sup o} having I = 0. A ninth vector meson coupled to the baryon current can be accommodated naturally in the scheme. It is predicted that the eight baryons should all have the same spin and parity and that pseudoscalar and vector mesons should form octets with possible additional singlets. The mathematics of the unitary group is described by considering three fictitious leptons, nu , e {sup -}, and mu {sup -}, which may throw light on the structure of weak interactions. (D. L.C.)

ASP: Automated symbolic computation of approximate symmetries of differential equations

NASA Astrophysics Data System (ADS)

Jefferson, G. F.; Carminati, J.

2013-03-01

A recent paper (Pakdemirli et al. (2004) [12]) compared three methods of determining approximate symmetries of differential equations. Two of these methods are well known and involve either a perturbation of the classical Lie symmetry generator of the differential system (Baikov, Gazizov and Ibragimov (1988) [7], Ibragimov (1996) [6]) or a perturbation of the dependent variable/s and subsequent determination of the classical Lie point symmetries of the resulting coupled system (Fushchych and Shtelen (1989) [11]), both up to a specified order in the perturbation parameter. The third method, proposed by Pakdemirli, Yürüsoy and Dolapçi (2004) [12], simplifies the calculations required by Fushchych and Shtelen's method through the assignment of arbitrary functions to the non-linear components prior to computing symmetries. All three methods have been implemented in the new MAPLE package ASP (Automated Symmetry Package) which is an add-on to the MAPLE symmetry package DESOLVII (Vu, Jefferson and Carminati (2012) [25]). To our knowledge, this is the first computer package to automate all three methods of determining approximate symmetries for differential systems. Extensions to the theory have also been suggested for the third method and which generalise the first method to systems of differential equations. Finally, a number of approximate symmetries and corresponding solutions are compared with results in the literature.

Baryon magnetic moments: Symmetries and relations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parreno, Assumpta; Savage, Martin; Tiburzi, Brian

Magnetic moments of the octet baryons are computed using lattice QCD in background magnetic fields, including the first treatment of the magnetically coupled Σ0- Λ system. Although the computations are performed for relatively large values of the up and down quark masses, we gain new insight into the symmetries and relations between magnetic moments by working at a three-flavor mass-symmetric point. While the spinflavor symmetry in the large Nc limit of QCD is shared by the naïve constituent quark model, we find instances where quark model predictions are considerably favored over those emerging in the large Nc limit. We suggestmore » further calculations that would shed light on the curious patterns of baryon magnetic moments.« less

Implementing the SU(2) Symmetry for the DMRG

NASA Astrophysics Data System (ADS)

Alvarez, Gonzalo

2010-03-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992), Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This talk will explain how the DMRG++ codefootnotetextarXiv:0902.3185 or Computer Physics Communications 180 (2009) 1572-1578. has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries will be discussed for typical tight-binding models of strongly correlated electronic systems. The computational bottleneck of the algorithm, and the use of shared memory parallelization will also be addressed. Finally, a roadmap for future work on DMRG++ will be presented.

Molecular Symmetry Analysis of Low-Energy Torsional and Vibrational States in the S_{0} and S_{1} States of p-XYLENE to Interpret the Rempi Spectrum

NASA Astrophysics Data System (ADS)

Groner, Peter; Gardner, Adrian M.; Tuttle, William Duncan; Wright, Timothy G.

2017-06-01

The electronic transition S_{1} ← S_{0} of p-xylene (pXyl) has been observed by REMPI spectroscopy. Its analysis required a detailed investigation of the molecular symmetry of pXyl whose methyl groups are almost free internal rotors. The molecular symmetry group of pXyl has 72 operators. This group, called [33]D_{2h}, is isomorphic to G_{36}(EM), the double group for ethane and dimethyl acetylene even though it is NOT a double group for pXyl. Loosely speaking, the group symbol, [33]D_{2h}, indicates that is for a molecule with two threefold rotors on a molecular frame with D_{2h} point group symmetry. The transformation properties of the (i) free internal rotor basis functions for the torsional coordinates, (ii) the asymmetric rotor (Wang) basis functions for the Eulerian angles, (iii) nuclear spin functions, (iv) potential function, and (v) transitions dipole moment functions were determined. The forms of the torsional potential in the S_{0} and S_{1} states and the dependence of the first order torsional splittings on the potential coefficients have been obtained. AM Gardner, WD Tuttle, P. Groner, TG Wright, J. Chem. Phys., submitted Dec 2016 P Groner, JR Durig, J. Chem. Phys., 66 (1977) 1856 PR Bunker, P Jensen, Molecular Symmetry and Spectroscopy (1998, NRC Research Press, Ottawa, 2nd ed.)

Continuous Symmetry and Chemistry Teachers: Learning Advanced Chemistry Content through Novel Visualization Tools

ERIC Educational Resources Information Center

Tuvi-Arad, Inbal; Blonder, Ron

2010-01-01

In this paper we describe the learning process of a group of experienced chemistry teachers in a specially designed workshop on molecular symmetry and continuous symmetry. The workshop was based on interactive visualization tools that allow molecules and their symmetry elements to be rotated in three dimensions. The topic of continuous symmetry is…

Emergence of a new S U (4 ) symmetry in the baryon spectrum

NASA Astrophysics Data System (ADS)

Denissenya, M.; Glozman, L. Ya.; Pak, M.

2015-10-01

Recently, a large degeneracy of J =1 mesons—that is, larger than the S U (2 )L×S U (2 )R×U (1 )A symmetry of the QCD Lagrangian—has been discovered upon truncation of the near-zero modes from the valence quark propagators. It has been found that this degeneracy represents the S U (4 ) group that includes the chiral rotations as well as the mixing of left- and right-handed quarks. This symmetry group turns out to be a symmetry of confinement in QCD. Consequently, one expects that the same symmetry should persist upon the near-zero mode removal in other hadron sectors as well. It has been shown that indeed the J =2 mesons follow the same symmetry pattern upon the low-lying mode elimination. Here we demonstrate the S U (4 ) symmetry of baryons once the near-zero modes are removed from the quark propagators. We also show a degeneracy of states belonging to different irreducible representations of S U (4 ). This implies a larger symmetry that includes S U (4 ) as a subgroup.

Unity of quark and lepton interactions with symplectic gauge symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajpoot, S.

1982-07-01

Properties of symplectic groups are reviewed and the gauge structure of Sp(2n) derived. The electroweak unification of leptons within Sp(8) gauge symmetry and grand unification of quarks and leptons within Sp(10) gauge symmetry are discussed.

Symmetry Groups of the Austenite Lattice and Construction of Self-Accommodation Complexes of Martensite Crystals in Alloys with the Shape-Memory Effect

NASA Astrophysics Data System (ADS)

Khundjua, A. G.; Ptitsin, A. G.; Brovkina, E. A.

2018-01-01

The internal structure of experimentally observed self-accommodation complexes of martensite crystals, which is determined by the system of twinning planes, is studied in this work. The direct correlation of the construction type of the complexes with the subgroups of the austenite lattice symmetry group is shown.

Black Hole Entropy from Bondi-Metzner-Sachs Symmetry at the Horizon.

PubMed

Carlip, S

2018-03-09

Near the horizon, the obvious symmetries of a black hole spacetime-the horizon-preserving diffeomorphisms-are enhanced to a larger symmetry group with a three-dimensional Bondi-Metzner-Sachs algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry and show that it is strong enough to determine the black hole entropy in any dimension.

Lie Symmetry Analysis and Conservation Laws of a Generalized Time Fractional Foam Drainage Equation

NASA Astrophysics Data System (ADS)

Wang, Li; Tian, Shou-Fu; Zhao, Zhen-Tao; Song, Xiao-Qiu

2016-07-01

In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann—Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method. Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No. 201410290039, the Fundamental Research Funds for the Central Universities under Grant Nos. 2015QNA53 and 2015XKQY14, the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Mines, the General Financial Grant from the China Postdoctoral Science Foundation under Grant No. 2015M570498, and Natural Sciences Foundation of China under Grant No. 11301527

Numerical preservation of symmetry properties of continuum problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caramana, E.J.; Whalen, P.

1997-12-31

The authors investigate the problem of perfectly preserving a symmetry associated naturally with one coordinate system when calculated in a different coordinate system. This allows a much wider range of problems that may be viewed as perturbations of the given symmetry to be investigated. They study the problem of preserving cylindrical symmetry in two-dimensional cartesian geometry and spherical symmetry in two-dimensional cylindrical geometry. They show that this can be achieved by a simple modification of the gradient operator used to compute the force in a staggered grid Lagrangian hydrodynamics algorithm. In the absence of the supposed symmetry they show thatmore » the new operator produces almost no change in the results because it is always close to the original gradient operator. Their technique this results in a subtle manipulation of the spatial truncation error in favor of the assumed symmetry but only to the extent that it is naturally present in the physical situation. This not only extends the range of previous algorithms and the use of new ones for these studies, but for spherical or cylindrical calculations reduces the sensitivity of the results to grid setup with equal angular zoning that has heretofore been necessary with these problems. Although this work is in two-dimensions, it does point the way to solving this problem in three-dimensions. This is particularly important for the ASCI initiative. The manner in which these results can be extended to three-dimensions will be discussed.« less

On systems having Poincaré and Galileo symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holland, Peter, E-mail: peter.holland@gtc.ox.ac.uk

Using the wave equation in d≥1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d=1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated withmore » the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d>1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell’s equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.« less

Common reflection point migration and velocity analysis for anisotropic media

NASA Astrophysics Data System (ADS)

Oropeza, Ernesto V.

An efficient Kirchhoff-style prestack depth migration, called 'parsimonious' migration was developed a decade ago for isotropic 2D and 3D media. The common-reflection point (CRP) migration velocity analysis (MVA) was developed later for isotropic media. The isotropic parsimonious migration produces incorrect images when the media is actually anisotropic. Similarly, isotropic CRP MVA produces incorrect inversions when the medium is anisotropic. In this study both parsimonious depth migration and common-reflection point migration velocity analysis are extended for application to 2D tilted transversely isotropic (TTI) media and illustrated with synthetic P-wave data. While the framework of isotropic parsimonious migration may be retained, the extension to TTI media requires redevelopment of each of the numerical components, including calculation of the phase and group velocity for TTI media, development of a new two-point anisotropic ray tracer, and substitution of an initial-angle and anisotropic shooting ray-trace algorithm to replace the isotropic one. The 2D model parameterization consists of Thomsen's parameters (Vpo, epsilon, delta) and the tilt angle of the symmetry axis of the TI medium. The parsimonious anisotropic migration algorithm is successfully applied to synthetic data from a TTI version of the Marmousi-2 model. The quality of the image improves by weighting the impulse response by the calculation of the anisotropic Fresnel radius. The accuracy and speed of this migration makes it useful for anisotropic velocity model building. The common-reflection point migration velocity analysis for TTI media for P-waves includes (and inverts for) Vpo, epsilon, and delta. The orientation of the anisotropic symmetry axis have to be constrained. If it constrained orthogonal to the layer bottom (as it conventionally is), it is estimated at each CRP and updated at each iteration without intermediate picking. The extension to TTI media requires development of a new

Symmetry, stability, and computation of degenerate lasing modes

NASA Astrophysics Data System (ADS)

Liu, David; Zhen, Bo; Ge, Li; Hernandez, Felipe; Pick, Adi; Burkhardt, Stephan; Liertzer, Matthias; Rotter, Stefan; Johnson, Steven G.

2017-02-01

We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

Asymptotic symmetries of colored gravity in three dimensions

NASA Astrophysics Data System (ADS)

Joung, Euihun; Kim, Jaewon; Kim, Jihun; Rey, Soo-Jong

2018-03-01

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU( N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU( N, N) × SU( N, N) gauge group, the theory contains graviton, SU( N) Chern-Simons gauge fields and massless spin-two multiplets in the SU( N) adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of \\widehat{su(N)} Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.

Learning in the machine: The symmetries of the deep learning channel.

PubMed

Baldi, Pierre; Sadowski, Peter; Lu, Zhiqin

2017-11-01

In a physical neural system, learning rules must be local both in space and time. In order for learning to occur, non-local information must be communicated to the deep synapses through a communication channel, the deep learning channel. We identify several possible architectures for this learning channel (Bidirectional, Conjoined, Twin, Distinct) and six symmetry challenges: (1) symmetry of architectures; (2) symmetry of weights; (3) symmetry of neurons; (4) symmetry of derivatives; (5) symmetry of processing; and (6) symmetry of learning rules. Random backpropagation (RBP) addresses the second and third symmetry, and some of its variations, such as skipped RBP (SRBP) address the first and the fourth symmetry. Here we address the last two desirable symmetries showing through simulations that they can be achieved and that the learning channel is particularly robust to symmetry variations. Specifically, random backpropagation and its variations can be performed with the same non-linear neurons used in the main input-output forward channel, and the connections in the learning channel can be adapted using the same algorithm used in the forward channel, removing the need for any specialized hardware in the learning channel. Finally, we provide mathematical results in simple cases showing that the learning equations in the forward and backward channels converge to fixed points, for almost any initial conditions. In symmetric architectures, if the weights in both channels are small at initialization, adaptation in both channels leads to weights that are essentially symmetric during and after learning. Biological connections are discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Symmetry in running.

PubMed

Raibert, M H

1986-03-14

Symmetry plays a key role in simplifying the control of legged robots and in giving them the ability to run and balance. The symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A legged system running with these symmetries travels with a fixed forward speed and a stable upright posture. The symmetries used for controlling legged robots may help in elucidating the legged behavior of animals. Measurements of running in the cat and human show that the feet and body sometimes move as predicted by the even and odd symmetry functions.

Semiconducting icosahedral boron arsenide crystal growth for neutron detection

NASA Astrophysics Data System (ADS)

Whiteley, C. E.; Zhang, Y.; Gong, Y.; Bakalova, S.; Mayo, A.; Edgar, J. H.; Kuball, M.

2011-03-01

Semiconducting icosahedral boron arsenide, B12As2, is an excellent candidate for neutron detectors, thermoelectric converters, and radioisotope batteries, for which high quality single crystals are required. Thus, the present study was undertaken to grow B12As2 crystals by precipitation from metal solutions (nickel) saturated with elemental boron (or B12As2 powder) and arsenic in a sealed quartz ampoule. B12As2 crystals of 10-15 mm were produced when a homogeneous mixture of the three elements was held at 1150 °C for 48-72 h and slowly cooled (3.5 °C/h). The crystals varied in color and transparency from black and opaque to clear and transparent. X-ray topography (XRT), and elemental analysis by energy dispersive X-ray spectroscopy (EDS) confirmed that the crystals had the expected rhombohedral structure and chemical stoichiometry. The concentrations of residual impurities (nickel, carbon, etc.) were low, as measured by Raman spectroscopy and secondary ion mass spectrometry (SIMS). Additionally, low etch-pit densities (4.4×107 cm-2) were observed after etching in molten KOH at 500 °C. Thus, the flux growth method is viable for growing large, high-quality B12As2 crystals.

The quantum structure of anionic hydrogen clusters

NASA Astrophysics Data System (ADS)

Calvo, F.; Yurtsever, E.

2018-03-01

A flexible and polarizable interatomic potential has been developed to model hydrogen clusters interacting with one hydrogen anion, (H2)nH-, in a broad range of sizes n = 1-54 and parametrized against coupled cluster quantum chemical calculations. Using path-integral molecular dynamics simulations at 1 K initiated from the putative classical global minima, the equilibrium structures are found to generally rely on icosahedral shells with the hydrogen molecules pointing toward the anion, producing geometric magic numbers at sizes n = 12, 32, and 44 that are in agreement with recent mass spectrometry measurements. The energetic stability of the clusters is also connected with the extent of vibrational delocalization, measured here by the fluctuations among inherent structures hidden in the vibrational wave function. As the clusters grow, the outer molecules become increasingly free to rotate, and strong finite size effects are also found between magic numbers, associated with more prominent vibrational delocalization. The effective icosahedral structure of the 44-molecule cluster is found to originate from quantum nuclear effects as well, the classical structure showing no particular symmetry.

Conservation laws and symmetries of a generalized Kawahara equation

NASA Astrophysics Data System (ADS)

Gandarias, Maria Luz; Rosa, Maria; Recio, Elena; Anco, Stephen

2017-06-01

The generalized Kawahara equation ut = a(t)uxxxxx + b(t)uxxx + c(t) f (u)ux appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation ut = αuux + βu2ux + γuxxx + μuxxxxx. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

Tensor network states and algorithms in the presence of a global SU(2) symmetry

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder; Vidal, Guifre

2012-11-01

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g., with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely, (i) [Singh, Pfeifer, and Vidal, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.050301 82, 050301 (2010)] and (ii) [Singh, Pfeifer, and Vidal, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.115125 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible, and multiplicity free, acting as a global internal symmetry. Then, in (ii) we described the implementation of Abelian group symmetries in much more detail, considering a U(1) symmetry (e.g., conservation of global particle number) as a concrete example. In this paper, we describe the implementation of non-Abelian group symmetries in great detail. For concreteness, we consider an SU(2) symmetry (e.g., conservation of global quantum spin). Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we

The symmetries of the fine gradings of sl(n{sup k},C) associated with direct product of Pauli groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Han Gang

2010-09-15

A grading of a Lie algebra is called fine if it could not be further refined. For a fine grading of a simple Lie algebra, we define its Weyl group to describe the symmetry of this grading. It is already known that the Weyl group of the fine grading of sl(n,C) induced by the action of the group {Pi}{sub n} of the generalized Pauli matrices of rank n is SL(2,Z{sub n}), where Z{sub n} is the cyclic group of order n. In this paper, we consider the fine grading of sl(n{sup k},C) induced by the action of the group ofmore » k-fold tensor product of the generalized Pauli matrices of rank n. We prove that its Weyl group is Sp(2k,Z{sub n}) and is generated by transvections; therefore, this generalizes the previous result.« less

Dirac neutrinos with S4 flavor symmetry in warped extra dimensions

NASA Astrophysics Data System (ADS)

Ding, Gui-Jun; Zhou, Ye-Ling

2013-11-01

We present a warped extra dimension model with the custodial symmetry SU(2×SU(2×U(1×PLR based on the flavor symmetry S4×Z2×Z2', and the neutrinos are taken to be Dirac particles. At leading order, the democratic lepton mixing is derived exactly, and the high-dimensional operators introduce corrections of order λc to all the three lepton mixing angles such that agreement with the experimental data can be achieved. The neutrino mass spectrum is predicted to be of the inverted hierarchy and the second octant of θ23 is preferred. We suggest the modified democratic mixing, which is obtained by permuting the second and the third rows of the democratic mixing matrix, should be a good first order approximation to understanding sizable θ13 and the first octant of θ23. The constraints on the model from the electroweak precision measurements are discussed. Furthermore, we investigate the lepton mixing patterns for all the possible residual symmetries Gν and Gl in the neutrino and charged lepton sectors, respectively. For convenience, we work in the base in which m≡mlml† is diagonal, where ml is the charged lepton mass matrix. It is easy to see that the symmetry transformation matrix Gl, which is determined by the condition Gl†mGl=m, is a diagonal and non-degenerate 3×3 phase matrix. In the case that neutrinos are Majorana particles, the light neutrino mass matrix for DC mixing is of the form mνDC=UDC*diag(m1,m2,m3)UDC†. The symmetry transformations Gi, which satisfy GiTmνDCGi=mνDC, are determined to be G1=+u1u1†-u2u2†-u3u3†, G2=-u1u1†+u2u2†-u3u3† and G3=-u1u1†-u2u2†+u3u3† besides the identity transformation, where ui is the ith column of UDC. They satisfy Gi2=1, GiGj=GjGi=Gk(i≠j≠k). Consequently the symmetry group of the neutrino mass matrix mνDC is the Klein four group K4≅Z2×Z2. Denoting the underlying family symmetry group at high energies as G, then the symmetry transformations Gl and Gi should be the elements of G. In the

THE EIGHTFOLD WAY: A THEORY OF STRONG INTERACTION SYMMETRY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gell-Mann, M.

1961-03-15

A new model of the higher symmetry of elementary particles is introduced ln which the eight known baryons are treated as a supermultiplet, degenerate in the limit of unitary symmetry but split into isotopic spin multiplets by a symmetry-breaking term. The symmetry violation is sscribed phenomenologically to the mass differences. The baryons correspond to an eight-dimensional irreducible representation of the unitary group. The pion and K meson fit into a similar set of eight particles along with a predicted pseudoscalar meson X/sup o/ having I = 0. A ninth vector meson coupled to the baryon current can be accomodated natarallymore » in the scheme. It is predicted that the eight baryons should all have the same spin and parity and that pseudoscalar and vector mesons should form octets with possible additional singlets. The mathematics of the unitary group is described by considering three fictitious leptons, nu , e/sup -/ , and mu /sup -/, which may throw light on the structure of weak interactions. (D. L.C.)« less

Generalized classes of continuous symmetries in two-mode Dicke models

NASA Astrophysics Data System (ADS)

Moodie, Ryan I.; Ballantine, Kyle E.; Keeling, Jonathan

2018-03-01

As recently realized experimentally [Nature (London) 543, 87 (2017), 10.1038/nature21067], one can engineer models with continuous symmetries by coupling two cavity modes to trapped atoms via a Raman pumping geometry. Considering specifically cases where internal states of the atoms couple to the cavity, we show an extended range of parameters for which continuous symmetry breaking can occur, and we classify the distinct steady states and time-dependent states that arise for different points in this extended parameter regime.

Coherent backscattering enhancement in cavities. Highlights of the role of symmetry.

PubMed

Gallot, Thomas; Catheline, Stefan; Roux, Philippe

2011-04-01

Through experiments and simulations, the consequences of symmetry on coherent backscattering enhancement (CBE) are studied in cavities. Three main results are highlighted. First, the CBE outside the source is observed: (a) on a single symmetric point in a one-dimensional (1-D) cavity, in a disk and in a symmetric chaotic plate; (b) on three symmetric points in a two-dimensional (2-D) rectangle; and (c) on seven symmetric points in a three-dimensional (3-D) parallelepiped cavity. Second, the existence of enhanced intensity lines and planes in 2-D and 3-D simple-shape cavities is demonstrated. Third, it is shown how the anti-symmetry caused by the special boundary conditions is responsible for the existence of a coherent backscattering decrement with a dimensional dependence of R = (½)(d), with d = 1,2,3 as the dimensionality of the cavity.

The symmetry of man.

PubMed

Ermolenko, Alexander E; Perepada, Elena A

2007-01-01

The paper contains a description of basic regularities in the manifestation of symmetry of human structural organization and its ontogenetic and phylogenetic development. A concept of macrobiocrystalloid with inherent complex symmetry is proposed for the description of the human organism in its integrity. The symmetry can be characterized as two-plane radial (quadrilateral), where the planar symmetry is predominant while the layout of organs of radial symmetry is subordinated to it. Out of the two planes of symmetry (sagittal and horizontal), the sagittal plane is predominant. The symmetry of the chromosome, of the embrio at the early stages of cell cleavage as well as of some organs and systems in their phylogenetic development is described. An hypothesis is postulated that the two-plane symmetry is formed by two mechanisms: a) the impact of morphogenetic fields of the whole crystalloid organism during embriogenesis and, b) genetic mechanisms of the development of chromosomes having two-plane symmetry.

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

DOE PAGES

Braun, Volker; Cvetič, Mirjam; Donagi, Ron; ...

2017-07-26

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braun, Volker; Cvetič, Mirjam; Donagi, Ron

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less

Decoherence and discrete symmetries in deformed relativistic kinematics

NASA Astrophysics Data System (ADS)

Arzano, Michele

2018-01-01

Models of deformed Poincaré symmetries based on group valued momenta have long been studied as effective modifications of relativistic kinematics possibly capturing quantum gravity effects. In this contribution we show how they naturally lead to a generalized quantum time evolution of the type proposed to model fundamental decoherence for quantum systems in the presence of an evaporating black hole. The same structures which determine such generalized evolution also lead to a modification of the action of discrete symmetries and of the CPT operator. These features can in principle be used to put phenomenological constraints on models of deformed relativistic symmetries using precision measurements of neutral kaons.

Mimicking glide symmetry dispersion with coupled slot metasurfaces

NASA Astrophysics Data System (ADS)

Camacho, Miguel; Mitchell-Thomas, Rhiannon C.; Hibbins, Alastair P.; Sambles, J. Roy; Quevedo-Teruel, Oscar

2017-09-01

In this letter, we demonstrate that the dispersion properties associated with glide symmetry can be achieved in systems that only possess reflection symmetry by balancing the influence of two sublattices. We apply this approach to a pair of coupled slots cut into an infinite perfectly conducting plane. Each slot is notched on either edge, with the complete two-slot system having only mirror symmetry. By modifying the relative size of the notches on either side of the slots, we show that a linear dispersion relation with a degeneracy with non-zero group velocity at the Brillouin zone boundary can be achieved. These properties, until now, only found in systems with glide symmetry are numerically and experimentally validated. We also show that these results can be used for the design of ultra-wideband one-dimensional leaky wave antennas in coplanar waveguide technology.

Point defects in crystalline zircon (zirconium silicate), ZrSiO4: electron paramagnetic resonance studies

NASA Astrophysics Data System (ADS)

Tennant, W. C.; Claridge, R. F. C.; Walsby, C. J.; Lees, N. S.

This article outlines the present state of knowledge of paramagnetic defects in crystalline zircon as obtained mainly, but not exclusively, from electron paramagnetic resonance (EPR) studies in crystalline zircon (zirconium silicate, ZrSiO4). The emphasis is on single-crystal studies where, in principle, unambiguous analysis is possible. Firstly, the crystallography of zircon is presented. Secondly, the relationships between available crystal-site symmetries and the symmetries of observed paramagnetic species in zircon, and how these observations lead to unambiguous assignments of point-group symmetries for particular paramagnetic species are detailed. Next, spin-Hamiltonian (SH) analysis is discussed with emphasis on the symmetry relationships that necessarily exist amongst the Laue classes of the crystal sites in zircon, the paramagnetic species occupying those sites and the SH itself. The final sections of the article then survey the results of EPR studies on zircon over the period 1960-2002.

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming

2015-07-01

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice modelsmore » as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Quantum phase transitions between a class of symmetry protected topological states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsui, Lokman; Jiang, Hong -Chen; Lu, Yuan -Ming

2015-04-30

The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1(G,U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realizedmore » in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less

Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations

PubMed Central

Ceyhan, Elvan

2014-01-01

We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures. We use Pielou's and Dixon's symmetry tests which are defined using contingency tables based on the NN relationships between the data points. We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou's first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used. Under RL, we derive the asymptotic distribution for Dixon's symmetry test and also observe that the usual independence test seems to be appropriate for Pielou's second type of test. Moreover, we apply variants of Fisher's exact test on the shared NN contingency table for Pielou's second test and determine the most appropriate version for our setting. We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test. We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations. The methods are illustrated on a real-life ecological data set. PMID:24605061

Axial point groups: rank 1, 2, 3 and 4 property tensor tables.

PubMed

Litvin, Daniel B

2015-05-01

The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites.

Time-reversal and rotation symmetry breaking superconductivity in Dirac materials

NASA Astrophysics Data System (ADS)

Chirolli, Luca; de Juan, Fernando; Guinea, Francisco

2017-05-01

We consider mixed symmetry superconducting phases in Dirac materials in the odd-parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of a finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by peculiar bulk quasiparticles, with Weyl nodes and nodal lines, and distinctive surface states. These findings are consistent with recent experiments on NbxBi2Se3 that report evidence of point nodes, nematicity, and TRSB superconductivity induced by Nb magnetic moments.

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

Alternative schemes of predicting lepton mixing parameters from discrete flavor and C P symmetry

NASA Astrophysics Data System (ADS)

Lu, Jun-Nan; Ding, Gui-Jun

2017-01-01

We suggest two alternative schemes to predict lepton mixing angles as well as C P violating phases from a discrete flavor symmetry group combined with C P symmetry. In the first scenario, the flavor and C P symmetry is broken to the residual groups of the structure Z2×C P in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters θν and θl. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant C P transformation, all lepton mixing parameters are determined in terms of three free parameters θ1 ,2 ,3. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters θν ,l and θ1 ,2 ,3 is taken into account. We have studied the lepton mixing patterns arising from the flavor group S4 and C P symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.

Lungeing on hard and soft surfaces: Movement symmetry of trotting horses considered sound by their owners.

PubMed

Pfau, T; Jennings, C; Mitchell, H; Olsen, E; Walker, A; Egenvall, A; Tröster, S; Weller, R; Rhodin, M

2016-01-01

Lungeing is often part of the clinical lameness examination. The difference in movement symmetry, which is a commonly employed lameness measure, has not been quantified between surfaces. To compare head and pelvic movement symmetry between surfaces and reins during lungeing. Quantitative gait analysis in 23 horses considered sound by their owners. Twenty-three horses were assessed in-hand and on the lunge on both reins on hard and soft surfaces with inertial sensors. Seven movement symmetry parameters were quantified and used to establish 2 groups, namely symmetrical (n = 9) and forelimb-lame horses (n = 14), based on values from straight-line assessment. Movement symmetry values for left rein measurements were side corrected to allow comparison of the amount of movement symmetry between reins. A mixed model (P<0.05) was used to study effects on movement symmetry of surface (hard/soft) and rein (inside/outside with respect to movement symmetry on the straight). In forelimb-lame horses, surface and rein were identified as significantly affecting all head movement symmetry measures (rein, all P<0.0001; surface, all P<0.042). In the symmetrical group, no significant influence of surface or rein was identified for head movement symmetry (rein, all P>0.245; surface, all P>0.073). No significant influence of surface or rein was identified for any of the pelvic movement symmetry measures in either group. While more symmetrical horses showed a consistent amount of movement symmetry across surfaces/reins, horses objectively quantified as lame on the straight showed decreased movement symmetry during lungeing, in particular with the lame limb on the inside of a hard circle. The variation within group questions straight-line movement symmetry as a sole measure of lameness without quantification of movement symmetry on the lunge, ideally on hard and soft surfaces to evaluate differences between reins and surfaces. In future, thresholds for lungeing need to be determined using

Symmetrical group theory for mathematical complexity reduction of digital holograms

NASA Astrophysics Data System (ADS)

Perez-Ramirez, A.; Guerrero-Juk, J.; Sanchez-Lara, R.; Perez-Ramirez, M.; Rodriguez-Blanco, M. A.; May-Alarcon, M.

2017-10-01

This work presents the use of mathematical group theory through an algorithm to reduce the multiplicative computational complexity in the process of creating digital holograms. An object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image, where the image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity ( k - 1) × N for the case of sparse matrices and binary images, where k is the number of pixels other than zero and N is the total points in the image.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer.

PubMed

Sharma, Sandeep

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.

A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

NASA Astrophysics Data System (ADS)

Sharma, Sandeep

2015-01-01

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.

Nanosized (mu12-Pt)Pd164-xPtx(CO)72(PPh3)20 (x approximately 7) containing Pt-centered four-shell 165-atom Pd-Pt core with unprecedented intershell bridging carbonyl ligands: comparative analysis of icosahedral shell-growth patterns with geometrically related Pd145(CO)x(PEt3)30 (x approximately 60) containing capped three-shell Pd145 core.

PubMed

Mednikov, Evgueni G; Jewell, Matthew C; Dahl, Lawrence F

2007-09-19

Presented herein are the preparation and crystallographic/microanalytical/magnetic/spectroscopic characterization of the Pt-centered four-shell 165-atom Pd-Pt cluster, (mu(12)-Pt)Pd(164-x)Pt(x)(CO)(72)(PPh(3))(20) (x approximately 7), 1, that replaces the geometrically related capped three-shell icosahedral Pd(145) cluster, Pd(145)(CO)(x)(PEt(3))(30) (x approximately 60), 2, as the largest crystallographically determined discrete transition metal cluster with direct metal-metal bonding. A detailed comparison of their shell-growth patterns gives rise to important stereochemical implications concerning completely unexpected structural dissimilarities as well as similarities and provides new insight concerning possible synthetic approaches for generation of multi-shell metal clusters. 1 was reproducibly prepared in small yields (<10%) from the reaction of Pd(10)(CO)(12)(PPh(3))(6) with Pt(CO)(2)(PPh(3))(2). Its 165-atom metal-core geometry and 20 PPh(3) and 72 CO ligands were established from a low-temperature (100 K) CCD X-ray diffraction study. The well-determined crystal structure is attributed largely to 1 possessing cubic T(h) (2/m3) site symmetry, which is the highest crystallographic subgroup of the noncrystallographic pseudo-icosahedral I(h) (2/m35) symmetry. The "full" four-shell Pd-Pt anatomy of 1 consists of: (a) shell 1 with the centered (mu(12)-Pt) atom encapsulated by the 12-atom icosahedral Pt(x)Pd(12-x) cage, x = 1.2(3); (b) shell 2 with the 42-atom nu(2) icosahedral Pt(x)Pd(42-x) cage, x = 3.5(5); (c) shell 3 with the anti-Mackay 60-atom semi-regular rhombicosidodecahedral Pt(x)Pd(60-x) cage, x = 2.2(6); (d) shell 4 with the 50-atom nu(2) pentagonal dodecahedral Pd(50) cage. The total number of crystallographically estimated Pt atoms, 8 +/- 3, which was obtained from least-squares (Pt(x)/Pd(1-x))-occupancy analysis of the X-ray data that conclusively revealed the central atom to be pure Pt (occupancy factor, x = 1.00(3)), is fortuitously in agreement

Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.

PubMed

Heyl, Markus; Vojta, Matthias

2014-10-31

One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.

Complete theory of symmetry-based indicators of band topology.

PubMed

Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

2017-06-30

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

Large gauge transformations and little group for soft photons

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Seo, Min-Seok; Shiu, Gary

2017-11-01

Recently, large gauge transformation (LGT), the residual gauge symmetry after gauge fixing that survives at null infinity, has drawn much attention concerning soft theorems and the memory effect. We point out that LGT charges in quantum electrodynamics are in fact one of noncompact generators of the two dimensional Euclidean group. Moreover, by comparing two equivalent descriptions of gauge transformation, we suggest that LGT is simply another way of describing the gauged little group for massless soft photons.

Application of symmetry properties to polarimetric remote sensing with JPL AIRSAR data

NASA Technical Reports Server (NTRS)

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

1992-01-01

Based on symmetry properties, polarimetric remote sensing of geophysical media is studied. From the viewpoint of symmetry groups, media with reflection, rotation, azimuthal, and centrical symmetries are considered. The symmetries impose relations among polarimetric scattering coefficients, which are valid to all scattering mechanisms in the symmetrical configurations. Various orientation distributions of non-spherical scatterers can be identified from the scattering coefficients by a comparison with the symmetry calculations. Experimental observations are then analyzed for many geophysical scenes acquired with the Jet Propulsion Laboratory (JPL) airborne polarimetric SAR at microwave frequencies over sea ice and vegetation. Polarimetric characteristics of different ice types are compared with symmetry behaviors. The polarimetric response of a tropical rain forest reveals characteristics close to the centrical symmetry properties, which can be used as a distributed target to relatively calibrate polarimetric radars without any deployment of manmade calibration targets.

Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay constant

NASA Astrophysics Data System (ADS)

Kim, Jihn E.; Nam, Soonkeon; Semetzidis, Yannis K.

2018-01-01

Pseudoscalars appearing in particle physics are reviewed systematically. From the fundamental point of view at an ultraviolet completed theory, they can be light if they are realized as pseudo-Goldstone bosons of some spontaneously broken global symmetries. The spontaneous breaking scale is parametrized by the decay constant f. The global symmetry is defined by the lowest order terms allowed in the effective theory consistent with the gauge symmetry in question. Since any global symmetry is known to be broken at least by quantum gravitational effects, all pseudoscalars should be massive. The mass scale is determined by f and the explicit breaking terms ΔV in the effective potential and also anomaly terms ΔΛG4 for some non-Abelian gauge groups G. The well-known example by non-Abelian gauge group breaking is the potential for the “invisible” QCD axion, via the Peccei-Quinn symmetry, which constitutes a major part of this review. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms ΔV in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a “quintessential axion.” In general, (ΔV )1/4 is considered to be smaller than f, and hence the pseudo-Goldstone boson mass scales are considered to be smaller than the decay constants. In such a case, the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model, which is known as “natural inflation.” We review all these ideas in the bosonic collective motion framework.

Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy

NASA Astrophysics Data System (ADS)

Takasaki, K.

1990-08-01

Symmetry properties of the space of complex (or formal) hyper-Kähler metrics are studied in the language of hyper-Kähler hierarchies. The construction of finite symmetries is analogous to the theory of Riemann-Hilbert transformations, loop group elements now taking values in a (pseudo-) group of canonical transformations of a simplectic manifold. In spite of their highly nonlinear and involved nature, infinitesimal expressions of these symmetries are shown to have a rather simple form. These infinitesimal transformations are extended to the Plebanski key functions to give rise to a nonlinear realization of a Poisson loop algebra. The Poisson algebra structure turns out to originate in a contact structure behind a set of symplectic structures inherent in the hyper-Kähler hierarchy. Possible relations to membrane theory are briefly discussed.

Multiple Weyl points and the sign change of their topological charges in woodpile photonic crystals

NASA Astrophysics Data System (ADS)

Chang, Ming-Li; Xiao, Meng; Chen, Wen-Jie; Chan, C. T.

2017-03-01

We show that Weyl points with topological charges 1 and 2 can be found in very simple chiral woodpile photonic crystals and the distribution of the charges can be changed by changing the material parameters without altering space-group symmetry. The underlying physics can be understood through a tight-binding model. Gapless surface states and their backscattering immune properties also are demonstrated in these systems. Obtaining Weyl points in these easily fabricated woodpile photonic crystals will facilitate the realization of Weyl point physics in optical and IR frequencies.

Generalization of Friedberg-Lee symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang Chaoshang; Li Tianjun; George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A and M University, College Station, Texas 77843

2008-07-01

We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)xU(1) global flavor symmetry in the lepton sector.more » After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)xU(1) flavor symmetry breaking.« less

Aspects of Higher-Spin Conformal Field Theories and Their Renormalization Group Flows

NASA Astrophysics Data System (ADS)

Diab, Kenan S.

In this thesis, we study conformal field theories (CFTs) with higher-spin symmetry and the renormalization group flows of some models with interactions that weakly break the higher-spin symmetry. When the higher-spin symmetry is exact, we will present CFT analogues of two classic results in quantum field theory: the Coleman-Mandula theorem, which is the subject of chapter 2, and the Weinberg-Witten theorem, which is the subject of chapter 3. Schematically, our Coleman-Mandula analogue states that a CFT that contains a symmetric conserved current of spin s > 2 in any dimension d > 3 is effectively free, and our Weinberg-Witten analogue states that the presence of certain short, higher-spin, "sufficiently asymmetric" representations of the conformal group is either inconsistent with conformal symmetry or leads to free theories in d = 4 dimensions. In both chapters, the basic strategy is to solve certain Ward identities in convenient kinematical limits and thereby show that the number of solutions is very limited. In the latter chapter, Hofman-Maldacena bounds, which constrain one-point functions of the stress tensor in general states, play a key role. Then, in chapter 4, we will focus on the particular examples of the O(N) and Gross-Neveu model in continuous dimensions. Using diagrammatic techniques, we explicitly calculate how the coefficients of the two-point function of a U(1) current and the two-point function of the stress tensor (CJ and CT, respectively) are renormalized in the 1/N and epsilon expansions. From the higher-spin perspective, these models are interesting since they are related via the AdS/CFT correspondence to Vasiliev gravity. In addition to checking and extending a number of previously-known results about CT and CJ in these theories, we find that in certain dimensions, CJ and CT are not monotonic along the renormalization group flow. Although it was already known that certain supersymmetric models do not satisfy a "CJ"- or " CT"-theorem, this

Symmetry breaking in tensor models

NASA Astrophysics Data System (ADS)

Benedetti, Dario; Gurau, Razvan

2015-11-01

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.

Robust group-wise rigid registration of point sets using t-mixture model

NASA Astrophysics Data System (ADS)

Ravikumar, Nishant; Gooya, Ali; Frangi, Alejandro F.; Taylor, Zeike A.

2016-03-01

A probabilistic framework for robust, group-wise rigid alignment of point-sets using a mixture of Students t-distribution especially when the point sets are of varying lengths, are corrupted by an unknown degree of outliers or in the presence of missing data. Medical images (in particular magnetic resonance (MR) images), their segmentations and consequently point-sets generated from these are highly susceptible to corruption by outliers. This poses a problem for robust correspondence estimation and accurate alignment of shapes, necessary for training statistical shape models (SSMs). To address these issues, this study proposes to use a t-mixture model (TMM), to approximate the underlying joint probability density of a group of similar shapes and align them to a common reference frame. The heavy-tailed nature of t-distributions provides a more robust registration framework in comparison to state of the art algorithms. Significant reduction in alignment errors is achieved in the presence of outliers, using the proposed TMM-based group-wise rigid registration method, in comparison to its Gaussian mixture model (GMM) counterparts. The proposed TMM-framework is compared with a group-wise variant of the well-known Coherent Point Drift (CPD) algorithm and two other group-wise methods using GMMs, using both synthetic and real data sets. Rigid alignment errors for groups of shapes are quantified using the Hausdorff distance (HD) and quadratic surface distance (QSD) metrics.

Providing nearest neighbor point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer

DOEpatents

Archer, Charles J.; Faraj, Ahmad A.; Inglett, Todd A.; Ratterman, Joseph D.

2012-10-23

Methods, apparatus, and products are disclosed for providing nearest neighbor point-to-point communications among compute nodes of an operational group in a global combining network of a parallel computer, each compute node connected to each adjacent compute node in the global combining network through a link, that include: identifying each link in the global combining network for each compute node of the operational group; designating one of a plurality of point-to-point class routing identifiers for each link such that no compute node in the operational group is connected to two adjacent compute nodes in the operational group with links designated for the same class routing identifiers; and configuring each compute node of the operational group for point-to-point communications with each adjacent compute node in the global combining network through the link between that compute node and that adjacent compute node using that link's designated class routing identifier.

Symmetry Beyond Perturbation Theory: Floppy Molecules and Rotation-Vibration States

NASA Astrophysics Data System (ADS)

Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per

2015-06-01

In the customary approach to the theoretical description of the nuclear motion in molecules, the molecule is seen as a near-static structure rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction, which fails in fluxional molecules, where all vibrational motions are large compared to the linear extension of the molecule. An example is protonated methane (CH_5^+). For this molecule, customary theory fails to simulate reliably even the low-energy spectrum. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions can be symmetry classified separately in the molecular symmetry (MS) group. In the present contribution we discuss a fundamental group theoretical approach to the problem of determining the symmetries of molecular rotation-vibration states. We will show that all MS groups discussed so far are subgroups of the special orthogonal group in three dimensions SO(3) This leads to a group theoretical foundation of the technique of equivalent rotations. The MS group of protonated methane (G240) represents, to the best of our knowledge, the first example of an MS group which is not a subgroup of SO(3) (nor of O(3) nor of SU(2)). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. We want to discuss the consequences of this. In conclusion, we show that the prototypical floppy molecule CH_5^+ represents a new class of molecules, where usual group theoretical methods for determining selection rules and spectral assignments fail so that new methods have to be developed. P. Kumar and D. Marx, Physical Chemistry Chemical Physics 8, 573 (2006) Z. Jin, B. J. Braams, and J. M. Bowman, The Journal of Physical Chemistry A 110, 1569 (2006) A. S. Petit, J. E

Effect of chiral symmetry on chaotic scattering from Majorana zero modes.

PubMed

Schomerus, H; Marciani, M; Beenakker, C W J

2015-04-24

In many of the experimental systems that may host Majorana zero modes, a so-called chiral symmetry exists that protects overlapping zero modes from splitting up. This symmetry is operative in a superconducting nanowire that is narrower than the spin-orbit scattering length, and at the Dirac point of a superconductor-topological insulator heterostructure. Here we show that chiral symmetry strongly modifies the dynamical and spectral properties of a chaotic scatterer, even if it binds only a single zero mode. These properties are quantified by the Wigner-Smith time-delay matrix Q=-iℏS^{†}dS/dE, the Hermitian energy derivative of the scattering matrix, related to the density of states by ρ=(2πℏ)^{-1}TrQ. We compute the probability distribution of Q and ρ, dependent on the number ν of Majorana zero modes, in the chiral ensembles of random-matrix theory. Chiral symmetry is essential for a significant ν dependence.

Symmetry of extremely floppy molecules: Molecular states beyond rotation-vibration separation

NASA Astrophysics Data System (ADS)

Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per

2015-10-01

Traditionally, molecules are theoretically described as near-static structures rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction, which fails in highly fluxional molecules, where all vibrational motions have amplitudes comparable in size to the linear dimensions of the molecule. An example is protonated methane (CH 5+ ) [P. Kumar and D. Marx, Phys. Chem. Chem. Phys. 8, 573 (2006); Z. Jin et al., J. Phys. Chem. A 110, 1569 (2006); and A. S. Petit et al., J. Phys. Chem. A 118, 7206 (2014)]. For these molecules, customary theory fails to simulate reliably even the low-energy spectrum [T. Oka, Science 347, 1313-1314 (2015) and O. Asvany et al., Science 347, 1346-1349 (2015)]. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions can be symmetry classified separately in the molecular symmetry (MS) group [P. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, NRC Monograph Publishing Program (NRC Research Press, 2006)]. In this article, we discuss a fundamental group theoretical approach to the problem of determining the symmetries of molecular rotation-vibration states. We will show that all MS groups discussed so far are isomorphic to subgroups of the special orthogonal group in three dimensions SO(3). This leads to a group theoretical foundation of the technique of equivalent rotations [H. Longuet-Higgins, Mol. Phys. 6, 445 (1963)]. The group G240 (the MS group of protonated methane) represents, to the best of our knowledge, the first example of a MS group which is not isomorphic to a subgroup of SO(3) (nor of O(3) or of SU(2)). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. We discuss here the consequences of this. In

A point particle model of lightly bound skyrmions

NASA Astrophysics Data System (ADS)

Gillard, Mike; Harland, Derek; Kirk, Elliot; Maybee, Ben; Speight, Martin

2017-04-01

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number 1 ≤ B ≤ 8 obtained by numerical simulation of the full field theory. For 9 ≤ B ≤ 23, a large number of static solutions of the point particle model are found, all closely resembling size B subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.

Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2017-10-01

In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov's method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.

Symmetry Breaking in a random passive scalar

NASA Astrophysics Data System (ADS)

Kilic, Zeliha; McLaughlin, Richard; Camassa, Roberto

2017-11-01

We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. Analytical results are compared directly to Monte Carlo simulations. Time permitting we will compare the predictions to experimental observations.

Symmetry Enriched Topological Phases and Their Edge Theories

NASA Astrophysics Data System (ADS)

Heinrich, Christopher

In this thesis we investigate topological phases of matter that have a global, unbroken symmetry group--also known as symmetry enriched topological (SET) phases. We address three questions about these phases: (1) how can we build exactly solvable models that realize them? (2) how can we determine if their edge theories can be gapped without breaking the symmetry? and (3) how do we understand the phenomenon of decoupled charge and neutral modes which occurs in certain fractional quantum Hall states? More specifically, we address the first question by constructing exactly solvable models for a wide class of symmetry enriched topological (SET) phases, which we call symmetry-enriched string nets. The construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group G, and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples. For the second question, we focus on the edge theories of 2D SET phases with Z2 symmetry. The central problem we seek to solve is to determine which edge theories can be gapped without breaking the symmetry. Previous attempts to answer this question in special cases relied on constructing perturbations of a particular type to gap the edge. This method proves the edge can be gapped when the appropriate perturbations can be found, but is inconclusive if they cannot be found. We build on this previous work by deriving a necessary and sufficient algebraic condition for when the edge can be gapped. Our results apply to Z2 symmetry protected topological phases as well as Abelian Z2 SET phases. Finally, in the fourth chapter, we describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges

Pd surface and Pt subsurface segregation in Pt1-c Pd c nanoalloys

NASA Astrophysics Data System (ADS)

De Clercq, A.; Giorgio, S.; Mottet, C.

2016-02-01

The structure and chemical arrangement of Pt1-c Pd c nanoalloys with the icosahedral and face centered cubic symmetry are studied using Monte Carlo simulations with a tight binding interatomic potential fitted to density-functional theory calculations. Pd surface segregation from the lowest to the highest coordinated sites is predicted by the theory together with a Pt enrichment at the subsurface, whatever the structure and the size of the nanoparticles, and which subsists when increasing the temperature. The onion-shell chemical configuration is found for both symmetries and is initiated from the Pd surface segregation. It is amplified in the icosahedral symmetry and small sizes but when considering larger sizes, the oscillating segregation profile occurs near the surface on about three to four shells whatever the structure. Pd segregation results from the significant lower cohesive energy of Pd as compared to Pt and the weak ordering tendency leads to the Pt subsurface segregation. The very weak size mismatch does not prevent the bigger atoms (Pt) from occupying subsurface sites which are in compression whereas the smaller ones (Pd) occupy the central site of the icosahedra where the compression is an order of magnitude higher.

Measurement of Radiation Symmetry in Z-Pinch Driven Hohlraums

NASA Astrophysics Data System (ADS)

Hanson, David L.

2001-10-01

The z-pinch driven hohlraum (ZPDH) is a promising approach to high yield inertial confinement fusion currently being characterized in experiments on the Sandia Z accelerator [1]. In this concept [2], x rays are produced by an axial z-pinch in a primary hohlraum at each end of a secondary hohlraum. A fusion capsule in the secondary is imploded by a symmetric x-ray flux distribution, effectively smoothed by wall reemission during transport to the capsule position. Capsule radiation symmetry, a critical issue in the design of such a system, is influenced by hohlraum geometry, wall motion and time-dependent albedo, as well as power balance and pinch timing between the two z-pinch x-ray sources. In initial symmetry studies on Z, we used solid low density burnthrough spheres to diagnose highly asymmetric, single-sided-drive hohlraum geometries. We then applied this technique to the more symmetric double z-pinch geometry [3]. As a result of design improvements, radiation flux symmetry in Z double-pinch wire array experiments now exceeds the measurement sensitivity of this self-backlit foam ball symmetry diagnostic (15% max-min flux asymmetry). To diagnose radiation symmetry at the 2 - 5% level attainable with our present ZPDH designs, we are using high-energy x rays produced by the recently-completed Z-Beamlet laser backlighter for point-projection imaging of thin-wall implosion and symmetry capsules. We will present the results of polar flux symmetry measuremets on Z for several ZPDH capsule geometries together with radiosity and radiation-hydrodynamics simulations for comparison. [1] M. E. Cuneo et al., Phys. Plasmas 8,2257(2001); [2] J. H. Hammer et al., Phys. Plasmas 6,2129(1999); [3] D. L. Hanson et al., Bull. Am. Phys. Soc. 45,360(2000).

Nuclear magnetic resonance in low-symmetry superconductors

NASA Astrophysics Data System (ADS)

Cavanagh, D. C.; Powell, B. J.

2018-01-01

We consider the nuclear spin-lattice relaxation rate 1 /T1 in superconductors with accidental nodes, i.e., zeros of the order parameter that are not enforced by its symmetries. Such nodes in the superconducting gap are not constrained by symmetry to a particular position on the Fermi surface. We show, analytically and numerically, that a Hebel-Slichter-like peak occurs even in the absence of an isotropic component of the superconducting gap. For a gap with symmetry-required nodes the Fermi velocity at the node must point along the node. For accidental nodes this is not, in general, the case. This leads to additional terms in spectral function and hence the density of states. These terms lead to a logarithmic divergence in 1 /T1T at T →Tc- in models neglecting disorder and interactions [except for those leading to superconductivity; here T is temperature, Tc-=limδ→0(Tc-δ ) , and Tc is the critical temperature]. This contrasts with the usual Hebel-Slichter peak which arises from the coherence factors due to the isotropic component of the gap and leads to a divergence in 1 /T1T somewhat below Tc. The divergence in superconductors with accidental nodes is controlled by either disorder or additional electron-electron interactions. However, for reasonable parameters, neither of these effects removes the peak altogether. This provides a simple experimental method to distinguish between symmetry-required and accidental nodes.

Unconventional Topological Phase Transition in Two-Dimensional Systems with Space-Time Inversion Symmetry

NASA Astrophysics Data System (ADS)

Ahn, Junyeong; Yang, Bohm-Jung

2017-04-01

We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.

Symmetries of Chimera States

NASA Astrophysics Data System (ADS)

Kemeth, Felix P.; Haugland, Sindre W.; Krischer, Katharina

2018-05-01

Symmetry broken states arise naturally in oscillatory networks. In this Letter, we investigate chaotic attractors in an ensemble of four mean-coupled Stuart-Landau oscillators with two oscillators being synchronized. We report that these states with partially broken symmetry, so-called chimera states, have different setwise symmetries in the incoherent oscillators, and in particular, some are and some are not invariant under a permutation symmetry on average. This allows for a classification of different chimera states in small networks. We conclude our report with a discussion of related states in spatially extended systems, which seem to inherit the symmetry properties of their counterparts in small networks.

Neutrinos and flavor symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tanimoto, Morimitsu

2015-07-15

We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.

Majorana dark matter with B+L gauge symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chao, Wei; Guo, Huai-Ke; Zhang, Yongchao

Here, we present a new model that extends the Standard Model (SM) with the local B + L symmetry, and point out that the lightest new fermion, introduced to cancel anomalies and stabilized automatically by the B + L symmetry, can serve as the cold dark matter candidate. We also study constraints on the model from Higgs measurements, electroweak precision measurements as well as the relic density and direct detections of the dark matter. Our numerical results reveal that the pseudo-vector coupling of with Z and the Yukawa coupling with the SM Higgs are highly constrained by the latest resultsmore » of LUX, while there are viable parameter space that could satisfy all the constraints and give testable predictions.« less

Majorana dark matter with B+L gauge symmetry

DOE PAGES

Chao, Wei; Guo, Huai-Ke; Zhang, Yongchao

2017-04-07

Here, we present a new model that extends the Standard Model (SM) with the local B + L symmetry, and point out that the lightest new fermion, introduced to cancel anomalies and stabilized automatically by the B + L symmetry, can serve as the cold dark matter candidate. We also study constraints on the model from Higgs measurements, electroweak precision measurements as well as the relic density and direct detections of the dark matter. Our numerical results reveal that the pseudo-vector coupling of with Z and the Yukawa coupling with the SM Higgs are highly constrained by the latest resultsmore » of LUX, while there are viable parameter space that could satisfy all the constraints and give testable predictions.« less

All-atom molecular dynamics of the HBV capsid reveals insights into biological function and cryo-EM resolution limits

PubMed Central

Perilla, Juan R; Schlicksup, Christopher John; Venkatakrishnan, Balasubramanian; Zlotnick, Adam; Schulten, Klaus

2018-01-01

The hepatitis B virus capsid represents a promising therapeutic target. Experiments suggest the capsid must be flexible to function; however, capsid structure and dynamics have not been thoroughly characterized in the absence of icosahedral symmetry constraints. Here, all-atom molecular dynamics simulations are leveraged to investigate the capsid without symmetry bias, enabling study of capsid flexibility and its implications for biological function and cryo-EM resolution limits. Simulation results confirm flexibility and reveal a propensity for asymmetric distortion. The capsid’s influence on ionic species suggests a mechanism for modulating the display of cellular signals and implicates the capsid’s triangular pores as the location of signal exposure. A theoretical image reconstruction performed using simulated conformations indicates how capsid flexibility may limit the resolution of cryo-EM. Overall, the present work provides functional insight beyond what is accessible to experimental methods and raises important considerations regarding asymmetry in structural studies of icosahedral virus capsids. PMID:29708495

Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota-Satsuma coupled KdV system

NASA Astrophysics Data System (ADS)

Saberi, Elaheh; Reza Hejazi, S.

2018-02-01

In the present paper, Lie point symmetries of the time-fractional generalized Hirota-Satsuma coupled KdV (HS-cKdV) system based on the Riemann-Liouville derivative are obtained. Using the derived Lie point symmetries, we obtain similarity reductions and conservation laws of the considered system. Finally, some analytic solutions are furnished by means of the invariant subspace method in the Caputo sense.

New pyridinium-based fluorescent dyes: A comparison of symmetry and side-group effects on G-Quadruplex DNA binding selectivity and application in live cell imaging.

PubMed

Lu, Yu-Jing; Hu, Dong-Ping; Zhang, Kun; Wong, Wing-Leung; Chow, Cheuk-Fai

2016-07-15

A series of C1-, C2-and C3-symmetric pyridinium conjugates with different styrene-like side groups were synthesized and were utilized as G-quadruplex selective fluorescent probes. The new compounds were well-characterized. Their selectivity, sensitivity, and stability towards G-quadruplex were studied by fluorescence titration, native PAGE experiments, FRET and circular dichroism (CD) analyses. These new compounds investigated in the fluorescence assays were preferentially bound with G-quadruplex DNA compared with other type of nucleic acids and it is fascinating to realize the effects of molecular symmetry and associated side groups showing unexpectedly great influence on the fluorescent signal enhancement for the discrimination of G-quadruplexes DNA from other nucleic acids. This may correlate with the pocket symmetry and shape of the G-quadruplex DNA inherently. Among the compounds, a C2-symmetric dye (2,6-bis-((E)-2-(1H-indol-3-yl)-vinyl)-1-methylpyridin-1-ium iodide) with indolyl-groups substituted was screened out from the series giving the best selectivity and sensitivity towards G-quadruplexes DNA, particularly telo21, due to its high equilibrium binding constant (K=2.17×10(5)M(-1)). In addition, the limit of detection (LOD) of the dye to determine telo21 DNA in bioassays was found as low as 33nM. The results of the study give insight and certain crucial factors, such as molecular symmetry and the associated side groups, on developing of effective fluorescent dyes for G-quadruplex DNA applications including G-quadruplex structure stabilization, biosensing and clinical applications. The compound was also demonstrated as a very selective G-quadruplex fluorescent agent for living cell staining and imaging. Copyright © 2016 Elsevier B.V. All rights reserved.

Crossing symmetry in alpha space

NASA Astrophysics Data System (ADS)

Hogervorst, Matthijs; van Rees, Balt C.

2017-11-01

We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which are labeled by a complex number α. This leads to a systematic method for computing conformal block decompositions. Analyzing bootstrap equations in alpha space turns crossing symmetry into an eigenvalue problem for an integral operator K. The operator K is closely related to the Wilson transform, and some of its eigenfunctions can be found in closed form.

Nuclear tetrahedral symmetry: possibly present throughout the periodic table.

PubMed

Dudek, J; Goźdź, A; Schunck, N; Miśkiewicz, M

2002-06-24

More than half a century after the fundamental, spherical shell structure in nuclei had been established, theoretical predictions indicated that the shell gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the TD(d) ("double-tetrahedral") symmetry group. Strong shell-gap structure is enhanced by the existence of the four-dimensional irreducible representations of TD(d); it can be seen as a geometrical effect that does not depend on a particular realization of the mean field. Possibilities of discovering the TD(d) symmetry in experiment are discussed.

Crystallographic interpretation of Galois symmetries for magnetic pentagonal ring

NASA Astrophysics Data System (ADS)

Milewski, J.; Lulek, T.; Łabuz, M.

2017-03-01

Galois symmetry of exact Bethe Ansatz eigenstates for the magnetic pentagonal ring within the XXX model are investigated by a comparison with crystallographic constructions of space groups. It follows that the arithmetic symmetry of Bethe parameters for the interior of the Brillouin zone admits crystallographic interpretation, in terms of the periodic square Z2 ×Z2 , that is the two-dimensional crystal lattice with Born-Karman period two in both directions.

Implementation of the SU(2) Hamiltonian Symmetry for the DMRG Algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alvarez, Gonzalo

2012-01-01

In the Density Matrix Renormalization Group (DMRG) algorithm (White, 1992, 1993) and Hamiltonian symmetries play an important role. Using symmetries, the matrix representation of the Hamiltonian can be blocked. Diagonalizing each matrix block is more efficient than diagonalizing the original matrix. This paper explains how the the DMRG++ code (Alvarez, 2009) has been extended to handle the non-local SU(2) symmetry in a model independent way. Improvements in CPU times compared to runs with only local symmetries are discussed for the one-orbital Hubbard model, and for a two-orbital Hubbard model for iron-based superconductors. The computational bottleneck of the algorithm and themore » use of shared memory parallelization are also addressed.« less

The non-autonomous YdKN equation and generalized symmetries of Boll equations

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Scimiterna, C.; Levi, D.

2017-05-01

In this paper, we study the integrability of a class of nonlinear non-autonomous quad graph equations compatible around the cube introduced by Boll in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. We show that all these equations possess three-point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever-Novikov equation or of its non-autonomous extension. We also prove that all those symmetries are integrable as they pass the algebraic entropy test.

Re"CYC"ling molecular regulators in the evolution and development of flower symmetry.

PubMed

Spencer, Victoria; Kim, Minsung

2018-07-01

Flower forms are both highly diverse and multifaceted. As well as varying in colour, size, organ number, and much more, flowers show different types of symmetry. Floral symmetry can be grouped into three main categories: asymmetry, bilateral symmetry and radial symmetry, characterised by zero, one, and multiple planes of symmetry, respectively. This review will first explore floral symmetry from a classical morphological view, then from a modern molecular perspective. The recent molecular work on symmetry in monocots and eudicots will be discussed, followed by an in-depth discussion into the evolution of CYC genes, particularly in the capitulum of the sunflower family (Asteraceae). Whilst recent studies on non-model species are helping to bring new light to this field, more species coverage is required to understand how traits such as bilateral symmetry have evolved so many times, and whether the same molecular regulators were recruited for this function. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

The near-symmetry of proteins.

PubMed

Bonjack-Shterengartz, Maayan; Avnir, David

2015-04-01

The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. © 2014 Wiley Periodicals, Inc.

Formation of fivefold axes in the FCC-metal nanoclusters

NASA Astrophysics Data System (ADS)

Myasnichenko, Vladimir S.; Starostenkov, Mikhail D.

2012-11-01

Formation of atomistic structures of metallic Cu, Au, Ag clusters and bimetallic Cu-Au clusters was studied with the help of molecular dynamics using the many-body tight-binding interatomic potential. The simulation of the crystallization process of clusters with the number of atoms ranging from 300 to 1092 was carried out. The most stable configurations of atoms in the system, corresponding to the minimum of potential energy, was found during super-fast cooling from 1000 K. Atoms corresponding to fcc, hcp, and Ih phases were identified by the method of common neighbor analysis. Incomplete icosahedral core can be discovered at the intersection of one of the Ih axes with the surface of monometallic cluster. The decahedron-shaped structure of bimetallic Cu-Au cluster with seven completed icosahedral cores was obtained. The principles of the construction of small bimetallic clusters with icosahedral symmetry and increased fractal dimensionality were offered.

On the Importance of Electronic Symmetry for Triplet State Delocalization

DOE PAGES

Richert, Sabine; Bullard, George; Rawson, Jeff; ...

2017-03-29

The influence of electronic symmetry on triplet state delocalization in linear zinc porphyrin oligomers is explored by electron paramagnetic resonance techniques. Using a combination of transient continuous wave and pulse electron nuclear double resonance spectroscopies, it is demonstrated experimentally that complete triplet state delocalization requires the chemical equivalence of all porphyrin units. These results are supported by density functional theory calculations, showing uneven delocalization in a porphyrin dimer in which a terminal ethynyl group renders the two porphyrin units inequivalent. When the conjugation length of the molecule is further increased upon addition of a second terminal ethynyl group that restoresmore » the symmetry of the system, the triplet state is again found to be completely delocalized. Finally, the observations suggest that electronic symmetry is of greater importance for triplet state delocalization than other frequently invoked factors such as conformational rigidity or fundamental length-scale limitations.« less

Clash of symmetries in a Randall-Sundrum-like spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dando, Gareth; George, Damien P.; Volkas, Raymond R.

2005-08-15

We present a toy model that exhibits clash-of-symmetries style Higgs field kink configurations in a Randall-Sundrum-like spacetime. The model has two complex scalar fields {phi}{sub 1,2}, with a sextic potential obeying global U(1)xU(1) and discrete {phi}{sub 1}{r_reversible}{phi}{sub 2} interchange symmetries. The scalar fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological constant. We show that the coupled Einstein-Higgs field equations have an interesting analytic solution provided the sextic potential adopts a particular form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sundrum type of spacetime. The thin-brane Randall-Sundrum limit, whereby the Higgs field kinksmore » become step functions, is carefully defined in terms of the fundamental parameters in the action. The 'clash-of-symmetries' feature, defined in previous papers, is manifested here through the fact that both of the U(1) symmetries are spontaneously broken at all nonasymptotic points in the extra dimension w. One of the U(1)'s is asymptotically restored as w{yields}-{infinity}, with the other U(1) restored as w{yields}+{infinity}. The spontaneously broken discrete symmetry ensures topological stability. In the gauged version of this model we find new flat-space solutions, but in the warped metric case we have been unable to find any solutions with nonzero gauge fields.« less

Symmetry Relations in Chemical Kinetics Arising from Microscopic Reversibility

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2006-01-01

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding or unfolding are pointed out.

Dynamical Evolution of an Effective Two-Level System with {\\mathscr{P}}{\\mathscr{T}} Symmetry

NASA Astrophysics Data System (ADS)

Du, Lei; Xu, Zhihao; Yin, Chuanhao; Guo, Liping

2018-05-01

We investigate the dynamics of parity- and time-reversal (PT ) symmetric two-energy-level atoms in the presence of two optical and a radio-frequency (rf) fields. The strength and relative phase of fields can drive the system from unbroken to broken PT symmetric regions. Compared with the Hermitian model, Rabi-type oscillation is still observed, and the oscillation characteristics are also adjusted by the strength and relative phase in the region of unbroken PT symmetry. At exception point (EP), the oscillation breaks down. To better understand the underlying properties we study the effective Bloch dynamics and find the emergence of the z components of the fixed points is the feature of the PT symmetry breaking and the projections in x-y plane can be controlled with high flexibility compared with the standard two-level system with PT symmetry. It helps to study the dynamic behavior of the complex PT symmetric model.

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

NASA Astrophysics Data System (ADS)

Becker, D.; Reuter, M.

2014-11-01

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a 'bi-metric' ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein-Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non

Symmetry of semi-reduced lattices.

PubMed

Stróż, Kazimierz

2015-05-01

derivable via geometric information (Himes & Mighell, 1987; Le Page, 1982). It is illustrated that corresponding arithmetic and geometric holohedries share space distribution of symmetry elements. Moreover, completeness of the s.r.d. types reveals their combinatorial structure and simplifies the crystallographic description of structural phase transitions, especially those observed with the use of powder diffraction. The research proves that there are excellent theoretical and practical reasons for looking at crystal lattice symmetry from an entirely new and surprising point of view - the combinatorial set {\\bb V} of matrices, their semi-reduced lattice context and their geometric properties.

Biomechanical symmetry in elite rugby union players during dynamic tasks: an investigation using discrete and continuous data analysis techniques.

PubMed

Marshall, Brendan; Franklyn-Miller, Andrew; Moran, Kieran; King, Enda; Richter, Chris; Gore, Shane; Strike, Siobhán; Falvey, Éanna

2015-01-01

While measures of asymmetry may provide a means of identifying individuals predisposed to injury, normative asymmetry values for challenging sport specific movements in elite athletes are currently lacking in the literature. In addition, previous studies have typically investigated symmetry using discrete point analyses alone. This study examined biomechanical symmetry in elite rugby union players using both discrete point and continuous data analysis techniques. Twenty elite injury free international rugby union players (mean ± SD: age 20.4 ± 1.0 years; height 1.86 ± 0.08 m; mass 98.4 ± 9.9 kg) underwent biomechanical assessment. A single leg drop landing, a single leg hurdle hop, and a running cut were analysed. Peak joint angles and moments were examined in the discrete point analysis while analysis of characterising phases (ACP) techniques were used to examine the continuous data. Dominant side was compared to non-dominant side using dependent t-tests for normally distributed data or Wilcoxon signed-rank test for non-normally distributed data. The significance level was set at α = 0.05. The majority of variables were found to be symmetrical with a total of 57/60 variables displaying symmetry in the discrete point analysis and 55/60 in the ACP. The five variables that were found to be asymmetrical were hip abductor moment in the drop landing (p = 0.02), pelvis lift/drop in the drop landing (p = 0.04) and hurdle hop (p = 0.02), ankle internal rotation moment in the cut (p = 0.04) and ankle dorsiflexion angle also in the cut (p = 0.01). The ACP identified two additional asymmetries not identified in the discrete point analysis. Elite injury free rugby union players tended to exhibit bi-lateral symmetry across a range of biomechanical variables in a drop landing, hurdle hop and cut. This study provides useful normative values for inter-limb symmetry in these movement tests. When examining symmetry it is recommended to

Inflation, symmetry, and B-modes

DOE PAGES

Hertzberg, Mark P.

2015-04-20

Here, we examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by envoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with amore » cosmological constant and a massless scalar carries conformal symmetry. They claim this conformal symmetry is hidden when the action is written in the Einstein frame, and so has not been fully appreciated in the literature. They further claim that such a theory carries another hidden symmetry; a global SO(1,1) symmetry. By deforming around the global SO(1,1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend to give rise to B-modes with small amplitude. Here we explain that standard Einstein gravity does not in fact possess conformal symmetry. Instead these authors are merely introducing a redundancy into the description, not an actual conformal symmetry. Furthermore, we explain that the only real (global) symmetry in these models is not at all hidden, but is completely manifest when expressed in the Einstein frame; it is in fact the shift symmetry of a scalar field. When analyzed systematically as an effective field theory, deformations do not generally produce asymptotically flat potentials and small B-modes as suggested in these recent papers. Instead, deforming around the shift symmetry systematically, tends to produce models of inflation with B-modes of appreciable amplitude. Such simple models

Amplitude Excitations in a Symmetry-Breaking Quantum Phase Transition

NASA Astrophysics Data System (ADS)

Boguslawski, Matthew; H M, Bharath; Barrios, Maryrose; Chapman, Michael

Quantum phase transitions (QPT) can be characterized using a local order parameter. In a symmetry-breaking phase transition, this order parameter spontaneously breaks one or more of the symmetries of the Hamiltonian while crossing the quantum critical point (QCP). A spin-1 Bose Einstein condensate, in a single spatial mode, undergoes a QPT when the applied magnetic field is quenched through a critical value. The transverse spin component is an order parameter characterizing this QPT. It shares a U(1)Ã'SO(2) symmetry with the Hamiltonian, but one of these two symmetries is broken when the system is quenched through the QCP. As a result, two massless, coupled phonon-magnon modes are present along with a single massive, or Higgs-like mode which has the form of amplitude excitations of the order parameter. Here, we experimentally characterize this phase transition and the resulting amplitude excitations by inducing coherent oscillation in the spin population. We further use the amplitude oscillations to measure the energy gap between the ground state and the first excited state for different phases of the QPT. At the QCP, finite size effects lead to a non-zero gap, and our measurements are consistent with this prediction.

Generalized global symmetries in states with dynamical defects: The case of the transverse sound in field theory and holography

NASA Astrophysics Data System (ADS)

Grozdanov, Sašo; Poovuttikul, Napat

2018-05-01

In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalized global symmetries even when the microscopic origins of these symmetries are unknown. Using this philosophy, we build an effective theory of a 2 +1 -dimensional fluid state with two perpendicular sets of immersed elastic line defects. When the number of defects is independently conserved in each set, then the state possesses two one-form symmetries. Normally, such viscoelastic states are described as fluids coupled to Goldstone bosons associated with spontaneous breaking of translational symmetry caused by the underlying microscopic structure—the principle feature of which is a transverse sound mode. At the linear, nondissipative level, we verify that our theory, based entirely on symmetry principles, is equivalent to a viscoelastic theory. We then build a simple holographic dual of such a state containing dynamical gravity and two two-form gauge fields, and use it to study its hydrodynamic and higher-energy spectral properties characterized by nonhydrodynamic, gapped modes. Based on the holographic analysis of transverse two-point functions, we study consistency between low-energy predictions of the bulk theory and the effective boundary theory. Various new features of the holographic dictionary are explained in theories with higher-form symmetries, such as the mixed-boundary-condition modification of the quasinormal mode prescription that depends on the running coupling of the boundary double-trace deformations. Furthermore, we examine details of low- and high-energy parts of the spectrum that depend on temperature, line defect densities and the renormalization group scale.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

PubMed

Noel, Yves; D'arco, Philippe; Demichelis, Raffaella; Zicovich-Wilson, Claudio M; Dovesi, Roberto

2010-03-01

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented. (c) 2009 Wiley Periodicals, Inc.

Symmetry-protected gapless Z2 spin liquids

NASA Astrophysics Data System (ADS)

Lu, Yuan-Ming

2018-03-01

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical Z2 gauge fields. Requiring U(1 ) spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-1/2 systems on square, triangular, and kagome lattices, we show that all gapped symmetric Z2 spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped Z2 spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

Symmetry limit theory for cantilever beam-columns subjected to cyclic reversed bending

NASA Astrophysics Data System (ADS)

Uetani, K.; Nakamura, Tsuneyoshi

THE BEHAVIOR of a linear strain-hardening cantilever beam-column subjected to completely reversed plastic bending of a new idealized program under constant axial compression consists of three stages: a sequence of symmetric steady states, a subsequent sequence of asymmetric steady states and a divergent behavior involving unbounded growth of an anti-symmetric deflection mode. A new concept "symmetry limit" is introduced here as the smallest critical value of the tip-deflection amplitude at which transition from a symmetric steady state to an asymmetric steady state can occur in the response of a beam-column. A new theory is presented for predicting the symmetry limits. Although this transition phenomenon is phenomenologically and conceptually different from the branching phenomenon on an equilibrium path, it is shown that a symmetry limit may theoretically be regarded as a branching point on a "steady-state path" defined anew. The symmetry limit theory and the fundamental hypotheses are verified through numerical analysis of hysteretic responses of discretized beam-column models.

Symmetry-based reciprocity: evolutionary constraints on a proximate mechanism.

PubMed

Campennì, Marco; Schino, Gabriele

2016-01-01

Background. While the evolution of reciprocal cooperation has attracted an enormous attention, the proximate mechanisms underlying the ability of animals to cooperate reciprocally are comparatively neglected. Symmetry-based reciprocity is a hypothetical proximate mechanism that has been suggested to be widespread among cognitively unsophisticated animals. Methods. We developed two agent-based models of symmetry-based reciprocity (one relying on an arbitrary tag and the other on interindividual proximity) and tested their ability both to reproduce significant emergent features of cooperation in group living animals and to promote the evolution of cooperation. Results. Populations formed by agents adopting symmetry-based reciprocity showed differentiated "social relationships" and a positive correlation between cooperation given and received: two common aspects of animal cooperation. However, when reproduction and selection across multiple generations were added to the models, agents adopting symmetry-based reciprocity were outcompeted by selfish agents that never cooperated. Discussion. In order to evolve, hypothetical proximate mechanisms must be able to stand competition from alternative strategies. While the results of our simulations require confirmation using analytical methods, we provisionally suggest symmetry-based reciprocity is to be abandoned as a possible proximate mechanism underlying the ability of animals to reciprocate cooperative interactions.

Global Symmetries of Naive and Staggered Fermions in Arbitrary Dimensions

NASA Astrophysics Data System (ADS)

Kieburg, Mario; Würfel, Tim R.

2018-03-01

It is well-known that staggered fermions do not necessarily satisfy the same global symmetries as the continuum theory. We analyze the mechanism behind this phenomenon for arbitrary dimension and gauge group representation. For this purpose we vary the number of lattice sites between even and odd parity in each single direction. Since the global symmetries are manifest in the lowest eigenvalues of the Dirac operator, the spectral statistics and also the symmetry breaking pattern will be affected. We analyze these effects and compare our predictions with Monte-Carlo simulations of naive Dirac operators in the strong coupling limit. This proceeding is a summary of our work [1].

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

Analysis of boron carbides' electronic structure

NASA Technical Reports Server (NTRS)

Howard, Iris A.; Beckel, Charles L.

1986-01-01

The electronic properties of boron-rich icosahedral clusters were studied as a means of understanding the electronic structure of the icosahedral borides such as boron carbide. A lower bound was estimated on bipolaron formation energies in B12 and B11C icosahedra, and the associated distortions. While the magnitude of the distortion associated with bipolaron formation is similar in both cases, the calculated formation energies differ greatly, formation being much more favorable on B11C icosahedra. The stable positions of a divalent atom relative to an icosahedral borane was also investigated, with the result that a stable energy minimum was found when the atom is at the center of the borane, internal to the B12 cage. If incorporation of dopant atoms into B12 cages in icosahedral boride solids is feasible, novel materials might result. In addition, the normal modes of a B12H12 cluster, of the C2B10 cage in para-carborane, and of a B12 icosahedron of reduced (D sub 3d) symmetry, such as is found in the icosahedral borides, were calculated. The nature of these vibrational modes will be important in determining, for instance, the character of the electron-lattice coupling in the borides, and in analyzing the lattice contribution to the thermal conductivity.

Symmetry methods for option pricing

NASA Astrophysics Data System (ADS)

Davison, A. H.; Mamba, S.

2017-06-01

We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.

Spacetime symmetries and Kepler's third law

NASA Astrophysics Data System (ADS)

Le Tiec, Alexandre

2012-11-01

The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler’s third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence and gravitational redshift.

On the dynamical and geometrical symmetries of Keplerian motion

NASA Astrophysics Data System (ADS)

Wulfman, Carl E.

2009-05-01

The dynamical symmetries of classical, relativistic and quantum-mechanical Kepler systems are considered to arise from geometric symmetries in PQET phase space. To establish their interconnection, the symmetries are related with the aid of a Lie-algebraic extension of Dirac's correspondence principle, a canonical transformation containing a Cunningham-Bateman inversion, and a classical limit involving a preliminary canonical transformation in ET space. The Lie-algebraic extension establishes the conditions under which the uncertainty principle allows the local dynamical symmetry of a quantum-mechanical system to be the same as the geometrical phase-space symmetry of its classical counterpart. The canonical transformation converts Poincaré-invariant free-particle systems into ISO(3,1) invariant relativistic systems whose classical limit produces Keplerian systems. Locally Cartesian relativistic PQET coordinates are converted into a set of eight conjugate position and momentum coordinates whose classical limit contains Fock projective momentum coordinates and the components of Runge-Lenz vectors. The coordinate systems developed via the transformations are those in which the evolution and degeneracy groups of the classical system are generated by Poisson-bracket operators that produce ordinary rotation, translation and hyperbolic motions in phase space. The way in which these define classical Keplerian symmetries and symmetry coordinates is detailed. It is shown that for each value of the energy of a Keplerian system, the Poisson-bracket operators determine two invariant functions of positions and momenta, which together with its regularized Hamiltonian, define the manifold in six-dimensional phase space upon which motions evolve.

Novel symmetries in Christ-Lee model

NASA Astrophysics Data System (ADS)

Kumar, R.; Shukla, A.

2016-07-01

We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.

Proteomic Analysis of Sulfolobus solfataricus During Sulfolobus Turreted Icosahedral Virus Infection

PubMed Central

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

SYVA: A program to analyze symmetry of molecules based on vector algebra

NASA Astrophysics Data System (ADS)

Gyevi-Nagy, László; Tasi, Gyula

2017-06-01

Symmetry is a useful concept in physics and chemistry. It can be used to find out some simple properties of a molecule or simplify complex calculations. In this paper a simple vector algebraic method is described to determine all symmetry elements of an arbitrary molecule. To carry out the symmetry analysis, a program has been written, which is also capable of generating the framework group of the molecule, revealing the symmetry properties of normal modes of vibration and symmetrizing the structure. To demonstrate the capabilities of the program, it is compared to other common widely used stand-alone symmetry analyzer (SYMMOL, Symmetrizer) and molecular modeling (NWChem, ORCA, MRCC) software. SYVA can generate input files for molecular modeling programs, e.g. Gaussian, using precisely symmetrized molecular structures. Possible applications are also demonstrated by integrating SYVA with the GAMESS and MRCC software.

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

Development of a genetic system for the archaeal virus Sulfolobus turreted icosahedral virus (STIV).

PubMed

Wirth, Jennifer Fulton; Snyder, Jamie C; Hochstein, Rebecca A; Ortmann, Alice C; Willits, Deborah A; Douglas, Trevor; Young, Mark J

2011-06-20

Our understanding of archaeal viruses has been limited by the lack of genetic systems for examining viral function. We describe the construction of an infectious clone for the archaeal virus Sulfolobus turreted icosahedral virus (STIV). STIV was isolated from a high temperature (82°C) acidic (pH 2.2) hot spring in Yellowstone National Park and replicates in the archaeal model organism Sulfolobus solfataricus (Rice et al., 2004). While STIV is one of most studied archaeal viruses, little is known about its replication cycle. The development of an STIV infectious clone allows for directed gene disruptions and detailed genetic analysis of the virus. The utility of the STIV infectious clone was demonstrated by gene disruption of STIV open reading frame (ORF) B116 which resulted in crippled virus replication, while disruption of ORFs A197, C381 and B345 was lethal for virus replication. Copyright © 2011. Published by Elsevier Inc.

Constraining the physical state by symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fatibene, L., E-mail: lorenzo.fatibene@unito.it; INFN - Sezione Torino - IS QGSKY; Ferraris, M.

After reviewing the hole argument and its relations with initial value problem and general covariance, we shall discuss how much freedom one has to define the physical state in a generally covariant field theory (with or without internal gauge symmetries). Our analysis relies on Cauchy problems, thus it is restricted to globally hyperbolic spacetimes. We shall show that in generally covariant theories on a compact space (as well as for internal gauge symmetries on any spacetime) one has no freedom and one is forced to declare as physically equivalent two configurations which differ by a global spacetime diffeomorphism (or bymore » an internal gauge transformation) as it is usually prescribed. On the contrary, when space is not compact, the result does not hold true and one may have different options to define physically equivalent configurations, still preserving determinism. - Highlights: • Investigate the relation between the hole argument, covariance, determinism and physical state. • Show that if space is compact then any diffeomorphism is a gauge symmetry. • Show that if space is not compact then there may be more freedom in choosing gauge group.« less

Symmetries in laminated composite plates

NASA Technical Reports Server (NTRS)

Noor, A. K.

1976-01-01

The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.

Crystal structures and high-temperature phase-transitions in SrNdMRuO{sub 6} (M=Zn,Co,Mg,Ni) new double perovskites studied by symmetry-mode analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iturbe-Zabalo, E., E-mail: iturbe@ill.fr; Fisika Aplikatua II Saila, Zientzia eta Teknologia Fakultatea, UPV/EHU, P.O. Box 644, 48080 Bilbao; Igartua, J.M.

2013-02-15

Crystal structures of SrNdZnRuO{sub 6}, SrNdCoRuO{sub 6}, SrNdMgRuO{sub 6} and SrNdNiRuO{sub 6} double perovskites have been studied by X-ray, synchrotron radiation and neutron powder diffraction method, at different temperatures, and using the symmetry-mode analysis. All compounds adopt the monoclinic space group P2{sub 1}/n at room-temperature, and contain a completely ordered array of the tilted MO{sub 6} and RuO{sub 6} octahedra, whereas Sr/Nd cations are completely disordered. The analysis of the structures in terms of symmetry-adapted modes of the parent phase allows the identification of the modes responsible for the phase-transition. The high-temperature study (300-1250 K) has shown that the compoundsmore » present a temperature induced structural phase-transition: P2{sub 1}/n{yields}P4{sub 2}/n{yields}Fm3{sup Macron }m. - Graphical abstract: Representation of the dominant distortion modes of the symmetry mode decomposition of the room-temperature (P2{sub 1}/n), intermediate (P4{sub 2}/n) and cubic (Fm-3m) phase SrNdMRuO{sub 6} (M=Zn,Co,Mg,Ni), with respect to the parent phase Fm-3m. The dominant distortion modes are: in the monoclinic phase-GM{sub 4}{sup +} (blue arrow), X{sub 3}{sup +} (green arrow) and X{sub 5}{sup +} acting on A-site cations (red arrow); in the tetragonal phase-GM{sub 4}{sup +} (pink arrow), X{sub 3}{sup +} (light blue arrow) and X{sub 5}{sup +} acting on A-site cations (brown arrow). Highlights: Black-Right-Pointing-Pointer Structural study of four ruthenate double perovskites. Black-Right-Pointing-Pointer Room-temperature structural determination using symmetry-mode procedure. Black-Right-Pointing-Pointer Determination of temperature induced structural phase-transitions. Black-Right-Pointing-Pointer Symmetry adapted-mode analysis.« less

Structural rigidity in the capsid assembly of cowpea chlorotic mottle virus

NASA Astrophysics Data System (ADS)

Hespenheide, B. M.; Jacobs, D. J.; Thorpe, M. F.

2004-11-01

The cowpea chlorotic mottle virus (CCMV) has a protein cage, or capsid, which encloses its genetic material. The structure of the capsid consists of 180 copies of a single protein that self-assemble inside a cell to form a complete capsid with icosahedral symmetry. The icosahedral surface can be naturally divided into pentagonal and hexagonal faces, and the formation of either of these faces has been proposed to be the first step in the capsid assembly process. We have used the software FIRST to analyse the rigidity of pentameric and hexameric substructures of the complete capsid to explore the viability of certain capsid assembly pathways. FIRST uses the 3D pebble game to determine structural rigidity, and a brief description of this algorithm, as applied to body-bar networks, is given here. We find that the pentameric substructure, which corresponds to a pentagonal face on the icosahedral surface, provides the best structural properties for nucleating the capsid assembly process, consistent with experimental observations.

The Symmetries of QCD

ScienceCinema

Chivukula, Sekhar

2017-12-22

The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level.  Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter. 

Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors

NASA Astrophysics Data System (ADS)

Kobayashi, Shingo; Sumita, Shuntaro; Yanase, Youichi; Sato, Masatoshi

2018-05-01

Line nodes in the superconducting gap are known to be a source of Majorana flat bands (MFBs) on a surface. Here, we extend this relation to all symmetry-protected line nodes where an additional constraint arising from crystal symmetry destabilizes or hides the existence of MFBs. By establishing a one-to-one correspondence between group theoretical and topological classifications, we are able to classify the possible line-node-induced MFBs, including cases with (magnetic) nonsymmorphic space groups. Our theoretical analysis reveals MFBs in antiferromagnetic superconductors.

Symmetry associated with symmetry break: Revisiting ants and humans escaping from multiple-exit rooms

NASA Astrophysics Data System (ADS)

Ji, Q.; Xin, C.; Tang, S. X.; Huang, J. P.

2018-02-01

Crowd panic has incurred massive injuries or deaths throughout the world, and thus understanding it is particularly important. It is now a common knowledge that crowd panic induces "symmetry break" in which some exits are jammed while others are underutilized. Amazingly, here we show, by experiment, simulation and theory, that a class of symmetry patterns come to appear for ants and humans escaping from multiple-exit rooms while the symmetry break exists. Our symmetry pattern is described by the fact that the ratio between the ensemble-averaging numbers of ants or humans escaping from different exits is equal to the ratio between the widths of the exits. The mechanism lies in the effect of heterogeneous preferences of agents with limited information for achieving the Nash equilibrium. This work offers new insights into how to improve public safety because large public areas are always equipped with multiple exits, and it also brings an ensemble-averaging method for seeking symmetry associated with symmetry breaking.

Sulfolobus turreted icosahedral virus c92 protein responsible for the formation of pyramid-like cellular lysis structures.

PubMed

Snyder, Jamie C; Brumfield, Susan K; Peng, Nan; She, Qunxin; Young, Mark J

2011-07-01

Host cells infected by Sulfolobus turreted icosahedral virus (STIV) have been shown to produce unusual pyramid-like structures on the cell surface. These structures represent a virus-induced lysis mechanism that is present in Archaea and appears to be distinct from the holin/endolysin system described for DNA bacteriophages. This study investigated the STIV gene products required for pyramid formation in its host Sulfolobus solfataricus. Overexpression of STIV open reading frame (ORF) c92 in S. solfataricus alone is sufficient to produce the pyramid-like lysis structures in cells. Gene disruption of c92 within STIV demonstrates that c92 is an essential protein for virus replication. Immunolocalization of c92 shows that the protein is localized to the cellular membranes forming the pyramid-like structures.