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.

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…

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 describe the SU(2)-invariant version of the multiscale entanglement renormalization ansatz and apply it to study the low-energy spectrum of a quantum spin chain with a global SU(2) symmetry.

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.

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.

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.

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

Hermele, Michael; Chen, Xie

Here, we introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order and a symmetry group of the form G=U(1)xG', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In somemore » cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1)×Z T 2 and G=U(1)×Z P 2, where Z T 2 and Z P 2 are time-reversal and d=2 reflection symmetry, respectively.« 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.

Crystallization of micrometer-sized particles with molecular contours.

PubMed

Song, Pengcheng; Olmsted, Brian K; Chaikin, Paul; Ward, Michael D

2013-11-12

The crystallization of micrometer-sized particles with shapes mimicking those of tetrabenzoheptacene (TBH) and 1,2:5,6-dibenzanthracene (DBT), both flat polyacenes, in an electric field results in the formation of ordered 2D packings that mimic the plane group symmetries in their respective molecular crystal equivalents. Whereas the particles packed in low-density disordered arrangements under a gravitational gradient, dielectrophoresis (under an ac electric field) produced ordered high-density packings with readily identifiable plane group symmetry. The ordered colloidal assemblies were stable for hours, with the packing density decreasing slowly but with recognizable symmetry for up to 12 h for the TBH-shaped particles and up to 4 h for the DBT-shaped particles. This unexpected stability is attributed to jamming behavior associated with interlocking of the dogbone-shaped (TBH) and Z-block (DBT) particles, contrasting with the more rapid reduction of packing density and loss of hexagonal symmetry for disk-shaped particles upon removal of the electric field. The TBH-shaped and DBT-shaped particles assemble into the p2 plane group, which corresponds to the densest particle packing among the possible close-packed plane groups for these particle symmetries. The p2 symmetry observed for the TBH-shaped and DBT-shaped colloid crystal emulates the p2 symmetry of the (010) layers in their respective molecular crystals, which crystallize in monoclinic lattices. Notably, DBT-shaped particles also form ordered domains with pgg symmetry, replicating the plane group symmetry of the (100) layer in the orthorhombic polymorph of DBT. These observations illustrate that the 2D ordering of colloid particles can mimic the packing of molecules with similar shapes, demonstrating that packing can transcend length scales from the molecular to the colloidal.

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

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.

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.

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.

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.

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…

Flux-fusion anomaly test and bosonic topological crystalline insulators

DOE PAGES

Hermele, Michael; Chen, Xie

2016-10-13

Here, we introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with Z2 topological order and a symmetry group of the form G=U(1)xG', where G' is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In somemore » cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G' symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1)×Z T 2 and G=U(1)×Z P 2, where Z T 2 and Z P 2 are time-reversal and d=2 reflection symmetry, respectively.« less

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.

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).

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.

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.

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.

Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups

ERIC Educational Resources Information Center

Casas, Lluís; Estop, Euge`nia

2015-01-01

Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…

Geometry, topology, and response in condensed matter systems

NASA Astrophysics Data System (ADS)

Varjas, Daniel

Topological order provides a new paradigm to view phases of matter. Unlike conventional symmetry breaking order, these states are not distinguished by different patterns of symmetry breaking, instead by their intricate mathematical structure, topology. By the bulk-boundary correspondence, the nontrivial topology of the bulk results in robust gapless excitations on symmetry preserving surfaces. We utilize both of these views to study topological phases together with the analysis of their quantized physical responses to perturbations. First we study the edge excitations of strongly interacting abelian fractional quantum Hall liquids on an infinite strip geometry. We use the infinite density matrix renormalization group method to numerically measure edge exponents in model systems, including subleading orders. Using analytic methods we derive a generalized Luttinger's theorem that relates momenta of edge excitations. Next we consider topological crystalline insulators protected by space group symmetry. After reviewing the general formalism, we present results about the quantization of the magnetoelectric response protected by orientation-reversing space group symmetries. We construct and analyze insulating and superconducting tight-binding models with glide symmetry in three dimensions to illustrate the general result. Following this, we derive constraints on weak indices of three dimensional topological insulators imposed by space group symmetries. We focus on spin-orbit coupled insulators with and without time reversal invariance and consider both symmorphic and nonsymmorphic symmetries. Finally, we calculate the response of metals and generalize the notion of the magnetoelectric effect to noninteracting gapless systems. We use semiclassical dynamics to study the magnetopiezoelectric effect, the current response to elastic strain in static external magnetic fields.

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.

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.

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.

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…

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.

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.

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.

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.

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.

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.

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…

Globally optimal grouping for symmetric closed boundaries by combining boundary and region information.

PubMed

Stahl, Joachim S; Wang, Song

2008-03-01

Many natural and man-made structures have a boundary that shows a certain level of bilateral symmetry, a property that plays an important role in both human and computer vision. In this paper, we present a new grouping method for detecting closed boundaries with symmetry. We first construct a new type of grouping token in the form of symmetric trapezoids by pairing line segments detected from the image. A closed boundary can then be achieved by connecting some trapezoids with a sequence of gap-filling quadrilaterals. For such a closed boundary, we define a unified grouping cost function in a ratio form: the numerator reflects the boundary information of proximity and symmetry and the denominator reflects the region information of the enclosed area. The introduction of the region-area information in the denominator is able to avoid a bias toward shorter boundaries. We then develop a new graph model to represent the grouping tokens. In this new graph model, the grouping cost function can be encoded by carefully designed edge weights and the desired optimal boundary corresponds to a special cycle with a minimum ratio-form cost. We finally show that such a cycle can be found in polynomial time using a previous graph algorithm. We implement this symmetry-grouping method and test it on a set of synthetic data and real images. The performance is compared to two previous grouping methods that do not consider symmetry in their grouping cost functions.

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.

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.

Fourier-space TEM reconstructions with symmetry adapted functions for all rotational point groups.

PubMed

Trapani, Stefano; Navaza, Jorge

2013-05-01

A general-purpose and simple expression for the coefficients of symmetry adapted functions referred to conveniently oriented symmetry axes is given for all rotational point groups. The expression involves the computation of reduced Wigner-matrix elements corresponding to an angle specific to each group and has the computational advantage of leading to Fourier-space TEM (transmission electron microscopy) reconstruction procedures involving only real valued unknowns. Using this expression, a protocol for ab initio view and center assignment and reconstruction so far used for icosahedral particles has been tested with experimental data in other point groups. Copyright © 2013 Elsevier Inc. All rights reserved.

Atomically Phase-Matched Second-Harmonic Generation in a 2D Crystal

DTIC Science & Technology

2016-08-26

thin mate- rials. However, despite the inversion asymmetry of the single layer, the typical crystal stacking restores inversion symmetry for even...typically do not produce SH signals when inversion symmetry is restored in their multilayer counterparts. Group VI transition metal dichalcogenides (TMDCs...group D3h). However, adjacent layers of the 2H are mirrored to restore the inversion symmetry, while the layers in the 3R phase retain the same

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.

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.

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.

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 reduction for exact solution of (2+1)-dimensional Bogoyavlensky-Konopelchenko equation by geometric approach

NASA Astrophysics Data System (ADS)

Ray, S. Saha

2018-04-01

In this paper, the symmetry analysis and similarity reduction of the (2+1)-dimensional Bogoyavlensky-Konopelchenko (B-K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2+1)-dimensional B-K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2+1)-dimensional B-K equation is obtained.

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

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…

Self-similarity and self-inversion of quasicrystals

NASA Astrophysics Data System (ADS)

Madison, A. E.

2014-08-01

The discovery of quasicrystals played a revolutionary role in the condensed matter science and forced to renounce the dogma of the classical crystallography that the regular filling of the space by identical blocks is reduced solely to the Fedorov space groups. It is shown that aperiodic crystals, apart from the similarity, exhibit the self-inversion property. In a broadened sense, the self-inversion implies the possible composition of the inversion with translations, rotations, and homothety, whereas pure reflection by itself in a circle can be absent as an independent symmetry element. It is demonstrated that the symmetry of aperiodic tilings is described by Schottky groups (which belong to a particular type of Kleinian groups generated by the linear fractional Möbius transformations); in the theory of aperiodic crystals, the Schottky groups play the same role that the Fedorov groups play in the theory of crystal lattices. The local matching rules for the Penrose fractal tiling are derived, the problem of choice of the fundamental region of the group of motions of a quasicrystal is discussed, and the relation between the symmetry of aperiodic tilings and the symmetry of constructive fractals is analyzed.

Acute effects of unilateral whole body vibration training on single leg vertical jump height and symmetry in healthy men.

PubMed

Shin, Seungho; Lee, Kyeongjin; Song, Changho

2015-12-01

[Purpose] The aim of the present study was to investigate the acute effects of unilateral whole body vibration training on height and symmetry of the single leg vertical jump in healthy men. [Subjects] Thirty males with no history of lower limb dysfunction participated in this study. [Methods] The participants were randomly allocated to one of three groups: the unilateral vibratory stimulation group (n=10), bilateral vibratory stimulation group (n=10), and, no vibratory stimulation group (n=10). The subjects in the unilateral and bilateral stimulation groups participated in one session of whole body vibration training at 26 Hz for 3 min. The no vibratory stimulation group subjects underwent the same training for 3 min without whole body vibration. All participants performed the single leg vertical jump for each lower limb, to account for the strong and weak sides. The single leg vertical jump height and symmetry were measured before and after the intervention. [Results] The single leg vertical jump height of the weak lower limb significantly improved in the unilateral vibratory stimulation group, but not in the other groups. The single leg vertical jump height of the strong lower limb significantly improved in the bilateral vibratory stimulation group, but not in the other groups. The single leg vertical jump symmetry significantly improved in the unilateral vibratory stimulation group, but not in the other groups. [Conclusion] Therefore, the present study found that the effects of whole body vibration training were different depending on the type of application. To improve the single leg vertical jump height in the weak lower limbs as well as limb symmetry, unilateral vibratory stimulation might be more desirable.

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.

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.

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

NASA Astrophysics Data System (ADS)

Everett, Lisa L.; Stuart, Alexander J.

2009-04-01

We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio, ϕ=(1+5)/2. We present a basic toolbox for model building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the standard model.

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 case of G being a finite group, there should be some integers n and mi such that Gln=(=1 with n⩾3 which results from the requirement that Gl is non-degenerate. We have performed a systematic scan of the possible values of n up to n=200, we are unable to find solutions for the integers mi such that (=1, and hence the symmetry groups in these cases are infinite. Therefore we conclude that there is no discrete flavor symmetry group that contains all of the symmetries needed for the DC mixing, although one cannot rule out the possibility of a discrete group with a very large order. This is the reason why the discrete flavor symmetry origin of the DC mixing has not been proposed so far. Note that the S×S symmetry can immediately lead to the so-called democratic mass matrix in which each matrix element has the same value [53], where S and S are symmetric groups of degree three acting on the left-handed and the right-handed fermion fields respectively. However, the DC mixing cannot be uniquely determined by the democratic mass matrix, and in fact only the third row of DC mixing matrix is fixed.

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.)

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.

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.

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.

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.

What are mathematicians doing?

PubMed

Friedman, B

1966-10-21

Let me emphasize the point I have been trying to make. The mathematician's playing with the roots of equations, a play which had no practical motivations and almost no possibilities of practical application, led to the recognition of the importance of symmetry and groups. The study of theory of groups led to mathematical discoveries in geometry and differential equations, and finally to prediction of the existence of a new elementary particle. Surely a surprising outcome for the ivory-tower speculations of an impractical mathematician! Despite my professional bias, I must acknowledge that the importance of symmetry was recognized before mathematicians invented the theory of groups. In 1794 William Blake wrote: Tiger, Tiger, burning bright In the forests of the night, What immortal hand or eye Could frame thy fearful symmetry? However, to the mathematicians must be given the credit of recognizing that, to understand symmetry, you must study the theory of groups. I can now answer my original question, What are mathematicians doing? They are trying to make precise the intuitions of poets.

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

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

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.

The integrable quantum group invariant A2n-1(2) and Dn+1(2) open spin chains

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Pimenta, Rodrigo A.; Retore, Ana L.

2017-11-01

A family of A2n(2) integrable open spin chains with Uq (Cn) symmetry was recently identified in arxiv:arXiv:1702.01482. We identify here in a similar way a family of A2n-1(2) integrable open spin chains with Uq (Dn) symmetry, and two families of Dn+1(2) integrable open spin chains with Uq (Bn) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider Dn+1(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.

Trunk Exercises Improve Gait Symmetry in Parkinson Disease: A Blind Phase II Randomized Controlled Trial.

PubMed

Hubble, Ryan P; Naughton, Geraldine; Silburn, Peter A; Cole, Michael H

2018-03-01

Deficits in step-to-step symmetry and trunk muscle activations have been linked to falls in Parkinson disease. Given such symptoms are poorly managed with anti-parkinsonian medications, alternate therapies are needed. This blind phase II randomized controlled trial sought to establish whether exercise can improve step-to-step symmetry in Parkinson disease. Twenty-four Parkinson disease patients with a falls history completed baseline assessments of symptom severity, balance confidence, mobility, and quality of life. Step-to-step symmetry was assessed by deriving harmonic ratios from three-dimensional accelerations collected for the head and trunk. Patients were randomly assigned to either 12 wks of exercise and falls prevention education or falls prevention education only. Both groups repeated the baseline tests 12 and 24 wks after the initial assessment. The Australian and New Zealand Clinical Trials Registry number is ACTRN12613001175763. At 12 wks, the exercise group had statistically significant and clinically relevant improvements in anterior-posterior step-to-step trunk symmetry. In contrast, the education group recorded statistically significant and clinically meaningful reductions in medial-lateral and vertical step-to-step trunk symmetry at 12 wks. Given that step-to-step symmetry improved for the exercise group and declined for the education group after intervention, active interventions seem more suited to increasing independence and quality of life for people with Parkinson disease. Complete the self-assessment activity and evaluation online at http://www.physiatry.org/JournalCME CME OBJECTIVES: Upon completion of this article, the reader should be able to do the following: (1) Describe the effect deficits in trunk muscle function have on gait in individuals with Parkinson disease; (2) Identify the benefits of targeted trunk exercises on step-to-step symmetry; and (3) Discuss the benefits of improving step-to-step symmetry in individuals with Parkinson disease. Advanced ACCREDITATION: The Association of Academic Physiatrists is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians.The Association of Academic Physiatrists designates this Journal-based CME activity for a maximum of 0.5 AMA PRA Category 1 Credit(s)™. Physicians should only claim credit commensurate with the extent of their participation in the activity.

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 conclusion, we show that the prototypical, extremely floppy molecule CH 5+ represents a new class of molecules, where customary group theoretical methods for determining selection rules and spectral assignments fail so that new methods have to be developed.

Interaural asymmetry of hearing loss, Speech, Spatial and Qualities of Hearing Scale (SSQ) disabilities, and handicap.

PubMed

Noble, William; Gatehouse, Stuart

2004-02-01

A series of comparative analyses is presented between a group with relatively similar degrees of hearing loss in each ear (n = 103: symmetry group) and one with dissimilar losses (n = 50: asymmetry group). Asymmetry was defined as an interaural difference of more than 10dB in hearing levels averaged over 0.5. 1, 2 and 4kHz. Comparison was focused on self-rated disabilities as reflected in responses on the Speech, Spatial and Qualities of Hearing Scale (SSQ). The connections between SSQ ratings and a global self-rating of handicap were also observed. The interrelationships among SSQ items for the two groups were analysed to determine how the SSQ behaves when applied to groups in whom binaural hearing is more (asymmetry) versus less compromised. As expected, spatial hearing is severely disabled in the group with asymmetry; this group is generally more disabled than the symmetry group across all SSQ domains. In the linkages with handicap, spatial hearing, especially in dynamic settings, was strongly represented in the asymmetry group, while all aspects of hearing were moderately to strongly represented in the symmetry group. Item intercorrelations showed that speech hearing is a relatively autonomous function for the symmetry group, whereas it is enmeshed with segregation, clarity and naturalness factors for the asymmetry group. Spatial functions were more independent of others in the asymmetry group. The SSQ shows promise in the assessment of outcomes in the case of bilateral versus unilateral amplification and/or implantation.

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.

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.

Lie group classification of first-order delay ordinary differential equations

NASA Astrophysics Data System (ADS)

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

2018-05-01

A group classification of first-order delay ordinary differential equations (DODEs) accompanied by an equation for the delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs), which consists of linear DODEs and solution-independent delay relations, have infinite-dimensional symmetry algebras—as do nonlinear ones that are linearizable by an invertible transformation of variables. Genuinely nonlinear DODSs have symmetry algebras of dimension n, . It is shown how exact analytical solutions of invariant DODSs can be obtained using symmetry reduction.

Topological Luttinger liquids from decorated domain walls

NASA Astrophysics Data System (ADS)

Parker, Daniel E.; Scaffidi, Thomas; Vasseur, Romain

2018-04-01

We introduce a systematic construction of a gapless symmetry-protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids. The resulting strongly interacting phases provide a concrete example of a gapless symmetry-protected topological (gSPT) phase with robust symmetry-protected edge modes. Using boundary conformal field theory arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly coupled renormalization group fixed point. Our results are checked against extensive density matrix renormalization group calculations.

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.

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.

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.

On the systematic approach to the classification of differential equations by group theoretical methods

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Dimas, S.; Leach, P. G. L.; Tsoubelis, D.

2009-08-01

Complete symmetry groups enable one to characterise fully a given differential equation. By considering the reversal of an approach based upon complete symmetry groups we construct new classes of differential equations which have the equations of Bateman, Monge-Ampère and Born-Infeld as special cases. We develop a symbolic algorithm to decrease the complexity of the calculations involved.

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.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1990-01-01

It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.

Double line groups: structure, irreducible representations and spin splitting of the bands

NASA Astrophysics Data System (ADS)

Lazić, N.; Milivojević, M.; Vuković, T.; Damnjanović, M.

2018-06-01

Double line groups are derived, structurally examined and classified within 13 infinite families. Their irreducible representations, found and tabulated, single out the complete set of conserved quantum numbers in fermionic quasi-one-dimensional systems possessing either translational periodicity or incommensurate helical symmetry. Spin–orbit interaction is analyzed: the induced orbital band splitting and the consequent removal of the spin degeneracy are completely explained. Being incompatible with vertical mirror symmetry, as well as with simultaneous invariance under time-reversal and horizontal (roto)reflections, spin splitting and spin polarized currents may occur only in the systems with the first and the fifth family double line group symmetry. The effects are illustrated on carbon nanotubes.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2018-05-01

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

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.

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.

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.

Modular Extensions of Unitary Braided Fusion Categories and 2+1D Topological/SPT Orders with Symmetries

NASA Astrophysics Data System (ADS)

Lan, Tian; Kong, Liang; Wen, Xiao-Gang

2017-04-01

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category E. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry E are classified, up to {E_8} quantum Hall states, by the unitary modular tensor categories C over E and the modular extensions of each C. In the case C=E, we prove that the set M_{ext}(E) of all modular extensions of E has a natural structure of a finite abelian group. We also prove that the set M_{ext}(C) of all modular extensions of E, if not empty, is equipped with a natural M_{ext}(C)-action that is free and transitive. Namely, the set M_{ext}(C) is an M_{ext}(E)-torsor. As special cases, we explain in detail how the group M_{ext}(E) recovers the well-known group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16 fold ways. We also discuss briefly the behavior of the group M_{ext}(E) under the symmetry-breaking processes and its relation to Witt groups.

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.

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

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.

Helping Students Understand the Role of Symmetry in Chemistry Using the Particle-in-a-Box Model

ERIC Educational Resources Information Center

Manae, Meghna A.; Hazra, Anirban

2016-01-01

In a course on chemical applications of symmetry and group theory, students learn to use several useful tools (like character tables, projection operators, and correlation tables), but in the process of learning the mathematical details, they often miss the conceptual big picture about "why" and "how" symmetry leads to the…

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.

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.

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 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

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.)

Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order of I , O , and T Matter

NASA Astrophysics Data System (ADS)

Liu, Ke; Nissinen, Jaakko; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan

2016-10-01

The physics of nematic liquid crystals has been the subject of intensive research since the late 19th century. However, the focus of this pursuit has been centered around uniaxial and biaxial nematics associated with constituents bearing a D∞ h or D2 h symmetry, respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point-group symmetry. Given the progress in tailoring nanoparticles with particular shapes and interactions, this vast family of "generalized nematics" might become accessible in the laboratory. Little is known because the order parameter theories associated with the highly symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here, we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high-energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three-dimensional point-group symmetries. We find that the most symmetrical generalized nematics are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point-group symmetry chiral building blocks, such as I , O , and T symmetric matter.

Surface field theories of point group symmetry protected topological phases

NASA Astrophysics Data System (ADS)

Huang, Sheng-Jie; Hermele, Michael

2018-02-01

We identify field theories that describe the surfaces of three-dimensional bosonic point group symmetry protected topological (pgSPT) phases. The anomalous nature of the surface field theories is revealed via a dimensional reduction argument. Specifically, we study three different surface field theories. The first field theory is quantum electrodynamics in three space-time dimensions (QED3) with four flavors of fermions. We show this theory can describe the surfaces of a majority of bosonic pgSPT phases protected by a single mirror reflection, or by Cn v point group symmetry for n =2 ,3 ,4 ,6 . The second field theory is a variant of QED3 with charge-1 and charge-3 Dirac fermions. This field theory can describe the surface of a reflection symmetric pgSPT phase built by placing an E8 state on the mirror plane. The third field theory is an O (4 ) nonlinear sigma model with a topological theta term at θ =π , or, equivalently, a noncompact CP1 model. Using a coupled wire construction, we show this is a surface theory for bosonic pgSPT phases with U (1 ) ×Z2P symmetry. For the latter two field theories, we discuss the connection to gapped surfaces with topological order. Moreover, we conjecture that the latter two field theories can describe surfaces of more general bosonic pgSPT phases with Cn v point group symmetry.

2D Kac-Moody symmetry of 4D Yang-Mills theory

DOE PAGES

He, Temple; Mitra, Prahar; Strominger, Andrew

2016-10-25

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.

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).

Berry phases for Landau Hamiltonians on deformed tori

NASA Astrophysics Data System (ADS)

Lévay, Péter

1995-06-01

Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γϑ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γϑ the geodesic motion restricted to the fundamental domain of this group is chaotic.

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. Ford, and A. B. McCoy, The Journal of Physical Chemistry A 118, 7206 (2014). P.R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy (NRC Research Press, Ottawa, Canada, 1988 Being precise, we must include O(3) and SU(2), but our theory can be easily extended to these two groups. H. Longuet-Higgins, Molecular Physics 6, 445 (1963).

Phonon-Induced Topological Transition to a Type-II Weyl Semimetal

NASA Astrophysics Data System (ADS)

Wang, Lin-Lin; Jo, Na Hyun; Wu, Yun; Kaminski, Adam; Canfield, Paul C.; Johnson, Duane D.

The emergence of topological quantum states requires certain combinations of crystalline symmetry with or without time reversal symmetry. Without restricting to searches for crystal structures with non-symmorphic symmetry operations in the space groups, we have studied the interplay between crystal symmetry, atomic displacements (lattice vibration), band degeneracy and topology. For a system with a full gap opening between the two band manifolds near the Fermi energy, we show that small atomic displacements (accessible via optical phonons near room temperature) can lower the symmetry to induce type-II Weyl points at the boundary between a pair of closely-lying electron and hole pockets. DOE Ames Laboratory LDRD.

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.

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.

Symmetry in polarimetric remote sensing

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Hydrogen Ordering in Hexagonal Intermetallic AB5 Type Compounds

NASA Astrophysics Data System (ADS)

Sikora, W.; Kuna, A.

2008-04-01

Intermetallic compounds AB5 type (A = rare-earth atoms, B = transition metal) are known to store reversibly large amounts of hydrogen and as that are discussed in this work. It was shown that the alloy cycling stability can be significantly improved by employing the so-called non-stoichiometric compounds AB5+x and that is why analysis of change of structure turned out to be interesting. A tendency for ordering of hydrogen atoms is one of the most intriguing problems for the unsaturated hydrides. The symmetry analysis method in the frame of the theory of space group and their representation gives opportunity to find all possible transformations of the parent structure. In this work symmetry analysis method was applied for AB5+x structure type (P6/mmm parent symmetry space group). There were investigated all possible ordering types and accompanying atom displacements in positions 1a, 2c, 3g (fully occupied in stoichiometric compounds AB5), in positions 2e, 6l (where atom B could appear in non-stoichiometric compounds) and also 4h, 6m, 6k, 12n, 12o, which could be partly occupied by hydrogen as a result of hydrides. An analysis was carried out of all possible structures of lower symmetry, following from P6/mmm for we k=(0, 0, 0). Also the way of getting the structure described by the P63mc space group with double cell along the z-axiswe k=(0, 0, 0.5), as it is suggested in the work of Latroche et al. is discussed by the symmetry analysis. The analysis was obtained by computer program MODY. The program calculates the so-called basis vectors of irreducible representations of a given symmetry group, which can be used for calculation of possible ordering modes.

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

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.

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.

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

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.

Description of the atomic disorder (local order) in crystals by the mixed-symmetry method

NASA Astrophysics Data System (ADS)

Dudka, A. P.; Novikova, N. E.

2017-11-01

An approach to the description of local atomic disorder (short-range order) in single crystals by the mixed-symmetry method based on Bragg scattering data is proposed, and the corresponding software is developed. In defect-containing crystals, each atom in the unit cell can be described by its own symmetry space group. The expression for the calculated structural factor includes summation over different sets of symmetry operations for different atoms. To facilitate the search for new symmetry elements, an "atomic disorder expert" was developed, which estimates the significance of tested models. It is shown that the symmetry lowering for some atoms correlates with the existence of phase transitions (in langasite family crystals) and the anisotropy of physical properties (in rare-earth dodecaborides RB12).

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.

QCD In Extreme Conditions

NASA Astrophysics Data System (ADS)

Wilczek, Frank

Introduction Symmetry and the Phenomena of QCD Apparent and Actual Symmetries Asymptotic Freedom Confinement Chiral Symmetry Breaking Chiral Anomalies and Instantons High Temperature QCD: Asymptotic Properties Significance of High Temperature QCD Numerical Indications for Quasi-Free Behavior Ideas About Quark-Gluon Plasma Screening Versus Confinement Models of Chiral Symmetry Breaking More Refined Numerical Experiments High-Temperature QCD: Phase Transitions Yoga of Phase Transitions and Order Parameters Application to Glue Theories Application to Chiral Transitions Close Up on Two Flavors A Genuine Critical Point! (?) High-Density QCD: Methods Hopes, Doubts, and Fruition Another Renormalization Group Pairing Theory Taming the Magnetic Singularity High-Density QCD: Color-Flavor Locking and Quark-Hadron Continuity Gauge Symmetry (Non)Breaking Symmetry Accounting Elementary Excitations A Modified Photon Quark-Hadron Continuity Remembrance of Things Past More Quarks Fewer Quarks and Reality

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.

Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

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

Abedi-Fardad, J., E-mail: j.abedifardad@bonabu.ac.ir; Rezaei-Aghdam, A., E-mail: rezaei-a@azaruniv.edu; Haghighatdoost, Gh., E-mail: gorbanali@azaruniv.edu

2014-05-15

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

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.

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.

Group Theoretical Characterization of Wave Equations

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2017-12-01

Group theoretical methods, worked out in particular by Mackey and Wigner, allow to attain the explicit Quantum Theory of a free particle through a purely deductive development based on symmetry principles. The extension of these methods to the case of an interacting particle finds a serious obstacle in the loss of the symmetry condition for the transformations of Galilei's group. The known attempts towards such an extension introduce restrictions which lead to theories empirically too limited. In the present article we show how the difficulties raised by the loss of symmetry can be overcome without the restrictions that affect tha past attempts. According to our results, the different specific forms of the wave equation of an interacting particle are implied by particular first order invariance properties that characterize the interaction with respect to specific sub-groups of galileian transformations. Moreover, the possibility of yet unknown forms of the wave equation is left open.

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.

Generalized liquid crystals: Giant fluctuations and the vestigial chiral order of I , O , and T matter

DOE PAGES

Liu, Ke; Nissinen, Jaakko; Slager, Robert -Jan; ...

2016-10-31

Here, the physics of nematic liquid crystals has been the subject of intensive research since the late 19th century. However, the focus of this pursuit has been centered around uniaxial and biaxial nematics associated with constituents bearing a D ∞h or D 2h symmetry, respectively. In view of general symmetries, however, these are singularly special since nematic order can in principle involve any point-group symmetry. Given the progress in tailoring nanoparticles with particular shapes and interactions, this vast family of “generalized nematics” might become accessible in the laboratory. Little is known because the order parameter theories associated with the highlymore » symmetric point groups are remarkably complicated, involving tensor order parameters of high rank. Here, we show that the generic features of the statistical physics of such systems can be studied in a highly flexible and efficient fashion using a mathematical tool borrowed from high-energy physics: discrete non-Abelian gauge theory. Explicitly, we construct a family of lattice gauge models encapsulating nematic ordering of general three-dimensional point-group symmetries. We find that the most symmetrical generalized nematics are subjected to thermal fluctuations of unprecedented severity. As a result, novel forms of fluctuation phenomena become possible. In particular, we demonstrate that a vestigial phase carrying no more than chiral order becomes ubiquitous departing from high point-group symmetry chiral building blocks, such as I, O, and T symmetric matter.« less

Realization of non-symmorphic Dirac cones in PbFCl materials

NASA Astrophysics Data System (ADS)

Schoop, Leslie

While most 3D Dirac semimetals require two bands with different orbital character to be protected, there is also the possibility to find 3D Dirac semimetals that are guaranteed to exist in certain space groups. Those are resulting from the non-symmoprhic symmetry of the space group, which forces the bands to degenerate at high symmetry points in the Brillouin zone. Non-symmorphic space groups can force three- four, six and eight fold degeneracies which led to the proposal to find 3D Dirac Semimetals as well as new quasiparticles in such space groups. Problematic for realizing this types of Dirac materials is that they require and odd band filling in order to have the Fermi level located at or also near by the band crossing points. Therefore, although the first prediction for using non-symmoprhic symmetry to create a Dirac material was made in 2012, it took almost four years for an experimental verification of this type of Dirac crossing. In this talk I will introduce the material ZrSiS that has, besides other Dirac features, a Dirac cone protected by non-symmorphic symmetry at about 0.5 eV below the Fermi level and was the first material where this type of Dirac cone was imaged with ARPES. I will then proceed to discuss ways to shift this crossing to the Fermi edge and finally show an experimental verification of a fourfold Dirac crossing, protected by non-symmorphic symmetry, at the Fermi energy.

Chaotic Fluid Mixing in Crystalline Sphere Arrays

NASA Astrophysics Data System (ADS)

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

2017-12-01

We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insight are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

Renormalisation group corrections to neutrino mixing sum rules

NASA Astrophysics Data System (ADS)

Gehrlein, J.; Petcov, S. T.; Spinrath, M.; Titov, A. V.

2016-11-01

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix U is assumed to have an underlying approximate symmetry form Ũν, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase δ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of Ũν. We consider five extensively discussed possible symmetry forms of Ũν: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for δ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model.

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

An uplifting discussion of T-duality

NASA Astrophysics Data System (ADS)

Harvey, Jeffrey A.; Moore, Gregory W.

2018-05-01

It is well known that string theory has a T-duality symmetry relating circle compactifications of large and small radius. This symmetry plays a foundational role in string theory. We note here that while T-duality is order two acting on the moduli space of compactifications, it is order four in its action on the conformal field theory state space. More generally, involutions in the Weyl group W ( G) which act at points of enhanced G symmetry have canonical lifts to order four elements of G, a phenomenon first investigated by J. Tits in the mathematical literature on Lie groups and generalized here to conformal field theory. This simple fact has a number of interesting consequences. One consequence is a reevaluation of a mod two condition appearing in asymmetric orbifold constructions. We also briefly discuss the implications for the idea that T-duality and its generalizations should be thought of as discrete gauge symmetries in spacetime.

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.

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.

Fibonacci-Lucas SIC-POVMs

NASA Astrophysics Data System (ADS)

Grassl, Markus; Scott, Andrew J.

2017-12-01

We present a conjectured family of symmetric informationally complete positive operator valued measures which have an additional symmetry group whose size is growing with the dimension. The symmetry group is related to Fibonacci numbers, while the dimension is related to Lucas numbers. The conjecture is supported by exact solutions for dimensions d = 4, 8, 19, 48, 124, and 323 as well as a numerical solution for dimension d = 844.

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.

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…

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.

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.

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.

Effects of body-weight supported treadmill training on kinetic symmetry in persons with chronic stroke.

PubMed

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

2012-11-01

The purpose was to examine changes in kinetic symmetry in persons with chronic stroke immediately and 6-months after body-weight supported treadmill training. Fifteen participants at least six-months post stroke and able to ambulate between 0.4 and 0.8m/s and 20 participants without neurological conditions completed all phases of the study and were included in the analysis. The non-disabled group served as a comparison for describing changes in kinetic symmetry. The stroke group completed 24 sessions of body-weight supported treadmill training over 8-weeks with 20 minutes of total walking per session. Bilateral 3-dimensional motion analysis and gait speed were assessed 1-week before training (pre-test), 1-week after training (post-test) and 6-months after training (retention) in a repeated measures design. Relative propulsion of the paretic leg and relative positive work of the hip, knee and ankle joints of both legs were calculated to evaluate symmetry of kinetic forces. Statistically significant differences in relative propulsion and positive joint work within the paretic and non-paretic legs were not found over time. The stroke group significantly improved gait speed from pre- to post-test (p=.001) and pre-test to retention (p=.008). In comparison to the non-disabled group, forces produced by the stroke group were asymmetrical demonstrating compensatory adaptation. Although the participants with chronic stroke walked faster after body-weight supported treadmill training, the relative percentages of propulsion and positive work remained unchanged. These findings suggest that the increase in speed was likely due to strengthening existing compensatory strategies rather than through recovery of normal kinetic symmetry. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

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.

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

Space-Time Crystal and Space-Time Group

NASA Astrophysics Data System (ADS)

Xu, Shenglong; Wu, Congjun

2018-03-01

Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D +1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1 +1 D ) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2 +1 D , nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D +1 )-dimensional space-time crystal.

Space-Time Crystal and Space-Time Group.

PubMed

Xu, Shenglong; Wu, Congjun

2018-03-02

Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.

Long-range Coulomb interaction effects on the topological phase transitions between semimetals and insulators

NASA Astrophysics Data System (ADS)

Han, SangEun; Moon, Eun-Gook

2018-06-01

Topological states may be protected by a lattice symmetry in a class of topological semimetals. In three spatial dimensions, the Berry flux around gapless excitations in momentum space concretely defines a chirality, so a protecting symmetry may be referred to as a chiral symmetry. Prime examples include a Dirac semimetal (DSM) in a distorted spinel, BiZnSiO4, protected by a mirror symmetry, and a DSM in Na3Bi , protected by a rotational symmetry. In these states, topology and chiral symmetry are intrinsically tied. In this Rapid Communication, the characteristic interplay between a chiral symmetry order parameter and an instantaneous long-range Coulomb interaction is investigated with the standard renormalization group method. We show that a topological transition associated with chiral symmetry is stable under the presence of a Coulomb interaction and the electron velocity always becomes faster than the one of a chiral symmetry order parameter. Thus, the transition must not be relativistic, which implies that supersymmetry is intrinsically forbidden by the long-range Coulomb interaction. Asymptotically exact universal ratios of physical quantities such as the energy gap ratio are obtained, and connections with experiments and recent theoretical proposals are also discussed.

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

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

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

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.

Electronic Band Structure of Helical Polyisocyanides.

PubMed

Champagne, Benoît; Liégeois, Vincent; Fripiat, Joseph G; Harris, Frank E

2017-10-19

Restricted Hartree-Fock computations are reported for a methyl isocyanide polymer (repeating unit -C═N-CH 3 ), whose most stable conformation is expected to be a helical chain. The computations used a standard contracted Gaussian orbital set at the computational levels STO-3G, 3-21G, 6-31G, and 6-31G**, and studies were made for two line-group configurations motivated by earlier work and by studies of space-filling molecular models: (1) A structure of line-group symmetry L9 5 , containing a 9-fold screw axis with atoms displaced in the axial direction by 5/9 times the lattice constant, and (2) a structure of symmetry L4 1 that had been proposed, containing a 4-fold screw axis with translation by 1/4 of the lattice constant. Full use of the line-group symmetry was employed to cause most of the computational complexity to depend only on the size of the asymmetric repeating unit. Data reported include computed bond properties, atomic charge distribution, longitudinal polarizability, band structure, and the convoluted density of states. Most features of the description were found to be insensitive to the level of computational approximation. The work also illustrates the importance of exploiting line-group symmetry to extend the range of polymer structural problems that can be treated computationally.

Lie-algebraic classification of effective theories with enhanced soft limits

NASA Astrophysics Data System (ADS)

Bogers, Mark P.; Brauner, Tomáš

2018-05-01

A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently in ref. [1], and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO( n) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.

Likelihood-based molecular-replacement solution for a highly pathological crystal with tetartohedral twinning and sevenfold translational noncrystallographic symmetry

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

Sliwiak, Joanna; Jaskolski, Mariusz, E-mail: mariuszj@amu.edu.pl; A. Mickiewicz University, Grunwaldzka 6, 60-780 Poznan

With the implementation of a molecular-replacement likelihood target that accounts for translational noncrystallographic symmetry, it became possible to solve the crystal structure of a protein with seven tetrameric assemblies arrayed translationally along the c axis. The new algorithm found 56 protein molecules in reduced symmetry (P1), which was used to resolve space-group ambiguity caused by severe twinning. Translational noncrystallographic symmetry (tNCS) is a pathology of protein crystals in which multiple copies of a molecule or assembly are found in similar orientations. Structure solution is problematic because this breaks the assumptions used in current likelihood-based methods. To cope with such cases,more » new likelihood approaches have been developed and implemented in Phaser to account for the statistical effects of tNCS in molecular replacement. Using these new approaches, it was possible to solve the crystal structure of a protein exhibiting an extreme form of this pathology with seven tetrameric assemblies arrayed along the c axis. To resolve space-group ambiguities caused by tetartohedral twinning, the structure was initially solved by placing 56 copies of the monomer in space group P1 and using the symmetry of the solution to define the true space group, C2. The resulting structure of Hyp-1, a pathogenesis-related class 10 (PR-10) protein from the medicinal herb St John’s wort, reveals the binding modes of the fluorescent probe 8-anilino-1-naphthalene sulfonate (ANS), providing insight into the function of the protein in binding or storing hydrophobic ligands.« less

Provocation of Symmetry/Ordering Symptoms in Anorexia nervosa: A Functional Neuroimaging Study

PubMed Central

Giampietro, Vincent; Uher, Rudolf; Mataix-Cols, David; Brammer, Michael J.; Williams, Steven C. R.; Treasure, Janet; Campbell, Iain C.

2014-01-01

Anorexia nervosa (AN), obsessive–compulsive disorder (OCD), and obsessive–compulsive personality disorder (OCPD) are often co-morbid; however, the aetiology of such co-morbidity has not been well investigated. This study examined brain activation in women with AN and in healthy control (HC) women during the provocation of symmetry/ordering-related anxiety. During provocation, patients with AN showed more anxiety compared to HCs, which was correlated with the severity of symmetry/ordering symptoms. Activation in the right parietal lobe and right prefrontal cortex (rPFC) in response to provocation was reduced in the AN group compared with the HC group. The reduced right parietal activation observed in the AN group is consistent with parietal lobe involvement in visuospatial cognition and with studies of OCD reporting an association between structural abnormalities in this region and the severity of ‘ordering’ symptoms. Reduced rPFC activation in response to symmetry/ordering provocation has similarities with some, but not all, data collected from patients with AN who were exposed to images of food and bodies. Furthermore, the combination of data from the AN and HC groups showed that rPFC activation during symptom provocation was inversely correlated with the severity of symmetry/ordering symptoms. These data suggest that individuals with AN have a diminished ability to cognitively deal with illness-associated symptoms of provocation. Furthermore, our data also suggest that symptom provocation can progressively overload attempts by the rPFC to exert cognitive control. These findings are discussed in the context of the current neurobiological models of AN. PMID:24844926

Provocation of symmetry/ordering symptoms in Anorexia nervosa: a functional neuroimaging study.

PubMed

Suda, Masashi; Brooks, Samantha J; Giampietro, Vincent; Uher, Rudolf; Mataix-Cols, David; Brammer, Michael J; Williams, Steven C R; Treasure, Janet; Campbell, Iain C

2014-01-01

Anorexia nervosa (AN), obsessive-compulsive disorder (OCD), and obsessive-compulsive personality disorder (OCPD) are often co-morbid; however, the aetiology of such co-morbidity has not been well investigated. This study examined brain activation in women with AN and in healthy control (HC) women during the provocation of symmetry/ordering-related anxiety. During provocation, patients with AN showed more anxiety compared to HCs, which was correlated with the severity of symmetry/ordering symptoms. Activation in the right parietal lobe and right prefrontal cortex (rPFC) in response to provocation was reduced in the AN group compared with the HC group. The reduced right parietal activation observed in the AN group is consistent with parietal lobe involvement in visuospatial cognition and with studies of OCD reporting an association between structural abnormalities in this region and the severity of 'ordering' symptoms. Reduced rPFC activation in response to symmetry/ordering provocation has similarities with some, but not all, data collected from patients with AN who were exposed to images of food and bodies. Furthermore, the combination of data from the AN and HC groups showed that rPFC activation during symptom provocation was inversely correlated with the severity of symmetry/ordering symptoms. These data suggest that individuals with AN have a diminished ability to cognitively deal with illness-associated symptoms of provocation. Furthermore, our data also suggest that symptom provocation can progressively overload attempts by the rPFC to exert cognitive control. These findings are discussed in the context of the current neurobiological models of AN.

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.

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.

A review on symmetries for certain Aedes aegypti models

NASA Astrophysics Data System (ADS)

Freire, Igor Leite; Torrisi, Mariano

2015-04-01

We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.

Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries

NASA Astrophysics Data System (ADS)

Li, Cai-Chang; Lu, Jun-Nan; Ding, Gui-Jun

2018-02-01

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to Z 2 × CP in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters θ l and θ ν varying in the range of [0 , π). As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group Δ(6 n 2) and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters θ u and θ d . A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group Δ(6 n 2) and CP, and accordingly the smallest value of the group index n is n = 7.

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.

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.

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.

Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations.

PubMed

Gu, Yongyi; Qi, Jianming

2017-01-01

In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the [Formula: see text]-expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

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.

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

Chiral Haldane phases of SU(N ) quantum spin chains

NASA Astrophysics Data System (ADS)

Roy, Abhishek; Quella, Thomas

2018-04-01

Gapped quantum spin chains with symmetry PSU(N ) =SU(N ) /ZN are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N -1 Haldane phases which are distinguished by the occurrence of massless boundary spins. We give an expression for a universal AKLT Hamiltonian for an arbitrary symmetry group, including the case where inversion symmetry is broken. Using a diagrammatic method, we construct Hamiltonians for two of the topological classes in SU(N ) that arise when the physical spin is in the adjoint representation. Since our results are valid for all N , we also discuss the large-N limit.

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].

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.

Group Theory and Crystal Field Theory: A Simple and Rigorous Derivation of the Spectroscopic Terms Generated by the t[subscript 2g][superscript 2] Electronic Configuration in a Strong Octahedral Field

ERIC Educational Resources Information Center

Morpurgo, Simone

2007-01-01

The principles of symmetry and group theory are applied to the zero-order wavefunctions associated with the strong-field t[subscript 2g][superscript 2] configuration and their symmetry-adapted linear combinations (SALC) associated with the generated energy terms are derived. This approach will enable students to better understand the use of…

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.

Geometric description of a discrete power function associated with the sixth Painlevé equation.

PubMed

Joshi, Nalini; Kajiwara, Kenji; Masuda, Tetsu; Nakazono, Nobutaka; Shi, Yang

2017-11-01

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with [Formula: see text] symmetry. By constructing the action of [Formula: see text] as a subgroup of [Formula: see text], i.e. the symmetry group of P VI , we show how to relate [Formula: see text] to the symmetry group of the lattice. Moreover, by using translations in [Formula: see text], we explain the odd-even structure appearing in previously known explicit formulae in terms of the τ function.

The dark side of flipped trinification

NASA Astrophysics Data System (ADS)

Dong, P. V.; Huong, D. T.; Queiroz, Farinaldo S.; Valle, José W. F.; Vaquera-Araujo, C. A.

2018-04-01

We propose a model which unifies the Left-Right symmetry with the SU(3) L gauge group, called flipped trinification, and based on the SU(3) C ⊗ SU(3) L ⊗ SU(3) R ⊗ U(1) X gauge group. The model inherits the interesting features of both symmetries while elegantly explaining the origin of the matter parity, W P = (-1)3( B- L)+2 s , and dark matter stability. We develop the details of the spontaneous symmetry breaking mechanism in the model, determining the relevant mass eigenstates, and showing how neutrino masses are easily generated via the seesaw mechanism. Moreover, we introduce viable dark matter candidates, encompassing a fermion, scalar and possibly vector fields, leading to a potentially novel dark matter phenomenology.

SO(4) algebraic approach to the three-body bound state problem in two dimensions

NASA Astrophysics Data System (ADS)

Dmitrašinović, V.; Salom, Igor

2014-08-01

We use the permutation symmetric hyperspherical three-body variables to cast the non-relativistic three-body Schrödinger equation in two dimensions into a set of (possibly decoupled) differential equations that define an eigenvalue problem for the hyper-radial wave function depending on an SO(4) hyper-angular matrix element. We express this hyper-angular matrix element in terms of SO(3) group Clebsch-Gordan coefficients and use the latter's properties to derive selection rules for potentials with different dynamical/permutation symmetries. Three-body potentials acting on three identical particles may have different dynamical symmetries, in order of increasing symmetry, as follows: (1) S3 ⊗ OL(2), the permutation times rotational symmetry, that holds in sums of pairwise potentials, (2) O(2) ⊗ OL(2), the so-called "kinematic rotations" or "democracy symmetry" times rotational symmetry, that holds in area-dependent potentials, and (3) O(4) dynamical hyper-angular symmetry, that holds in hyper-radial three-body potentials. We show how the different residual dynamical symmetries of the non-relativistic three-body Hamiltonian lead to different degeneracies of certain states within O(4) multiplets.

Molecular symmetry: Why permutation-inversion (PI) groups don't render the point groups obsolete

NASA Astrophysics Data System (ADS)

Groner, Peter

2018-01-01

The analysis of spectra of molecules with internal large-amplitude motions (LAMs) requires molecular symmetry (MS) groups that are larger than and significantly different from the more familiar point groups. MS groups are described often by the permutation-inversion (PI) group method. It is shown that point groups still can and should play a significant role together with the PI groups for a class of molecules with internal rotors. In molecules of this class, several simple internal rotors are attached to a rigid molecular frame. The PI groups for this class are semidirect products like H ^ F, where the invariant subgroup H is a direct product of cyclic groups and F is a point group. This result is used to derive meaningful labels for MS groups, and to derive correlation tables between MS groups and point groups. MS groups of this class have many parallels to space groups of crystalline solids.

Changes in Gait Symmetry After Training on a Treadmill with Biofeedback in Chronic Stroke Patients: A 6-Month Follow-Up from a Randomized Controlled Trial

PubMed Central

Drużbicki, Mariusz; Guzik, Agnieszka; Przysada, Grzegorz; Kwolek, Andrzej; Brzozowska-Magoń, Agnieszka; Sobolewski, Marek

2016-01-01

Background One of the most significant challenges for patients who survive a stroke is relearning basic motor tasks such as walking. The goal of this study was to evaluate whether training on a treadmill with visual biofeedback improves gait symmetry, as well as spatiotemporal and kinematic gait parameters, in stroke patients. Material/Methods Thirty patients in the chronic phase after a stroke were randomly allocated into groups with a rehabilitation program of treadmill training with or without visual biofeedback. The training program lasted 10 days. Spatiotemporal and kinematic gait parameters were evaluated. For all parameters analyzed, a symmetrical index was calculated. Follow-up studies were performed 6 months after completion of the program. Results The symmetrical index had significantly normalized in terms of the step length (p=0.006), stance phase time, and inter-limb ratio in the intervention group. After 6 months, the improvement in the symmetry of the step length had been maintained. In the control group, no statistically significant change was observed in any of the parameters tested. There was no significant difference between the intervention group and the control group on completion of the program or at 6 months following the completion of the program. Conclusions Training on a treadmill has a significant effect on the improvement of spatiotemporal parameters and symmetry of gait in patients with chronic stroke. In the group with the treadmill training using visual biofeedback, no significantly greater improvement was observed. PMID:27941712

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

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.

Effects of Game-Based Constraint-Induced Movement Therapy on Balance in Patients with Stroke: A Single-Blind Randomized Controlled Trial.

PubMed

Choi, Ho-Suk; Shin, Won-Seob; Bang, Dae-Hyouk; Choi, Sung-Jin

2017-03-01

The aims of this work were to determine whether game-based constraint-induced movement therapy (CIMT) is effective at improving balance ability in patients with stroke, and to provide clinical knowledge of game-based training that allows application of CIMT to the lower extremities. Thirty-six patients with chronic stroke were randomly assigned to game-based CIMT (n = 12), general game-based training (n = 12), and conventional (n = 12) groups. All interventions were conducted 3 times a week for 4 weeks. The static balance control and weight-bearing symmetry were assessed, and the Functional Reach Test (FRT), modified Functional Reach Test (mFRT), and Timed Up and Go (TUG) test were performed to evaluate balance ability. All 3 groups showed significant improvement in anterior-posterior axis (AP-axis) distance, sway area, weight-bearing symmetry, FRT, mFRT, and TUG test after the intervention (P < 0.05). Post hoc analysis revealed significant differences in AP-axis, and sway area, weight-bearing symmetry of the game-based CIMT group compared with the other group (P < 0.05). Although the general game-based training and the game-based CIMT both improved on static and dynamic balance ability, game-based CIMT had a larger effect on static balance control, weight-bearing symmetry, and side-to-side weight shift.

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.

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

Anomaly constraints on deconfinement and chiral phase transition

NASA Astrophysics Data System (ADS)

Shimizu, Hiroyuki; Yonekura, Kazuya

2018-05-01

We study the constraints on thermal phase transitions of SU (Nc) gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions and (ii) Nf flavors of fundamental fermions with a nontrivial greatest common divisor, gcd (Nc,Nf)≠1 . For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version of the center symmetry, which we call center-flavor symmetry, and draw similar conclusions under a certain definition of confinement. Moreover, at zero temperature, our results give a partial explanation of the appearance of dual magnetic gauge groups in (supersymmetric) QCD when gcd (Nc,Nf)≠1 .

Utilization of group theory in studies of molecular clusters

NASA Astrophysics Data System (ADS)

Ocak, Mahir E.

The structure of the molecular symmetry group of molecular clusters was analyzed and it is shown that the molecular symmetry group of a molecular cluster can be written as direct products and semidirect products of its subgroups. Symmetry adaptation of basis functions in direct product groups and semidirect product groups was considered in general and the sequential symmetry adaptation procedure which is already known for direct product groups was extended to the case of semidirect product groups. By using the sequential symmetry adaptation procedure a new method for calculating the VRT spectra of molecular clusters which is named as Monomer Basis Representation (MBR) method is developed. In the MBR method, calculations starts with a single monomer with the purpose of obtaining an optimized basis for that monomer as a linear combination of some primitive basis functions. Then, an optimized basis for each identical monomer is generated from the optimized basis of this monomer. By using the optimized bases of the monomers, a basis is generated generated for the solution of the full problem, and the VRT spectra of the cluster is obtained by using this basis. Since an optimized basis is used for each monomer which has a much smaller size than the primitive basis from which the optimized bases are generated, the MBR method leads to an exponential optimization in the size of the basis that is required for the calculations. Application of the MBR method has been illustrated by calculating the VRT spectra of water dimer by using the SAPT-5st potential surface of Groenenboom et al. The rest of the calculations are in good agreement with both the original calculations of Groenenboom et al. and also with the experimental results. Comparing the size of the optimized basis with the size of the primitive basis, it can be said that the method works efficiently. Because of its efficiency, the MBR method can be used for studies of clusters bigger than dimers. Thus, MBR method can be used for studying the many-body terms and for deriving accurate potential surfaces.

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Broken SU(3) x SU(3) x SU(3) x SU(3) Symmetry

DOE R&D Accomplishments Database

Freund, P. G. O.; Nambu, Y.

1964-10-01

We argue that the "Eight-fold Way" version of the SU(3) symmetry should be extended to a product of up to four separate and badly broken SU(3) groups, including the gamma{sub 5} type SU(3) symmetry. A hierarchy of subgroups (or subalgebras) are considered within this framework, and two candidates are found to be interesting in view of experimental evidence. Main features of the theory are: 1) the baryons belong to a nonet; 2) there is an octet of axial vector gauge mesons in addition to one or two octets of vector mesons; 3) pseudoscalar and scalar mesons exist as "incomplete" multiplets arising from spontaneous breakdown of symmetry.

Integrating Symmetry in Stereochemical Analysis in Introductory Organic Chemistry

ERIC Educational Resources Information Center

Taagepera, Mare; Arasasingham, Ramesh D.; King, Susan; Potter, Frank; Martorell, Ingrid; Ford, David; Wu, Jason; Kearney, Aaron M.

2011-01-01

We report a comparative study using "knowledge space theory" (KAT) to assess the impact of a hands-on laboratory exercise that used molecular model kits to emphasize the connections between a plane of symmetry, Charity, and isomerism in an introductory organic chemistry course. The experimental design compared three groups of…

Physical Models that Provide Guidance in Visualization Deconstruction in an Inorganic Context

ERIC Educational Resources Information Center

Schiltz, Holly K.; Oliver-Hoyo, Maria T.

2012-01-01

Three physical model systems have been developed to help students deconstruct the visualization needed when learning symmetry and group theory. The systems provide students with physical and visual frames of reference to facilitate the complex visualization involved in symmetry concepts. The permanent reflection plane demonstration presents an…

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.

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.

Implementing a noise protected logical qubit in methyl groups via microwave irradiation

NASA Astrophysics Data System (ADS)

Annabestani, Razieh; Cory, David G.

2018-02-01

We propose a proof-of-principle experiment to encode one logical qubit in noise protected subspace of three identical spins in a methyl group. The symmetry analysis of the wavefunction shows that this fermionic system exhibits a symmetry correlation between the spatial degree of freedom and the spin degree of freedom. We show that one can use this correlation to populate the noiseless subsystem by relying on the interaction between the electric dipole moment of the methyl group with a circularly polarized microwave field. Logical gates are implemented by controlling both the intensity and phase of the applied field.

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

Symmetry analysis of the behavior of the family R6M23 compounds upon hydrogenation

NASA Astrophysics Data System (ADS)

Kuna, Agnieszka; Sikora, Wiesława

2011-06-01

Symmetry analysis was applied in this work to discuss the behavior of the family R6M23 compounds upon hydrogenation (deuteration), where different structural transformations and magnetic properties, depending on the type of R and M atoms and hydrogen (deuterium) concentrations, have been found. The crystallographic structure of these compounds is described by the Fm3m space group and contain 116 atoms per unit cell occupying the positions 24e(R), 4b, 24d, 32f1 and 32f2(M). Additionally in the elementary cell, there could be up to 100 atoms of hydrogen (or deuterium) occupying the interstitial positions 4a, 32f3, 96j1 and 96k1. The symmetry analysis in the frame of the theory of space groups and their representation gives the opportunity to find all possible transformations from high symmetry parent structure to the structures with symmetry belonging to one of its subgroups. For a given transformation it indicates possible displacements of atoms from initial positions in the parent structure, ordering of hydrogen over interstitial sites and also ordering of magnetic moments, described by the smallest possible number of free parameters. The analysis was carried out by means of the MODY computer program for vectors k = (0; 0; 0) and k = (0; 0; 1) describing the changes of translational symmetry and all positions occupied by the R, M and D atoms.

8th International Symposium on Quantum Theory and Symmetries (QTS8)

NASA Astrophysics Data System (ADS)

Bijker, Roelof; Krötzsch, Guillermo; Rosas-Ortiz, Óscar; Wolf, Kurt Bernardo

2014-05-01

The Quantum Theory and Symmetries (QTS) international symposia are periodic biannual meetings of the mathematical physics community with special interest in the methods of group theory in their many incarnations, particularly in the symmetries that arise in quantum systems. The QTSs alternate with the International Colloquia on Group Theoretical Methods in Physics since 1999, when Professor Heinz-Dietrich Doebner organized the first one in Goslar, Germany. Subsequent symposia were held in Krakóow, Poland (2001), Cincinnati, USA (2003), Varna, Bulgaria (2005), Valladolid, Spain (2007), Lexington, USA (2009), and Praha, Czech Republic (2011); the eighth QTS was awarded to Mexico (2013), and the next one (2015) will take place in Yerevan, Armenia. Conference photograph Further details, including committees and members, are available in the PDF

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 complex structures.

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.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

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.

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

Group invariant solutions of the Ernst equation of general relativity theory

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

Pryse, P.V.

The local symmetry group of the Ernst Equation for stationary, axisymmetric, vacuum space-time manifolds is computed by application of the method of Olver. Several implicit solutions of the equation are found by use of this group. Each of these solutions is given in terms of a function defined as a solution of an ordinary differential equation. One of these equations is integrated by quadratures by use of its own local symmetry group, the result being three explicit solutions of the Ernst Equation. For one of these solutions the metric of the space-time manifold is constructed and studied. The solutions hasmore » a ring curvature singularity and it is asymptotically flat in the sense that the curvature invariants approach zero at spatial infinity. The timelike and null geodesics on the symmetry axis and in the plane of the ring singularity are described. The test particles following these geodesics are seen to be repelled by the ring, which suggests the interpretation of this solution as representing the exterior gravitational field of a rotating ring of matter with negative gravitational mass.« less

Spectral assignment and orientational analysis in a vibrational sum frequency generation study of DPPC monolayers at the air/water interface

NASA Astrophysics Data System (ADS)

Feng, Rong-Juan; Li, Xia; Zhang, Zhen; Lu, Zhou; Guo, Yuan

2016-12-01

The interfacial behavior of the benchmark zwitterionic phospholipid molecule dipalmitoylphosphatidylcholine (DPPC) has been extensively investigated by surface-selective vibrational sum frequency generation spectroscopy (VSFG). However, there is still a lack of agreement between various orientational measurements of phospholipid monolayers at the air/water interface, mainly because of the difficulty in assigning congested VSFG features. In this study, polarization-dependent VSFG measurements reveal a frequency shift between the in-plane and out-of-plane antisymmetric stretching modes of the terminal methyl groups in the DPPC alkyl tails, favoring the model of Cs local symmetry rather than the previously assumed C3v symmetry. Further VSFG experiments of isotopically labeled DPPC successfully capture the vibrational signatures of the glycerol backbone. With the newly derived VSFG polarization selection rules for Cs symmetry and the refreshed spectral assignments, the average tilt angles of the alkyl tail groups, choline headgroup, and glycerol backbone of DPPC molecules can all be determined, showing the powerful capability of VSFG spectroscopy in revealing the structural details at interfaces. The VSFG polarization dependence rules and the orientational analysis procedures developed for Cs symmetry in this work are applicable to other bulky molecules in which the methyl group cannot freely rotate, and they therefore have general applications in future VSFG studies.

Bosonic anomalies, induced fractional quantum numbers, and degenerate zero modes: The anomalous edge physics of symmetry-protected topological states

NASA Astrophysics Data System (ADS)

Wang, Juven C.; Santos, Luiz H.; Wen, Xiao-Gang

2015-05-01

The boundary of symmetry-protected topological states (SPTs) can harbor new quantum anomaly phenomena. In this work, we characterize the bosonic anomalies introduced by the 1+1D non-onsite-symmetric gapless edge modes of (2+1)D bulk bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to G =∏iZNi=ZN1×ZN2×ZN3×⋯ ). We demonstrate that some classes of SPTs (termed "Type II") trap fractional quantum numbers (such as fractional ZN charges) at the 0D kink of the symmetry-breaking domain walls, while some classes of SPTs (termed "Type III") have degenerate zero energy modes (carrying the projective representation protected by the unbroken part of the symmetry), either near the 0D kink of a symmetry-breaking domain wall, or on a symmetry-preserving 1D system dimensionally reduced from a thin 2D tube with a monodromy defect 1D line embedded. More generally, the energy spectrum and conformal dimensions of gapless edge modes under an external gauge flux insertion (or twisted by a branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish many SPT classes. We provide a manifest correspondence from the physical phenomena, the induced fractional quantum number, and the zero energy mode degeneracy to the mathematical concept of cocycles that appears in the group cohomology classification of SPTs, thus achieving a concrete physical materialization of the cocycles. The aforementioned edge properties are formulated in terms of a long wavelength continuum field theory involving scalar chiral bosons, as well as in terms of matrix product operators and discrete quantum lattice models. Our lattice approach yields a regularization with anomalous non-onsite symmetry for the field theory description. We also formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.

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 to rehabilitation protocols that focus on range of motion, strength, and return to independence. PMID:23892267

Training symmetry of weight distribution after stroke: a randomized controlled pilot study comparing task-related reach, Bobath and feedback training approaches.

PubMed

Mudie, M H; Winzeler-Mercay, U; Radwan, S; Lee, L

2002-09-01

To determine (1) the most effective of three treatment approaches to retrain seated weight distribution long-term after stroke and (2) whether improvements could be generalized to weight distribution in standing. Inpatient rehabilitation unit. Forty asymmetrical acute stroke subjects were randomly allocated to one of four groups in this pilot study. Changes in weight distribution were compared between the 10 subjects of each of three treatment groups (task-specific reach, Bobath, or Balance Performance Monitor [BPM] feedback training) and a no specific treatment control group. One week of measurement only was followed by two weeks of daily training sessions with the treatment to which the subject was randomly allocated. Measurements were performed using the BPM daily before treatment sessions, two weeks after cessation of treatment and 12 weeks post study. Weight distribution was calculated in terms of mean balance (percentage of total body weight) or the mean of 300 balance points over a 30-s data run. In the short term, the Bobath approach was the most effective treatment for retraining sitting symmetry after stroke (p = 0.004). Training with the BPM and no training were also significant (p = 0.038 and p = 0.035 respectively) and task-specific reach training failed to reach significance (p = 0.26). At 12 weeks post study 83% of the BPM training group, 38% of the task-specific reach group, 29% of the Bobath group and 0% of the untrained group were found to be distributing their weight to both sides. Some generalization of symmetry training in sitting to standing was noted in the BPM training group which appeared to persist long term. Results should be treated with caution due to the small group sizes. However, these preliminary findings suggest that it might be possible to restore postural symmetry in sitting in the early stages of rehabilitation with therapy that focuses on creating an awareness of body position.

S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group

NASA Astrophysics Data System (ADS)

Schroers, B. J.; Bais, F. A.

1998-12-01

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.

From bosonic topological transition to symmetric fermion mass generation

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke

2018-03-01

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.

Phase Transitions in Definite Total Spin States of Two-Component Fermi Gases.

PubMed

Yurovsky, Vladimir A

2017-05-19

Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and antisymmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.

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

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.

Perceptual organization, visual attention, and objecthood.

PubMed

Kimchi, Ruth; Yeshurun, Yaffa; Spehar, Branka; Pirkner, Yossef

2016-09-01

We have previously demonstrated that the mere organization of some elements in the visual field into an object attracts attention automatically. Here, we explored three different aspects of this automatic attentional capture: (a) Does the attentional capture by an object involve a spatial component? (b) Which Gestalt organization factors suffice for an object to capture attention? (c) Does the strength of organization affect the object's ability to capture attention? Participants viewed multi-elements displays and either identified the color of one element or responded to a Vernier target. On some trials, a subset of the elements grouped by Gestalt factors into an object that was irrelevant to the task and not predictive of the target. An object effect - faster performance for targets within the object than for targets outside the object - was found even when the target appeared after the object offset, and was sensitive to target-object distance, suggesting that the capture of attention by an object is accompanied by a deployment of attention to the object location. Object effects of similar magnitude were found for objects grouped by a combination of factors (collinearity, closure, and symmetry, or closure and symmetry) or by a single factor when it was collinearity, but not symmetry, suggesting that collinearity, or closure combined with symmetry, suffices for automatic capture of attention by an object, but symmetry does not. Finally, the strength of grouping in modal completion, manipulated by varying contrast polarity between and within elements, affected the effectiveness of the attentional capture by the induced object. Copyright © 2015 Elsevier Ltd. All rights reserved.

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 holohedry provides a useful tool for solving practical lattice-related problems, especially in the context of lattice deformation. © 2011 International Union of Crystallography

Unity of quarks and leptons at the TeV scale

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

Foot, R.; Lew, H.

1990-08-01

The gauge group (SU(3)){sup 2}{direct product}(SU(2)){sup 2}{direct product}(U(1){sub {ital Y}{prime}}){sup 3} supplemented by quark-lepton, left-right, and generation discrete symmetries represents a new approach to the understanding of the particle content of the standard model. In particular, as a result of the large number of symmetries, the fermion sector of the model is very simple. After symmetry breaking, the standard model can be shown to emerge from this highly symmetric model at low energies.

Learning from data to design functional materials without inversion symmetry

PubMed Central

Balachandran, Prasanna V.; Young, Joshua; Lookman, Turab; Rondinelli, James M.

2017-01-01

Accelerating the search for functional materials is a challenging problem. Here we develop an informatics-guided ab initio approach to accelerate the design and discovery of noncentrosymmetric materials. The workflow integrates group theory, informatics and density-functional theory to uncover design guidelines for predicting noncentrosymmetric compounds, which we apply to layered Ruddlesden-Popper oxides. Group theory identifies how configurations of oxygen octahedral rotation patterns, ordered cation arrangements and their interplay break inversion symmetry, while informatics tools learn from available data to select candidate compositions that fulfil the group-theoretical postulates. Our key outcome is the identification of 242 compositions after screening ∼3,200 that show potential for noncentrosymmetric structures, a 25-fold increase in the projected number of known noncentrosymmetric Ruddlesden-Popper oxides. We validate our predictions for 19 compounds using phonon calculations, among which 17 have noncentrosymmetric ground states including two potential multiferroics. Our approach enables rational design of materials with targeted crystal symmetries and functionalities. PMID:28211456

Symmetries of a generic utricular projection: neural connectivity and the distribution of utricular information.

PubMed

Chartrand, Thomas; McCollum, Gin; Hanes, Douglas A; Boyle, Richard D

2016-02-01

Sensory contribution to perception and action depends on both sensory receptors and the organization of pathways (or projections) reaching the central nervous system. Unlike the semicircular canals that are divided into three discrete sensitivity directions, the utricle has a relatively complicated anatomical structure, including sensitivity directions over essentially 360° of a curved, two-dimensional disk. The utricle is not flat, and we do not assume it to be. Directional sensitivity of individual utricular afferents decreases in a cosine-like fashion from peak excitation for movement in one direction to a null or near null response for a movement in an orthogonal direction. Directional sensitivity varies slowly between neighboring cells except within the striolar region that separates the medial from the lateral zone, where the directional selectivity abruptly reverses along the reversal line. Utricular primary afferent pathways reach the vestibular nuclei and cerebellum and, in many cases, converge on target cells with semicircular canal primary afferents and afference from other sources. Mathematically, some canal pathways are known to be characterized by symmetry groups related to physical space. These groups structure rotational information and movement. They divide the target neural center into distinct populations according to the innervation patterns they receive. Like canal pathways, utricular pathways combine symmetries from the utricle with those from target neural centers. This study presents a generic set of transformations drawn from the known structure of the utricle and therefore likely to be found in utricular pathways, but not exhaustive of utricular pathway symmetries. This generic set of transformations forms a 32-element group that is a semi-direct product of two simple abelian groups. Subgroups of the group include order-four elements corresponding to discrete rotations. Evaluation of subgroups allows us to functionally identify the spatial implications of otolith and canal symmetries regarding action and perception. Our results are discussed in relation to observed utricular pathways, including those convergent with canal pathways. Oculomotor and other sensorimotor systems are organized according to canal planes. However, the utricle is evolutionarily prior to the canals and may provide a more fundamental spatial framework for canal pathways as well as for movement. The fullest purely otolithic pathway is likely that which reaches the lumbar spine via Deiters' cells in the lateral vestibular nucleus. It will be of great interest to see whether symmetries predicted from the utricle are identified within this pathway.

Remarks on the "Non-canonicity Puzzle": Lagrangian Symmetries of the Einstein-Hilbert Action

NASA Astrophysics Data System (ADS)

Kiriushcheva, N.; Komorowski, P. G.; Kuzmin, S. V.

2012-07-01

Given the non-canonical relationship between variables used in the Hamiltonian formulations of the Einstein-Hilbert action (due to Pirani, Schild, Skinner (PSS) and Dirac) and the Arnowitt-Deser-Misner (ADM) action, and the consequent difference in the gauge transformations generated by the first-class constraints of these two formulations, the assumption that the Lagrangians from which they were derived are equivalent leads to an apparent contradiction that has been called "the non-canonicity puzzle". In this work we shall investigate the group properties of two symmetries derived for the Einstein-Hilbert action: diffeomorphism, which follows from the PSS and Dirac formulations, and the one that arises from the ADM formulation. We demonstrate that unlike the diffeomorphism transformations, the ADM transformations (as well as others, which can be constructed for the Einstein-Hilbert Lagrangian using Noether's identities) do not form a group. This makes diffeomorphism transformations unique (the term "canonical" symmetry might be suggested). If the two Lagrangians are to be called equivalent, canonical symmetry must be preserved. The interplay between general covariance and the canonicity of the variables used is discussed.

Variational formulation for dissipative continua and an incremental J-integral

NASA Astrophysics Data System (ADS)

Rahaman, Md. Masiur; Dhas, Bensingh; Roy, D.; Reddy, J. N.

2018-01-01

Our aim is to rationally formulate a proper variational principle for dissipative (viscoplastic) solids in the presence of inertia forces. As a first step, a consistent linearization of the governing nonlinear partial differential equations (PDEs) is carried out. An additional set of complementary (adjoint) equations is then formed to recover an underlying variational structure for the augmented system of linearized balance laws. This makes it possible to introduce an incremental Lagrangian such that the linearized PDEs, including the complementary equations, become the Euler-Lagrange equations. Continuous groups of symmetries of the linearized PDEs are computed and an analysis is undertaken to identify the variational groups of symmetries of the linearized dissipative system. Application of Noether's theorem leads to the conservation laws (conserved currents) of motion corresponding to the variational symmetries. As a specific outcome, we exploit translational symmetries of the functional in the material space and recover, via Noether's theorem, an incremental J-integral for viscoplastic solids in the presence of inertia forces. Numerical demonstrations are provided through a two-dimensional plane strain numerical simulation of a compact tension specimen of annealed mild steel under dynamic loading.

Neutrino mixing in SO(10) GUTs with a non-Abelian flavor symmetry in the hidden sector

NASA Astrophysics Data System (ADS)

Smirnov, Alexei Yu.; Xu, Xun-Jie

2018-05-01

The relation between the mixing matrices of leptons and quarks, UPMNS≈VCKM†U0 , where U0 is a matrix of special forms [e.g., bimaximal (BM) and tribimaximal], can be a clue for understanding the lepton mixing and neutrino masses. It may imply the grand unification and the existence of a hidden sector with certain symmetry that generates U0 and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain U0. The residual symmetries of both the visible and hidden sectors are Z2×Z2 . Their embedding in a unified flavor group is considered. We find that there are only several possible structures of U0, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the SO(10) grand unified theory with the S4 flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of C P phase 14 4 ° ≲δCP≲21 0 ° in the minimal version.

Nodal surface semimetals: Theory and material realization

NASA Astrophysics Data System (ADS)

Wu, Weikang; Liu, Ying; Li, Si; Zhong, Chengyong; Yu, Zhi-Ming; Sheng, Xian-Lei; Zhao, Y. X.; Yang, Shengyuan A.

2018-03-01

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spin-orbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by space-time inversion symmetry and sublattice symmetry and characterized by a Z2 index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic twofold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group symmetry requirements are satisfied. Several concrete nodal-surface material examples are predicted via the first-principles calculations. The possibility of multi-nodal-surface materials is discussed.

Observability and Controllability of Networks: Symmetry in Representations of Brains and Controllers for Epidemics

NASA Astrophysics Data System (ADS)

Schiff, Steven

Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. We present a numerical and group representational framework, to quantify the observability and controllability of nonlinear networks with explicit symmetries that shows the connection between symmetries and nonlinear measures of observability and controllability. In addition to the topology of brain networks, we have advanced our ability to represent network nodes within the brain using conservation principles and more accurate biophysics that unifies the dynamics of spikes, seizures, and spreading depression. Lastly, we show how symmetries in controller design can be applied to infectious disease epidemics. NIH Grants 1R01EB014641, 1DP1HD086071.

Anomalous Suppression of Valley Splittings in Lead Salt Nanocrystals

NASA Astrophysics Data System (ADS)

Poddubny, Alexander; Nestoklon, Mikhail; Goupalov, Serguei

2012-02-01

Atomistic sp^3d^5s^* tight-binding theory of PbSe and PbS nanocrystals is developed. It is demonstrated, that the valley splittings of confined electrons and holes strongly and peculiarly depend on the geometry of a nanocrystal. When the nanocrystal lacks a microscopic center of inversion and has Td symmetry, the splittings are strongly suppressed as compared to the more symmetric nanocrystals with Oh symmetry, having an inversion center. This effect is quite unusual because typically a higher symmetry of a physical system implies a higher degeneracy of its energy levels, while in our case the suppression of the splittings occurs in NCs having lower symmetry. Nevertheless, we were able to explain this puzzling behavior using mathematical apparatus of the group theory.

The Efficacy of Simultaneous Breast Reconstruction and Contralateral Balancing Procedures in Reducing the Need for Second Stage Operations

PubMed Central

Clarke-Pearson, Emily M; Vornovitsky, Michael; Dayan, Joseph H; Samson, William; Sultan, Mark R

2014-01-01

Background Patients having unilateral breast reconstruction often require a second stage procedure on the contralateral breast to improve symmetry. In order to provide immediate symmetry and minimize the frequency and extent of secondary procedures, we began performing simultaneous contralateral balancing operations at the time of initial reconstruction. This study examines the indications, safety, and efficacy of this approach. Methods One-hundred and two consecutive breast reconstructions with simultaneous contralateral balancing procedures were identified. Data included patient age, body mass index (BMI), type of reconstruction and balancing procedure, specimen weight, transfusion requirement, complications and additional surgery under anesthesia. Unpaired t-tests were used to compare BMI, specimen weight and need for non-autologous transfusion. Results Average patient age was 48 years. The majority had autologous tissue-only reconstructions (94%) and the rest prosthesis-based reconstructions (6%). Balancing procedures included reduction mammoplasty (50%), mastopexy (49%), and augmentation mammoplasty (1%). Average BMI was 27 and average reduction specimen was 340 grams. Non-autologous blood transfusion rate was 9%. There was no relationship between BMI or reduction specimen weight and need for transfusion. We performed secondary surgery in 24% of the autologous group and 100% of the prosthesis group. Revision rate for symmetry was 13% in the autologous group and 17% in the prosthesis group. Conclusions Performing balancing at the time of breast reconstruction is safe and most effective in autologous reconstructions, where 87% did not require a second operation for symmetry. PMID:25276646

Bilateral Symmetry before and Six Months after Aberration-Free™ Correction with the SCHWIND AMARIS TotalTech Laser: Clinical Outcomes

PubMed Central

Arbelaez, Maria Clara; Vidal, Camila; Arba-Mosquera, Samuel

2010-01-01

Purpose To compare the preoperative and postoperative bilateral symmetry between OD and OS eyes that have undergone femto-LASIK using the Ziemer LDV femtosecond laser system, the SCHWIND AMARIS Excimer Laser and the Aberrationfree™ profiles implemented in the SCHWIND Custom Ablation Manager software. Methods A total of 25 LASIK patients were bilaterally evaluated at the six-month follow-up visit. In all cases standard examinations, pre- and postoperative analysis with corneal wavefront topography (OPTIKON Scout) were performed. Aberration-free™ aspheric treatments were devised using the Custom Ablation Manager software and ablations were performed by means of the SCHWIND AMARIS flying-spot excimer laser system (both SCHWIND eyetech- solutions). In all cases LASIK flaps were created using an LDV femtosecond laser (Ziemer Group). The OD/OS bilateral symmetry was evaluated in terms of corneal wavefront aberration. Results Preoperatively, 11 Zernike terms showed significant bilateral (OS-vs.-OD) symmetry, and only 6 Zernike terms were significantly different. Overall, 23 out of the 25 patients showed significant bilateral symmetry, and only 2 out of 25 patients showed significant differences. None of the aberration metrics changed from pre- to postoperative values by a clinically relevant amount. At the 6-month postoperative visit, 12 Zernike terms showed significant symmetry, and 8 terms were significantly different. Overall, 22 out of 25 patients showed significant bilateral symmetry (OS vs. OD), and only 3 out of 25 patients showed significant differences. Also, this postoperative examination revealed that 6 Zernike terms lost significant OS-vs.-OD symmetry, but 4 Zernike terms gained significant symmetry. Finally, 4 patients lost significant bilaterality, and 2 patients gained significant bilaterality: bilateral symmetry between eyes was better maintained in those patients with a clear preoperative bilateral symmetry. Conclusions Aberration-Free Treatments with the SCHWIND AMARIS did not induce clinically significant aberrations, maintained the global OD-vs.-OS bilateral symmetry, as well as the bilateral symmetry between corresponding Zernike terms (which influences binocular summation).

Raman Spectroscopy of Rdx Single Crystals Under Static Compression

NASA Astrophysics Data System (ADS)

Dreger, Zbigniew A.; Gupta, Yogendra M.

2007-12-01

To gain insight into the high pressure response of energetic crystal of RDX, Raman measurements were performed under hydrostatic compression up to 15 GPa. Several distinct changes in the spectra were found at 4.0±0.3 GPa, confirming the α-γ phase transition previously observed in polycrystalline samples. Symmetry correlation analyses indicate that the γ-polymorph may assume a space group isomorphous with a point group D2h with eight molecules occupying the C1 symmetry sites, similar to the α-phase. It is proposed that factor group coupling can account for the observed increase in the number of modes in the γ-phase.

Group theoretical derivation of the minimal coupling principle

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2017-04-01

The group theoretical methods worked out by Bargmann, Mackey and Wigner, which deductively establish the Quantum Theory of a free particle for which Galileian transformations form a symmetry group, are extended to the case of an interacting particle. In doing so, the obstacles caused by loss of symmetry are overcome. In this approach, specific forms of the wave equation of an interacting particle, including the equation derived from the minimal coupling principle, are implied by particular first-order invariance properties that characterize the interaction with respect to specific subgroups of Galileian transformations; moreover, the possibility of yet unknown forms of the wave equation is left open.

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.

Basic Theory of Fractional Conformal Invariance of Mei Symmetry and its Applications to Physics

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; Dai, Yun; Yang, Ming-Jing; Zhang, Xiao-Tian

2018-04-01

In this paper, we present a basic theory of fractional dynamics, i.e., the fractional conformal invariance of Mei symmetry, and find a new kind of conserved quantity led by fractional conformal invariance. For a dynamical system that can be transformed into fractional generalized Hamiltonian representation, we introduce a more general kind of single-parameter fractional infinitesimal transformation of Lie group, the definition and determining equation of fractional conformal invariance are given. And then, we reveal the fractional conformal invariance of Mei symmetry, and the necessary and sufficient condition whether the fractional conformal invariance would be the fractional Mei symmetry is found. In particular, we present the basic theory of fractional conformal invariance of Mei symmetry and it is found that, using the new approach, we can find a new kind of conserved quantity; as a special case, we find that an autonomous fractional generalized Hamiltonian system possesses more conserved quantities. Also, as the new method's applications, we, respectively, find the conserved quantities of a fractional general relativistic Buchduhl model and a fractional Duffing oscillator led by fractional conformal invariance of Mei symmetry.

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…

Design, Development and Implementation of a Technology Enhanced Hybrid Course on Molecular Symmetry: Students' Outcomes and Attitudes

ERIC Educational Resources Information Center

Antonoglou, L. D.; Charistos, N. D.; Sigalas, M. P.

2011-01-01

A hybrid course of Molecular Symmetry and Group Theory which combines traditional face-to-face instruction with an online web enhanced learning environment within a Course Management System was designed, developed, and implemented with a purpose to establish an active and student-centred educational setting. Multi-representational educational…

Representations of the Bondi—Metzner—Sachs group in three space—time dimensions

NASA Astrophysics Data System (ADS)

Melas, Evangelos

2017-01-01

The original Bondi-Metzner-Sachs group B is the common asymptotic symmetry group of all asymptotically at Lorentzian 4-dim space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here, we construct the IRS of B(2, 1), the analogue of B, in 3 space-time dimensions. The IRS are induced from ‘little groups’ which are compact. The finite ‘little groups’ are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.

Temperature-resolved study of three [M(M'O4)4(TBPO)4] complexes (MM' = URe, ThRe, ThTc).

PubMed

Helliwell, Madeleine; Collison, David; John, Gordon H; May, Iain; Sarsfield, Mark J; Sharrad, Clint A; Sutton, Andrew D

2006-02-01

The crystal structures of the title complexes were measured at several temperatures between room temperature and 100 K. Each sample shows reversible crystal-to-crystal phase transitions as the temperature is varied. The behaviour of [U(ReO4)4(TBPO)4] (I) and [Th(ReO4)4(TBPO)4] (II) (TBPO = tri-n-butylphosphine oxide) is very similar; at room temperature, crystals of (I) and (II) are isostructural, with space group I42m, and reducing the temperature to 100 K causes a lowering of the space-group symmetry to C-centred cells, space groups Cc for (I) and Cmc2(1) for (II). The variation of lattice symmetry of [Th(TcO4)4(TBPO)4] (III) was found to be somewhat different, with the body-centred cubic space group, I43m, occurring at 293 K, a reduction of symmetry at 230 K to the C-centred orthorhombic space group, Cmc2(1), and a further transition to the primitive orthorhombic space group, Pbc2(1), below 215 K. Elucidation of the correct space-group symmetry and the subsequent refinement was complicated in some cases by the twinning by pseudo-merohedry that arises from the lowering of the space-group symmetry, occurring as the temperature is reduced. All three of the crystal structures determined at room temperature have high atomic displacement parameters, particularly of the (n)Bu groups, and (III) shows disorder of some of the O atoms. The structures in the space group Cmc2(1), show some disorder of nBu groups, but are otherwise reasonably well ordered; the structures of (I) in Cc and (III) in Pbc2(1) are ordered, even to the ends of the alkyl chains. Inter-comparison of the structures measured below 293 K, using the program OFIT from the SHELXTL package, showed that generally, they are remarkably alike, with weighted r.m.s. deviations of the M, M' and P atoms of less than 0.1 A, as are the 293 K structures of (I) and (II) with their low-temperature counterparts. However, the structure of (III) measured in the space group Cmc2(1) is significantly different from both the structure of (III) at 293 K and that found below 215 K, with weighted r.m.s. deviations of the Th, Tc and P atoms of 0.40 and 0.37 A, respectively. An extensive network of weak intra- and intermolecular C-H...O hydrogen bonds found between the atoms of the nBu and [M'O4] groups probably influences the packing and the overall geometry of the molecules.

Symmetry analysis of the high-order equations for the description of the Fermi - Pasta - Ulam problem

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-01-01

Recently some new nonlinear equations for the description of the Fermi - Pasta - Ulam problem have been derived. The main aim of this work is to use the symmetry test to investigate these equations. We consider equations for the description of the α and α + β Fermi - Pasta - Ulam model. We find the infinitesimal operators and Lie groups, admitted by the equations. Using the groups we find the self-similar variables as well as the reductions to the ordinary differential equations. Some exact solutions are also constructed.

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.

"MONSTROUS MOONSHINE" and Physics

NASA Astrophysics Data System (ADS)

Pushkin, A. V.

The report presents some results obtained by the author on the quantum gravitation theory. Algebraic structure of this theory proves to be related to the commutative nonassociative Griess algebra. The theory symmetry is the automorphism group of Griess algebra: "Monster" simple group. Knowledge of the theory symmetry allows to compute observed physical values in the `zero' approximation. The report presents such computed results for values {m_{p}}/{m_{c}} and α, for the latter the `zero' approximation accuracy, controlled by the theory, being one order of magnitude higher than the accuracy of modern measurements.

Interleaved numerical renormalization group as an efficient multiband impurity solver

NASA Astrophysics Data System (ADS)

Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.

2016-06-01

Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.

Equivalence between a generalized dendritic network and a set of one-dimensional networks as a ground of linear dynamics.

PubMed

Koda, Shin-ichi

2015-05-28

It has been shown by some existing studies that some linear dynamical systems defined on a dendritic network are equivalent to those defined on a set of one-dimensional networks in special cases and this transformation to the simple picture, which we call linear chain (LC) decomposition, has a significant advantage in understanding properties of dendrimers. In this paper, we expand the class of LC decomposable system with some generalizations. In addition, we propose two general sufficient conditions for LC decomposability with a procedure to systematically realize the LC decomposition. Some examples of LC decomposable linear dynamical systems are also presented with their graphs. The generalization of the LC decomposition is implemented in the following three aspects: (i) the type of linear operators; (ii) the shape of dendritic networks on which linear operators are defined; and (iii) the type of symmetry operations representing the symmetry of the systems. In the generalization (iii), symmetry groups that represent the symmetry of dendritic systems are defined. The LC decomposition is realized by changing the basis of a linear operator defined on a dendritic network into bases of irreducible representations of the symmetry group. The achievement of this paper makes it easier to utilize the LC decomposition in various cases. This may lead to a further understanding of the relation between structure and functions of dendrimers in future studies.

Is it correct to always consider weight-bearing asymmetrically distributed in individuals with hemiparesis?

PubMed

Martins, Emerson Fachin; de Araujo Barbosa, Paulo Henrique Ferreira; de Menezes, Lidiane Teles; de Sousa, Pedro Henrique Côrtes; Costa, Abraão Souza

2011-11-01

Injuries may cause unilateral deterioration of brain areas related to postural control resulting in lateralized motor disability with abnormal asymmetry in weight-bearing distribution. Although overloading toward the nonaffected limb has been described as the preferred posture among individuals with hemiparesis, characterization of the weight-bearing asymmetry is poorly and indirectly described. Therefore, this study aimed to describe weight-bearing distribution during upright stance, establishing criteria to consider asymmetry in hemiparesis when analyzed within the limits defined by controls matched by age and gender. Forty subjects with (n = 20) or without hemiparesis (n = 20) were included in procedures to record weight-bearing values between hemibodies, and these values were used to calculate a symmetry ratio. Control presented 95% confidence interval (CI) of the mean for symmetry ratio ranging from 0.888 to 1.072, defining limits to symmetry. Four subjects with hemiparesis (20%) had symmetry ratios inside limits defined by controls (i.e., weight-bearing symmetrically distributed), and 11 (55%) subjects without hemiparesis showed symmetry ratios outside the limits, suggesting asymmetrical weight-bearing distribution. It was concluded that asymmetry, when present in a control group, was more frequently overloading nonpredominantly used hemibody (nondominant side), differing from a hemiparesis group commonly forced to assume the nonaffected side as the predominantly used hemibody and where the overload was observed.

Unifying the rotational and permutation symmetry of nuclear spin states: Schur-Weyl duality in molecular physics.

PubMed

Schmiedt, Hanno; Jensen, Per; Schlemmer, Stephan

2016-08-21

In modern physics and chemistry concerned with many-body systems, one of the mainstays is identical-particle-permutation symmetry. In particular, both the intra-molecular dynamics of a single molecule and the inter-molecular dynamics associated, for example, with reactive molecular collisions are strongly affected by selection rules originating in nuclear-permutation symmetry operations being applied to the total internal wavefunctions, including nuclear spin, of the molecules involved. We propose here a general tool to determine coherently the permutation symmetry and the rotational symmetry (associated with the group of arbitrary rotations of the entire molecule in space) of molecular wavefunctions, in particular the nuclear-spin functions. Thus far, these two symmetries were believed to be mutually independent and it has even been argued that under certain circumstances, it is impossible to establish a one-to-one correspondence between them. However, using the Schur-Weyl duality theorem we show that the two types of symmetry are inherently coupled. In addition, we use the ingenious representation-theory technique of Young tableaus to represent the molecular nuclear-spin degrees of freedom in terms of well-defined mathematical objects. This simplifies the symmetry classification of the nuclear wavefunction even for large molecules. Also, the application to reactive collisions is very straightforward and provides a much simplified approach to obtaining selection rules.

Unifying the rotational and permutation symmetry of nuclear spin states: Schur-Weyl duality in molecular physics

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

Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per, E-mail: jensen@uni-wuppertal.de

In modern physics and chemistry concerned with many-body systems, one of the mainstays is identical-particle-permutation symmetry. In particular, both the intra-molecular dynamics of a single molecule and the inter-molecular dynamics associated, for example, with reactive molecular collisions are strongly affected by selection rules originating in nuclear-permutation symmetry operations being applied to the total internal wavefunctions, including nuclear spin, of the molecules involved. We propose here a general tool to determine coherently the permutation symmetry and the rotational symmetry (associated with the group of arbitrary rotations of the entire molecule in space) of molecular wavefunctions, in particular the nuclear-spin functions. Thusmore » far, these two symmetries were believed to be mutually independent and it has even been argued that under certain circumstances, it is impossible to establish a one-to-one correspondence between them. However, using the Schur-Weyl duality theorem we show that the two types of symmetry are inherently coupled. In addition, we use the ingenious representation-theory technique of Young tableaus to represent the molecular nuclear-spin degrees of freedom in terms of well-defined mathematical objects. This simplifies the symmetry classification of the nuclear wavefunction even for large molecules. Also, the application to reactive collisions is very straightforward and provides a much simplified approach to obtaining selection rules.« less

Effects of computerized match-to-sample training on emergent fraction-decimal relations in individuals with fragile X syndrome.

PubMed

Hammond, Jennifer L; Hirt, Melissa; Hall, Scott S

2012-01-01

Individuals diagnosed with fragile X syndrome (FXS), the most common known form of inherited intellectual disability, are reported to exhibit considerable deficits in mathematical skills that are often attributed to brain-based abnormalities associated with the syndrome. We examined whether participants with FXS would display emergent fraction-decimal relations following brief, intensive match-to-sample training on baseline relations. The performance profiles on tests of symmetry and transitivity/equivalence of 11 participants with FXS, aged 10-23 years, following baseline match-to-sample training were compared to those of 11 age- and IQ-matched controls with idiopathic developmental disability. The results showed that both groups of participants showed significant improvements in the baseline (trained) relations, as expected. However, participants with FXS failed to show significant improvements in the (untrained) symmetry and transitivity/equivalence relations compared to those in the control group. A categorical analysis of the data indicated that five participants with FXS and eight controls showed at least "intermediate" emergence of symmetry relations, whereas one individual with FXS and three controls showed at least intermediate emergence of transitivity/equivalence relations. A correlation analysis of the data indicated that improvements in the symmetry relations were significantly associated with improvements in the transitivity/equivalence relations in the control group (r=.69, p=.018), but this was not the case in the FXS group (r=.34, p>.05). Participant IQ was significantly associated with improvements in the symmetry relations in individuals with FXS (r=.60, p=.049), but not in controls (r=.21, p>.05). Taken together, these results suggest that brief, computerized match-to-sample training may produce emergent mathematical relations for a subset of children with FXS and developmental disabilities. However, the ability of individuals with FXS to form transitivity/equivalence relations may be impaired relative to those with idiopathic developmental disabilities, which may be attributed to neurodevelopmental variables associated with the syndrome. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

Casimir energy between two parallel plates and projective representation of the Poincaré group

NASA Astrophysics Data System (ADS)

Akita, Takamaru; Matsunaga, Mamoru

2016-06-01

The Casimir effect is a physical manifestation of zero point energy of quantum vacuum. In a relativistic quantum field theory, Poincaré symmetry of the theory seems, at first sight, to imply that nonzero vacuum energy is inconsistent with translational invariance of the vacuum. In the setting of two uniform boundary plates at rest, quantum fields outside the plates have (1 +2 )-dimensional Poincaré symmetry. Taking a massless scalar field as an example, we have examined the consistency between the Poincaré symmetry and the existence of the vacuum energy. We note that, in quantum theory, symmetries are represented projectively in general and show that the Casimir energy is connected to central charges appearing in the algebra of generators in the projective representations.

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.

The heavy top quark and supersymmetry

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

Hall, L.J.

1997-01-01

Three aspects of supersymmetric theories are discussed: electroweak symmetry breaking, the issues of flavor, and gauge unification. The heavy top quark plays an important, sometimes dominant, role in each case. Additional symmetries lead to extensions of the Standard Model which can provide an understanding for many of the outstanding problems of particle physics. A broken supersymmetric extension of spacetime allows electroweak symmetry breaking to follow from the dynamics of the heavy top quark; an extension of isospin provides a constrained framework for understanding the pattern of quark and lepton masses; and a grand unified extension of the Standard Model gaugemore » group provides an elegant understanding of the gauge quantum numbers of the components of a generation. Experimental signatures for each of these additional symmetries are discussed.« less

New approach to flavor symmetry and an extended naturalness principle

NASA Astrophysics Data System (ADS)

Barr, S. M.

2010-09-01

A class of nonsupersymmetric extensions of the standard model is proposed in which there is a multiplicity of light scalar doublets in a multiplet of a nonabelian family group with the standard model Higgs doublet. Anthropic tuning makes the latter light, and consequently the other scalar doublets remain light because of the family symmetry. The family symmetry greatly constrains the pattern of flavor-changing neutral-current interactions (FCNC) and p decay operators coming from scalar-exchange. Such models show that useful constraints on model-building can come from an extended naturalness principle when the electroweak scale is anthropically tuned.

Visual Biofeedback Balance Training Using Wii Fit after Stroke: A Randomized Controlled Trial

PubMed Central

Barcala, Luciana; Grecco, Luanda André Collange; Colella, Fernanda; Lucareli, Paulo Roberto Garcia; Salgado, Afonso Shiguemi Inoue; Oliveira, Claudia Santos

2013-01-01

[Purpose] The aim of the present study was to investigate the effect of balance training with visual biofeedback on balance, body symmetry, and function among individuals with hemiplegia following a stroke. [Subjects and Methods] The present study was performed using a randomized controlled clinical trial with a blinded evaluator. The subjects were twenty adults with hemiplegia following a stroke. The experimental group performed balance training with visual biofeedback using Wii Fit® together with conventional physical therapy. The control group underwent conventional physical therapy alone. The intervention lasted five weeks, with two sessions per week. Body symmetry (baropodometry), static balance (stabilometry), functional balance (Berg Balance Scale), functional mobility (Timed Up and Go test), and independence in activities of daily living (Functional Independence Measure) were assessed before and after the intervention. [Results] No statistically significant differences were found between the experimental and control groups. In the intragroup analysis, both groups demonstrated a significant improvement in all variables studied. [Conclusion] The physical therapy program combined with balance training involving visual biofeedback (Wii Fit®) led to an improvement in body symmetry, balance, and function among stroke victims. However, the improvement was similar to that achieved with conventional physical therapy alone. PMID:24259909

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.

Effects of sensorimotor foot training on the symmetry of weight distribution on the lower extremities of patients in the chronic phase after stroke

PubMed Central

Goliwas, Magdalena; Kocur, Piotr; Furmaniuk, Lech; Majchrzycki, Marian; Wiernicka, Marzena; Lewandowski, Jacek

2015-01-01

[Purpose] To assess the effects of sensorimotor foot stimulation on the symmetry of weight distribution on the feet of patients in the chronic post-stroke phase. [Subjects and Methods] This study was a prospective, single blind, randomized controlled trial. In the study we examined patients with chronic stroke (post-stroke duration > 1 year). They were randomly allocated to the study group (n=8) or to the control group (n=12). Both groups completed a standard six-week rehabilitation programme. In the study group, the standard rehabilitation programme was supplemented with sensorimotor foot stimulation training. Each patient underwent two assessments of symmetry of weight distribution on the lower extremities with and without visual control, on a treadmill, with stabilometry measurements, and under static conditions. [Results] Only the study group demonstrated a significant increase in the weight placed on the leg directly affected by stroke, and a reduction in asymmetry of weight-bearing on the lower extremities. [Conclusion] Sensorimotor stimulation of the feet enhanced of weight bearing on the foot on the side of the body directly affected by stroke, and a decreased asymmetry of weight distribution on the lower extremities of patients in the chronic post-stroke phase. PMID:26504326

Effects of sensorimotor foot training on the symmetry of weight distribution on the lower extremities of patients in the chronic phase after stroke.

PubMed

Goliwas, Magdalena; Kocur, Piotr; Furmaniuk, Lech; Majchrzycki, Marian; Wiernicka, Marzena; Lewandowski, Jacek

2015-09-01

[Purpose] To assess the effects of sensorimotor foot stimulation on the symmetry of weight distribution on the feet of patients in the chronic post-stroke phase. [Subjects and Methods] This study was a prospective, single blind, randomized controlled trial. In the study we examined patients with chronic stroke (post-stroke duration > 1 year). They were randomly allocated to the study group (n=8) or to the control group (n=12). Both groups completed a standard six-week rehabilitation programme. In the study group, the standard rehabilitation programme was supplemented with sensorimotor foot stimulation training. Each patient underwent two assessments of symmetry of weight distribution on the lower extremities with and without visual control, on a treadmill, with stabilometry measurements, and under static conditions. [Results] Only the study group demonstrated a significant increase in the weight placed on the leg directly affected by stroke, and a reduction in asymmetry of weight-bearing on the lower extremities. [Conclusion] Sensorimotor stimulation of the feet enhanced of weight bearing on the foot on the side of the body directly affected by stroke, and a decreased asymmetry of weight distribution on the lower extremities of patients in the chronic post-stroke phase.

Placement of molecules in (not out of) the cell

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

Dauter, Zbigniew, E-mail: dauter@anl.gov

2013-01-01

The importance of presenting macromolecular structures in unified, standard ways is discussed. To uniquely describe a crystal structure, it is sufficient to specify the crystal unit cell and symmetry, and describe the unique structural motif which is repeated by the space-group symmetry throughout the whole crystal. It is somewhat arbitrary how such a unique motif can be defined and positioned with respect to the unit-cell origin. As a result of such freedom, some isomorphous structures are presented in the Protein Data Bank in different locations and appear as if they have different atomic coordinates, despite being completely equivalent structurally. Thismore » may easily confuse those users of the PDB who are less familiar with crystallographic symmetry transformations. It would therefore be beneficial for the community of PDB users to introduce standard rules for locating crystal structures of macromolecules in the unit cells of various space groups.« less

A general non-Abelian density matrix renormalization group algorithm with application to the C{sub 2} dimer

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

Sharma, Sandeep, E-mail: sanshar@gmail.com

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 ofmore » the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} 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 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} 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 {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.« less

Carry-Over of Force Production Symmetry in Athletes of Differing Strength Levels.

PubMed

Bailey, Christopher A; Sato, Kimitake; Burnett, Angus; Stone, Michael H

2015-11-01

This study sought to determine the level of association between bilateral force production symmetry assessment methods (standing weight distribution [WtD], unloaded and lightly loaded jumps, and isometric strength) and to determine whether the amount of symmetry carry-over between these tasks differs for strong and weak athletes. Subjects for this study included male (n = 31) and female (n = 32) athletes from National Collegiate Athletic Association Division I sports. Athletes performed WtD, unloaded and lightly loaded (20 kg) static and countermovement jumps, and isometric midthigh pull (IMTP) assessments on 2 adjacent force plates. Ground reaction force data were used to calculate symmetry variables and performance-related variables. Using Pearson zero order correlations, evaluations of the amount of symmetry carry-over were made. Weight distribution correlated strongly with jump peak force (PF) (r = 0.628-0.664). Strong relationships were also observed between loading conditions for jump variables (r = 0.568-0.957) as were the relationships between jump types for PF, peak power, and net impulse (r = 0.506-0.834). Based on the pooled sample, there was a lack of association between IMTP and WtD for jump symmetry variables. However, when examining strong and weak groups, rate of force development showed moderate to strong symmetry carry-over in the strongest athletes (r = 0.416-0.589). Stronger athletes appear to display similar explosive strength symmetry characteristics in dynamic and isometric assessments, unlike weaker athletes. Strength seems to influence the amount of force production symmetry carry-over between bilateral assessments. There may be optimal loads and variables for symmetry assessment, but these may differ based on population characteristics.

Symmetries and stability of chimera states in small, globally-coupled networks

NASA Astrophysics Data System (ADS)

Hart, Joseph D.; Bansal, Kanika; Murphy, Thomas E.; Roy, Rajarshi

It has recently been demonstrated that symmetries in a network's topology can help predict the patterns of synchronized clusters that can emerge in a network of coupled oscillators. This and related discoveries have led to increased interest in both network symmetries and cluster synchronization. In parallel with these discoveries, interest in chimera states-dynamical patterns in which a network separates into coherent and incoherent portions-has grown, and chimeras have now been observed in a variety of experimental systems. We present an opto-electronic experiment in which both chimera states and synchronized clusters are observed in a small, globally-coupled network. We show that the symmetries and sub-symmetries of the network permit the formation of the chimera and cluster states. A recently developed group theoretical approach enables us to predict the stability of the observed chimera and cluster states, and highlights the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization.

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.

The ATLAS diboson resonance in non-supersymmetric SO(10)

DOE PAGES

Evans, Jason L.; Nagata, Natsumi; Olive, Keith A.; ...

2016-02-18

SO(10) grand uni cation accommodates intermediate gauge symmetries with which gauge coupling uni cation can be realized without supersymmetry. In this paper, we discuss the possibility that a new massive gauge boson associated with an intermediate gauge symmetry explains the excess observed in the diboson resonance search recently reported by the ATLAS experiment. The model we find has two intermediate symmetries, SU(4) C Ⓧ SU(2) L Ⓧ SU(2) R and SU(3) C Ⓧ SU(2) L Ⓧ SU(2)R Ⓧ U(1) B-L, where the latter gauge group is broken at the TeV scale. This model achieves gauge coupling uni cation with amore » uni cation scale su fficiently high to avoid proton decay. In addition, this model provides a good dark matter candidates, whose stability is guaranteed by a Z 2 symmetry present after the spontaneous breaking of the intermediate gauge symmetries. In addition, we discuss prospects for testing these models in the forthcoming LHC experiments and dark matter detection experiments.« less

Exhaustive Classification of the Invariant Solutions for a Specific Nonlinear Model Describing Near Planar and Marginally Long-Wave Unstable Interfaces for Phase Transition

NASA Astrophysics Data System (ADS)

Ahangari, Fatemeh

2018-05-01

Problems of thermodynamic phase transition originate inherently in solidification, combustion and various other significant fields. If the transition region among two locally stable phases is adequately narrow, the dynamics can be modeled by an interface motion. This paper is devoted to exhaustive analysis of the invariant solutions for a modified Kuramoto-Sivashinsky equation in two spatial and one temporal dimensions is presented. This nonlinear partial differential equation asymptotically characterizes near planar interfaces, which are marginally long-wave unstable. For this purpose, by applying the classical symmetry method for this model the classical symmetry operators are attained. Moreover, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras, which yields the preliminary classification of group invariant solutions is constructed. Mainly, the Lie invariants corresponding to the infinitesimal symmetry generators as well as associated similarity reduced equations are also pointed out. Furthermore, the nonclassical symmetries of this nonlinear PDE are also comprehensively investigated.

Observable phase factors and symmetry of electric and magnetic charges

NASA Technical Reports Server (NTRS)

Hsu, J. P.

1978-01-01

The observable phase factor is taken as a basic concept for the description of electromagnetism. Generalization of this concept to SU(2) and SU(2) x U(1) groups is carried out in such a way that the monopoles with quantized charges appear naturally and that the symmetry between the electric and magnetic phenomena is preserved. Some physical implications are discussed.

Construction of Ligand Group Orbitals for Polyatomics and Transition-Metal Complexes Using an Intuitive Symmetry-Based Approach

ERIC Educational Resources Information Center

Johnson, Adam R.

2013-01-01

A molecular orbital (MO) diagram, especially its frontier orbitals, explains the bonding and reactivity for a chemical compound. It is therefore important for students to learn how to construct one. The traditional methods used to derive these diagrams rely on linear algebra techniques to combine ligand orbitals into symmetry-adapted linear…

$$ \\mathcal{N}=1 $$ deformations and RG flows of $$ \\mathcal{N}=2 $$ SCFTs

DOE PAGES

Maruyoshi, Kazunobu; Song, Jaewon

2017-02-14

Here, we study certainmore » $$ \\mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \\mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \\mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \\mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the ( A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \\mathcal{N}=1 $$ fixed points.« less

Solitons, Lie Group Analysis and Conservation Laws of a (3+1)-Dimensional Modified Zakharov-Kuznetsov Equation in a Multicomponent Magnetised Plasma

NASA Astrophysics Data System (ADS)

Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang

2017-11-01

In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.

Geometrically frustrated magnetic structures of the heavy-fermion compound CePdAl studied by powder neutron diffraction

NASA Astrophysics Data System (ADS)

Dönni, A.; Ehlers, G.; Maletta, H.; Fischer, P.; Kitazawa, H.; Zolliker, M.

1996-12-01

The heavy-fermion compound CePdAl with ZrNiAl-type crystal structure (hexagonal space group 0953-8984/8/50/043/img8) was investigated by powder neutron diffraction. The triangular coordination symmetry of magnetic Ce atoms on site 3f gives rise to geometrical frustration. CePdAl orders below 0953-8984/8/50/043/img9 with an incommensurate antiferromagnetic propagation vector 0953-8984/8/50/043/img10, and a longitudinal sine-wave (LSW) modulated spin arrangement. Magnetically ordered moments at Ce(1) and Ce(3) coexist with frustrated disordered moments at Ce(2). The experimentally determined magnetic structure is in agreement with group theoretical symmetry analysis considerations, calculated by the program MODY, which confirm that for Ce(2) an ordered magnetic moment parallel to the magnetically easy c-axis is forbidden by symmetry. Further low-temperature experiments give evidence for a second magnetic phase transition in CePdAl between 0.6 and 1.3 K. Magnetic structures of CePdAl are compared with those of the isostructural compound TbNiAl, where a non-zero ordered magnetic moment for the geometrically frustrated Tb(2) atoms is allowed by symmetry.

$$ \\mathcal{N}=1 $$ deformations and RG flows of $$ \\mathcal{N}=2 $$ SCFTs

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

Maruyoshi, Kazunobu; Song, Jaewon

Here, we study certainmore » $$ \\mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \\mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \\mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \\mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the ( A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \\mathcal{N}=1 $$ fixed points.« less

Quarks, Symmetries and Strings - a Symposium in Honor of Bunji Sakita's 60th Birthday

NASA Astrophysics Data System (ADS)

Kaku, M.; Jevicki, A.; Kikkawa, K.

1991-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Evening Banquet Speech * I. Quarks and Phenomenology * From the SU(6) Model to Uniqueness in the Standard Model * A Model for Higgs Mechanism in the Standard Model * Quark Mass Generation in QCD * Neutrino Masses in the Standard Model * Solar Neutrino Puzzle, Horizontal Symmetry of Electroweak Interactions and Fermion Mass Hierarchies * State of Chiral Symmetry Breaking at High Temperatures * Approximate |ΔI| = 1/2 Rule from a Perspective of Light-Cone Frame Physics * Positronium (and Some Other Systems) in a Strong Magnetic Field * Bosonic Technicolor and the Flavor Problem * II. Strings * Supersymmetry in String Theory * Collective Field Theory and Schwinger-Dyson Equations in Matrix Models * Non-Perturbative String Theory * The Structure of Non-Perturbative Quantum Gravity in One and Two Dimensions * Noncritical Virasoro Algebra of d < 1 Matrix Model and Quantized String Field * Chaos in Matrix Models ? * On the Non-Commutative Symmetry of Quantum Gravity in Two Dimensions * Matrix Model Formulation of String Field Theory in One Dimension * Geometry of the N = 2 String Theory * Modular Invariance form Gauge Invariance in the Non-Polynomial String Field Theory * Stringy Symmetry and Off-Shell Ward Identities * q-Virasoro Algebra and q-Strings * Self-Tuning Fields and Resonant Correlations in 2d-Gravity * III. Field Theory Methods * Linear Momentum and Angular Momentum in Quaternionic Quantum Mechanics * Some Comments on Real Clifford Algebras * On the Quantum Group p-adics Connection * Gravitational Instantons Revisited * A Generalized BBGKY Hierarchy from the Classical Path-Integral * A Quantum Generated Symmetry: Group-Level Duality in Conformal and Topological Field Theory * Gauge Symmetries in Extended Objects * Hidden BRST Symmetry and Collective Coordinates * Towards Stochastically Quantizing Topological Actions * IV. Statistical Methods * A Brief Summary of the s-Channel Theory of Superconductivity * Neural Networks and Models for the Brain * Relativistic One-Body Equations for Planar Particles with Arbitrary Spin * Chiral Property of Quarks and Hadron Spectrum in Lattice QCD * Scalar Lattice QCD * Semi-Superconductivity of a Charged Anyon Gas * Two-Fermion Theory of Strongly Correlated Electrons and Charge-Spin Separation * Statistical Mechanics and Error-Correcting Codes * Quantum Statistics

Quantitative facial asymmetry: using three-dimensional photogrammetry to measure baseline facial surface symmetry.

PubMed

Taylor, Helena O; Morrison, Clinton S; Linden, Olivia; Phillips, Benjamin; Chang, Johnny; Byrne, Margaret E; Sullivan, Stephen R; Forrest, Christopher R

2014-01-01

Although symmetry is hailed as a fundamental goal of aesthetic and reconstructive surgery, our tools for measuring this outcome have been limited and subjective. With the advent of three-dimensional photogrammetry, surface geometry can be captured, manipulated, and measured quantitatively. Until now, few normative data existed with regard to facial surface symmetry. Here, we present a method for reproducibly calculating overall facial symmetry and present normative data on 100 subjects. We enrolled 100 volunteers who underwent three-dimensional photogrammetry of their faces in repose. We collected demographic data on age, sex, and race and subjectively scored facial symmetry. We calculated the root mean square deviation (RMSD) between the native and reflected faces, reflecting about a plane of maximum symmetry. We analyzed the interobserver reliability of the subjective assessment of facial asymmetry and the quantitative measurements and compared the subjective and objective values. We also classified areas of greatest asymmetry as localized to the upper, middle, or lower facial thirds. This cluster of normative data was compared with a group of patients with subtle but increasing amounts of facial asymmetry. We imaged 100 subjects by three-dimensional photogrammetry. There was a poor interobserver correlation between subjective assessments of asymmetry (r = 0.56). There was a high interobserver reliability for quantitative measurements of facial symmetry RMSD calculations (r = 0.91-0.95). The mean RMSD for this normative population was found to be 0.80 ± 0.24 mm. Areas of greatest asymmetry were distributed as follows: 10% upper facial third, 49% central facial third, and 41% lower facial third. Precise measurement permitted discrimination of subtle facial asymmetry within this normative group and distinguished norms from patients with subtle facial asymmetry, with placement of RMSDs along an asymmetry ruler. Facial surface symmetry, which is poorly assessed subjectively, can be easily and reproducibly measured using three-dimensional photogrammetry. The RMSD for facial asymmetry of healthy volunteers clusters at approximately 0.80 ± 0.24 mm. Patients with facial asymmetry due to a pathologic process can be differentiated from normative facial asymmetry based on their RMSDs.

Emergent Phenomena at Oxide Interfaces

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

Hwang, H.Y.

2012-02-16

Transition metal oxides (TMOs) are an ideal arena for the study of electronic correlations because the s-electrons of the transition metal ions are removed and transferred to oxygen ions, and hence the strongly correlated d-electrons determine their physical properties such as electrical transport, magnetism, optical response, thermal conductivity, and superconductivity. These electron correlations prohibit the double occupancy of metal sites and induce a local entanglement of charge, spin, and orbital degrees of freedom. This gives rise to a variety of phenomena, e.g., Mott insulators, various charge/spin/orbital orderings, metal-insulator transitions, multiferroics, and superconductivity. In recent years, there has been a burstmore » of activity to manipulate these phenomena, as well as create new ones, using oxide heterostructures. Most fundamental to understanding the physical properties of TMOs is the concept of symmetry of the order parameter. As Landau recognized, the essence of phase transitions is the change of the symmetry. For example, ferromagnetic ordering breaks the rotational symmetry in spin space, i.e., the ordered phase has lower symmetry than the Hamiltonian of the system. There are three most important symmetries to be considered here. (i) Spatial inversion (I), defined as r {yields} -r. In the case of an insulator, breaking this symmetry can lead to spontaneous electric polarization, i.e. ferroelectricity, or pyroelectricity once the point group belongs to polar group symmetry. (ii) Time-reversal symmetry (T) defined as t {yields} -t. In quantum mechanics, the time-evolution of the wave-function {Psi} is given by the phase factor e{sup -iEt/{h_bar}} with E being the energy, and hence time-reversal basically corresponds to taking the complex conjugate of the wave-function. Also the spin, which is induced by the 'spinning' of the particle, is reversed by time-reversal. Broken T-symmetry is most naturally associated with magnetism, since the spin operator changes sign with T-operation. (iii) Gauge symmetry (G), which is associated with a change in the phase of the wave-function as {Psi} {yields} e{sup i{theta}}{Psi}. Gauge symmetry is connected to the law of charge conservation, and broken G-symmetry corresponds to superconductivity/superfluidity. To summarize, the interplay among these electronic degrees of freedom produces various forms of symmetry breaking patterns of I, T, and G, leading to novel emergent phenomena, which can appear only by the collective behavior of electrons and cannot be expected from individual electrons. Figure 1 shows this schematically by means of several representative phenomena. From this viewpoint, the interfaces of TMOs offer a unique and important laboratory because I is already broken by the structure itself, and the detailed form of broken I-symmetry can often be designed. Also, two-dimensionality usually enhances the effects of electron correlations by reducing their kinetic energy. These two features of oxide interfaces produce many novel effects and functions that cannot be attained in bulk form. Given that the electromagnetic responses are a major source of the physical properties of solids, and new gauge structures often appear in correlated electronic systems, we put 'emergent electromagnetism' at the center of Fig. 1.« less

Effect of facial neuromuscular re-education on facial symmetry in patients with Bell's palsy: a randomized controlled trial.

PubMed

Manikandan, N

2007-04-01

To determine the effect of facial neuromuscular re-education over conventional therapeutic measures in improving facial symmetry in patients with Bell's palsy. Randomized controlled trial. Neurorehabilitation unit. Fifty-nine patients diagnosed with Bell's palsy were included in the study after they met the inclusion criteria. Patients were randomly divided into two groups: control (n = 30) and experimental (n = 29). Control group patients received conventional therapeutic measures while the facial neuromuscular re-education group patients received techniques that were tailored to each patient in three sessions per day for six days per week for a period of two weeks. All the patients were evaluated using a Facial Grading Scale before treatment and after three months. The Facial Grading Scale scores showed significant improvement in both control (mean 32 (range 9.7-54) to 54.5 (42.2-71.7)) and the experimental (33 (18-43.5) to 66 (54-76.7)) group. Facial Grading Scale change scores showed that experimental group (27.5 (20-43.77)) improved significantly more than the control group (16.5 (12.2-24.7)). Analysis of Facial Grading Scale subcomponents did not show statistical significance, except in the movement score (12 (8-16) to 24 (12-18)). Individualized facial neuromuscular re-education is more effective in improving facial symmetry in patients with Bell's palsy than conventional therapeutic measures.

Europan double ridge morphometry as a test of formation models

NASA Astrophysics Data System (ADS)

Dameron, Ashley C.; Burr, Devon M.

2018-05-01

Double ridges on the Jovian satellite Europa consist of two parallel ridges with a central trough. Although these features are nearly ubiquitous on Europa, their formation mechanism(s) is (are) not yet well-understood. Previous hypotheses for their formation can be divided into two groups based on 1) the expected interior slope angles and 2) the magnitude of interior/exterior slope symmetry. The published hypotheses in the first ("fracture") group entail brittle deformation of the crust, either by diapirism, shear heating, or buckling due to compression. Because these mechanisms imply uplift of near-vertical fractures, their predicted interior slopes are steeper than the angle of repose (AOR) with shallower exterior slopes. The second ("flow") group includes cryosedimentary and cryovolcanic processes - explosive or effusive cryovolcanism and tidal squeezing -, which are predicted to form ridge slopes at or below the AOR. Explosive cryovolcanism would form self-symmetric ridges, whereas effusive cryolavas and cryo-sediments deposited during tidal squeezing would likely not exhibit slope symmetry. To distinguish between these two groups of hypothesized formation mechanisms, we derived measurements of interior slope angle and interior/exterior slope symmetry at multiple locations on Europa through analysis of data from the Galileo Solid State Imaging (SSI) camera. Two types of data were used: i) elevation data from five stereo-pair digital elevation models (DEMs) covering four ridges (580 individual measurements), and ii) ridge shadow length measurements taken on individual images over 40 ridges (200 individual measurements). Our results shows that slopes measured on our DEMs, located in the Cilix and Banded Plains regions, typically fall below the AOR, and slope symmetry is dominant. Two different shadow measurement techniques implemented to calculate interior slopes yielded slope angles that also fall below the AOR. The shallow interior slopes derived from both techniques weigh against brittle deformation mechanisms. Although shallow slopes could result from degradation, interior/exterior ridge symmetry weighs against ridge degradation as the sole reason for shallow interior slopes. Thus, our results suggest that, for the double ridges analyzed in this work, cryovolcanic or cryosedimentary formation is more likely than brittle deformation, and of those formation mechanisms, explosive cryovolcanism is the double ridge formation mechanism best supported on the basis of interior-exterior slope symmetry.

Symmetry-based reciprocity: evolutionary constraints on a proximate mechanism

PubMed Central

Campennì, Marco

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. PMID:26998412

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.

Bosons with Synthetic Rashba Spin-Orbit Coupling at Finite Power

NASA Astrophysics Data System (ADS)

Anderson, Brandon; Clark, Charles

2013-05-01

Isotropic spin-orbit couplings, such as Rashba in two dimensions, have a continuous symmetry that produces a large degeneracy in the momentum-space dispersion. This degeneracy leads to an enhanced density-of-states, producing novel phases in systems of bosonic atoms. This model is idealistic, however, in that the symmetry of the lasers will weakly break the continuous symmetry to a discrete one in experimental manifestations. This perturbation typically scales inversely with the optical power, and only at infinite power will ideal symmetry be restored. In this talk, we consider the effects of this weak symmetry breaking in a system of bosons at finite power with synthetic Rashba coupling. We solve the mean-field equations and find new phases, such as a stripe phase with a larger symmetry group. We then consider the experimentally relevant scheme where the spin-orbit fields are turned on adiabatically from an initial spin-polarized state. At intermediate power, stripe phases are found, while at sufficiently high power it appears that the system quenches to phases similar to that of the ideal limit. Techniques for optimizing the adiabatic ramping sequence are discussed. NSF PFC Grant PHY-0822671 and by the ARO under the DARPA OLE program.

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.

A stem-group cnidarian described from the mid-Cambrian of China and its significance for cnidarian evolution.

PubMed

Park, Tae-yoon; Woo, Jusun; Lee, Dong-Jin; Lee, Dong-Chan; Lee, Seung-bae; Han, Zuozhen; Chough, Sung Kwun; Choi, Duck K

2011-08-23

Palaeontological data of extinct groups often sheds light on the evolutionary sequences leading to extant groups, but has failed to resolve the basal metazoan phylogeny including the origin of the Cnidaria. Here we report the occurrence of a stem-group cnidarian, Cambroctoconus orientalis gen. et sp. nov., from the mid-Cambrian of China, which is a colonial organism with calcareous octagonal conical cup-shaped skeletons. It bears cnidarian features including longitudinal septa arranged in octoradial symmetry and colonial occurrence, but lacks a jelly-like mesenchyme. Such morphological characteristics suggest that the colonial occurrence with polyps of octoradial symmetry is the plesiomorphic condition of the Cnidaria and appeared earlier than the jelly-like mesenchyme during the course of evolution. © 2011 Macmillan Publishers Limited. All rights reserved.

A stem-group cnidarian described from the mid-Cambrian of China and its significance for cnidarian evolution

PubMed Central

Park, Tae-yoon; Woo, Jusun; Lee, Dong-Jin; Lee, Dong-Chan; Lee, Seung-bae; Han, Zuozhen; Chough, Sung Kwun; Choi, Duck K.

2011-01-01

Palaeontological data of extinct groups often sheds light on the evolutionary sequences leading to extant groups, but has failed to resolve the basal metazoan phylogeny including the origin of the Cnidaria. Here we report the occurrence of a stem-group cnidarian, Cambroctoconus orientalis gen. et sp. nov., from the mid-Cambrian of China, which is a colonial organism with calcareous octagonal conical cup-shaped skeletons. It bears cnidarian features including longitudinal septa arranged in octoradial symmetry and colonial occurrence, but lacks a jelly-like mesenchyme. Such morphological characteristics suggest that the colonial occurrence with polyps of octoradial symmetry is the plesiomorphic condition of the Cnidaria and appeared earlier than the jelly-like mesenchyme during the course of evolution. PMID:21863009

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 can give rise to a neutral mode--i.e. an edge mode that does not carry electric charge. These models consist of two counter-propagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the nu = 2/3 state is the most prominent example.

The Formalism of Quantum Mechanics Specified by Covariance Properties

NASA Astrophysics Data System (ADS)

Nisticò, G.

2009-03-01

The known methods, due for instance to G.W. Mackey and T.F. Jordan, which exploit the transformation properties with respect to the Euclidean and Galileian group to determine the formalism of the Quantum Theory of a localizable particle, fail in the case that the considered transformations are not symmetries of the physical system. In the present work we show that the formalism of standard Quantum Mechanics for a particle without spin can be completely recovered by exploiting the covariance properties with respect to the group of Euclidean transformations, without requiring that these transformations are symmetries of the physical system.

Computational Power of Symmetry-Protected Topological Phases.

PubMed

Stephen, David T; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert

2017-07-07

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Computational Power of Symmetry-Protected Topological Phases

NASA Astrophysics Data System (ADS)

Stephen, David T.; Wang, Dong-Sheng; Prakash, Abhishodh; Wei, Tzu-Chieh; Raussendorf, Robert

2017-07-01

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Molecular symmetry group analysis of the low-wavenumber torsions and vibration-torsions in the S1 state and ground state cation of p-xylene: An investigation using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy

NASA Astrophysics Data System (ADS)

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

2017-03-01

For the first time, a molecular symmetry group (MSG) analysis has been undertaken in the investigation of the electronic spectroscopy of p-xylene (p-dimethylbenzene). Torsional and vibration-torsional (vibtor) levels in the S1 state and ground state of the cation of p-xylene are investigated using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the present work, we concentrate on the 0-350 cm-1 region, where there are a number of torsional and vibtor bands and we discuss the assignment of this region. In Paper II [W. D. Tuttle et al., J. Chem. Phys. 146, 124309 (2017)], we examine the 350-600 cm-1 region where vibtor levels are observed as part of a Fermi resonance. The similarity of much of the observed spectral activity to that in the related substituted benzenes, toluene and para-fluorotoluene, is striking, despite the different symmetries. The discussion necessitates a consideration of the MSG of p-xylene, which has been designated G72, but we shall also designate [{3,3}]D2h and we include the symmetry operations, character table, and direct product table for this. We also discuss the symmetries of the internal rotor (torsional) levels and the selection rules for the particular electronic transition of p-xylene investigated here.

Hurwitz Algebras and the Octonion Algebra

NASA Astrophysics Data System (ADS)

Burdik, Čestmir; Catto, Sultan

2018-02-01

We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

Physics architecture

NASA Astrophysics Data System (ADS)

Konopleva, Nelly

2017-03-01

Fundamental physical theory axiomatics is closely connected with methods of experimental measurements. The difference between the theories using global and local symmetries is explained. It is shown that symmetry group localization leads not only to the change of the relativity principle, but to the fundamental modification of experimental programs testing physical theory predictions. It is noticed that any fundamental physical theory must be consistent with the measurement procedures employed for its testing. These ideas are illustrated by events of my biography connected with Yang-Mills theory transformation from an ordinary phenomenological model to a fundamental physical theory based on local symmetry principles like the Einsteinian General Relativity. Baldin position in this situation is demonstrated.

Dannie Heineman Prize for Mathematical Physics Prize Lecture: Correlation Functions in Integrable Models II: The Role of Quantum Affine Symmetry

NASA Astrophysics Data System (ADS)

Jimbo, Michio

2013-03-01

Since the beginning of 1980s, hidden infinite dimensional symmetries have emerged as the origin of integrability: first in soliton theory and then in conformal field theory. Quest for symmetries in quantum integrable models has led to the discovery of quantum groups. On one hand this opened up rapid mathematical developments in representation theory, combinatorics and other fields. On the other hand it has advanced understanding of correlation functions of lattice models, leading to multiple integral formulas in integrable spin chains. We shall review these developments which continue up to the present time.

Constructing an explicit AdS/CFT correspondence with Cartan geometry

NASA Astrophysics Data System (ADS)

Hazboun, Jeffrey S.

2018-04-01

An explicit AdS/CFT correspondence is shown for the Lie group SO (4 , 2). The Lie symmetry structures allow for the construction of two physical theories through the tools of Cartan geometry. One is a gravitational theory that has anti-de Sitter symmetry. The other is also a gravitational theory but is conformally symmetric and lives on 8-dimensional biconformal space. These "extra" four dimensions have the degrees of freedom used to construct a Yang-Mills theory. The two theories, based on AdS or conformal symmetry, have a natural correspondence in the context of their Lie algebras alone where neither SUSY, nor holography, is necessary.

Comparison of hemihypoglossal-facial nerve transposition with a cross-facial nerve graft and muscle transplant for the rehabilitation of facial paralysis using the facial clima method.

PubMed

Hontanilla, Bernardo; Vila, Antonio

2012-02-01

To compare quantitatively the results obtained after hemihypoglossal nerve transposition and microvascular gracilis transfer associated with a cross facial nerve graft (CFNG) for reanimation of a paralysed face, 66 patients underwent hemihypoglossal transposition (n = 25) or microvascular gracilis transfer and CFNG (n = 41). The commissural displacement (CD) and commissural contraction velocity (CCV) in the two groups were compared using the system known as Facial clima. There was no inter-group variability between the groups (p > 0.10) in either variable. However, intra-group variability was detected between the affected and healthy side in the transposition group (p = 0.036 and p = 0.017, respectively). The transfer group had greater symmetry in displacement of the commissure (CD) and commissural contraction velocity (CCV) than the transposition group and patients were more satisfied. However, the transposition group had correct symmetry at rest but more asymmetry of CCV and CD when smiling.

Pseudo-merohedral twinning and noncrystallographic symmetry in orthorhombic crystals of SIVmac239 Nef core domain bound to different-length TCRζ fragments

PubMed Central

Kim, Walter M.; Sigalov, Alexander B.; Stern, Lawrence J.

2010-01-01

HIV/SIV Nef mediates many cellular processes through interactions with various cytoplasmic and membrane-associated host proteins, including the signalling ζ subunit of the T-­cell receptor (TCRζ). Here, the crystallization strategy, methods and refinement procedures used to solve the structures of the core domain of the SIVmac239 isolate of Nef (Nefcore) in complex with two different TCRζ fragments are described. The structure of SIVmac239 Nefcore bound to the longer TCRζ polypeptide (Leu51–Asp93) was determined to 3.7 Å resolution (R work = 28.7%) in the tetragonal space group P43212. The structure of SIVmac239 Nefcore in complex with the shorter TCRζ polypeptide (Ala63–Arg80) was determined to 2.05 Å resolution (R work = 17.0%), but only after the detection of nearly perfect pseudo-merohedral crystal twinning and proper assignment of the orthorhombic space group P212121. The reduction in crystal space-group symmetry induced by the truncated TCRζ polypeptide appears to be caused by the rearrangement of crystal-contact hydrogen-bonding networks and the substitution of crystallographic symmetry operations by similar noncrystallographic symmetry (NCS) operations. The combination of NCS rotations that were nearly parallel to the twin operation (k, h, −l) and a and b unit-cell parameters that were nearly identical predisposed the P212121 crystal form to pseudo-merohedral twinning. PMID:20124696

The vertical, the horizontal and the rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications

NASA Astrophysics Data System (ADS)

Braun, A. P.; Watari, T.

2015-01-01

The four-form field strength in F-theory compactifications on Calabi-Yau four-folds takes its value in the middle cohomology group H 4. The middle cohomology is decomposed into a vertical, a horizontal and a remaining component, all three of which are present in general. We argue that a flux along the remaining or vertical component may break some symmetry, while a purely horizontal flux does not influence the unbroken part of the gauge group or the net chirality of charged matter fields. This makes the decomposition crucial to the counting of flux vacua in the context of F-theory GUTs. We use mirror symmetry to derive a combinatorial formula for the dimensions of these components applicable to any toric Calabi-Yau hypersurface, and also make a partial attempt at providing a geometric characterization of the four-cycles Poincaré dual to the remaining component of H 4. It is also found in general elliptic Calabi-Yau fourfolds supporting SU(5) gauge symmetry that a remaining component can be present, for example, in a form crucial to the symmetry breaking SU(5) - → SU(3) C × SU(2) L × U(1) Y . The dimension of the horizontal component is used to derive an estimate of the statistical distribution of the number of generations and the rank of 7-brane gauge groups in the landscape of F-theory flux vacua.

A Finite Abelian Group of Two-Letter Inversions

ERIC Educational Resources Information Center

Balbuena, Sherwin E.

2015-01-01

In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete…

Effects of Gait Training With Body Weight Support on a Treadmill Versus Overground in Individuals With Stroke.

PubMed

Gama, Gabriela L; Celestino, Melissa L; Barela, José A; Forrester, Larry; Whitall, Jill; Barela, Ana M

2017-04-01

To investigate the effects of gait training with body weight support (BWS) on a treadmill versus overground in individuals with chronic stroke. Randomized controlled trial. University research laboratory. Individuals (N=28) with chronic stroke (>6mo from the stroke event). Participants were randomly assigned to receive gait training with BWS on a treadmill (n=14) or overground (n=14) 3 times a week for 6 weeks. Gait speed measured using the 10-meter walk test, endurance measured using the 6-minute walk test, functional independence measured using the motor domain of the FIM, lower limb recovery measured using the lower extremity domain of the Fugl-Meyer assessment, step length, step length symmetry ratio, and single-limb support duration. Measurements were obtained at baseline, immediately after the training session, and 6 weeks after the training session. At 1 week after the last training session, both groups improved in all outcome measures except paretic step length and step length symmetry ratio, which were improved only in the overground group (P=.01 and P=.01, respectively). At 6 weeks after the last training session, all improvements remained and the treadmill group also improved paretic step length (P<.001) but not step length symmetry ratio (P>.05). Individuals with chronic stroke equally improve gait speed and other gait parameters after 18 sessions of BWS gait training on either a treadmill or overground. Only the overground group improved step length symmetry ratio, suggesting a role of integrating overground walking into BWS interventions poststroke. Copyright © 2016 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

The deviations of the Al6Li3Cu quasicrystal from icosahedral symmetry : a reminiscence of a cubic crystal

NASA Astrophysics Data System (ADS)

Donnadieu, Patricia

1994-05-01

The (Al6Li3Cu) (T2) quasicrystals are known to exhibit large deviations from the icosahedral symmetry. Series of electron diffraction patterns are used to investigate these imperfections in as-cast T, samples. A detailed analysis of the 5-fold and 3-fold symmetry diffraction patterns shows that they are compatible with the m3 point group instead of the m35 icosahedral group. This symmetry reduction is interprétéd as reminiscent of the cubic approximant phase (R-Al5Li3Cu) rather than of higher order approximant phases. This interpretation is supported by previous observations on crystal/quasicrystal phase transformation in the AlLiCu system. Les quasicristaux de phase T2(Al6Li3Cu) montrent d'importantes déviations à la symétrie icosaédrique. Ces imperfections sont mises en évidence par diffraction électronique dans des échantillons de phase T2 brut de coulée. Un examen détaillé des diagrammes de diffraction de symétrie d'ordre 3 et 5 révèle qu'ils sont compatibles avec le groupe ponctuel m3 au lieu du groupe de l'icosaèdre (m35). Cette réduction de symétrie est interprétée comme une réminiscence de la phase cubique approximante (R-Al5Li3Cu) et non l'apparition d'approximant d'ordre plus élevé. Cette interprétation est suggérée par des observations antérieures sur la transformation cristal/quasicristal dans le système AlLiCu.

Asymmetric activation of temporalis, masseter, and sternocleidomastoid muscles in temporomandibular disorder patients.

PubMed

Ries, Lilian Gerdi Kittel; Alves, Marcelo Correa; Bérzin, Fausto

2008-01-01

The aim of this study was to analyze the symmetry of the electromyographic (EMG) activity of the temporalis, masseter, and sternocleidomastoid (SCM) muscles in volunteers divided into a control group and a temporomandibular disorder (TMD) group. The surface EMG recordings were made during mandibular rest position, maximal intercuspal position, and during the chewing cycle. Normalized EMG waves of paired muscles were compared by computing a percentage overlapping coefficient (POC). The difference between the groups and between the static and dynamic clenching tests was analyzed through repeated measures, ANOVA. Symmetry of the temporalis, masseter, and SCM muscles activity was smaller in the TMD group compared to the control group. The mandibular postures were also significantly different among themselves. The asymmetric activation of jaw and neck muscles was interpreted as a compensatory strategy to achieve stability for the mandibular and cervical systems during masticatory function.

Twisted injectivity in projected entangled pair states and the classification of quantum phases

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

Buerschaper, Oliver, E-mail: obuerschaper@perimeterinstitute.ca

We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry is expressed as a matrix product operator (MPO) with bond dimension greater than 1 and acts on the virtual boundary of a PEPS tensor. We show that it gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians which are gapped, frustration-free and include fixed points of the renormalization group flow. Based on this insight, we advance the classification of 2D gapped quantum spin systems bymore » showing how this new standard form for PEPS determines the emergent topological order of these local Hamiltonians. Specifically, we identify their universality class as DIJKGRAAF–WITTEN topological quantum field theory (TQFT). - Highlights: • We introduce a new standard form for projected entangled pair states via a twisted group symmetry which is given by nontrivial matrix product operators. • We construct a large family of gapped, frustration-free Hamiltonians in two dimensions from this new standard form. • We rigorously show how this new standard form for low energy states determines the emergent topological order.« less

Quantum Hall Valley Nematics: From Field Theories to Microscopic Models

NASA Astrophysics Data System (ADS)

Parameswaran, Siddharth

The interplay between quantum Hall ordering and spontaneously broken ``internal'' symmetries in two-dimensional electron systems with spin or pseudospin degrees of freedom gives rise to a variety of interesting phenomena, including novel phases, phase transitions, and topological excitations. I will discuss a theory of broken-symmetry quantum Hall states, applicable to a class of multivalley systems, where the symmetry at issue is a point-group element that combines a spatial rotation with a permutation of valley indices. I will explore its ramifications for the phase diagram of a variety of experimental systems, such as AlAs and Si quantum wells and the surface states of bismuth. I will also discuss unconventional transport phenomena in these phases in the presence of quenched randomness, and the possible mechanisms of selection between degenerate broken-symmetry phases in clean systems. I acknowledge support from NSF DMR-1455366.

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.

Léon Rosenfeld's general theory of constrained Hamiltonian dynamics

NASA Astrophysics Data System (ADS)

Salisbury, Donald

Léon Rosenfeld published in Annalen der Physik in 1930 a groundbreaking paper showing how to construct a Hamiltonian formalism for Lagrangian theories which admitted an underlying local gauge symmetry. The theory included both ``internal'' transformations such as the U(1) symmetry group of electromagnetism, and ``external'' symmetries typified by Einstein's general theory of relativity. His comprehensive analysis predated by two decades the formalism known as the Dirac-Bergmann approach, and I will present evidence that each of these giants were to some extent influenced by Rosenfeld's theory. Of particular significance is Rosenfeld's incorporation of arbitrary functions into the phase space generator of temporal evolution, and his construction of the phase space generator of symmetry transformations. The existing Hamiltonian formalisms have of course played a central role both in the demonstration of the renormalizability of Yang-Mills theories and current efforts in constructing a quantum theory of gravity.

Permutational symmetries for coincidence rates in multimode multiphotonic interferometry

NASA Astrophysics Data System (ADS)

Khalid, Abdullah; Spivak, Dylan; Sanders, Barry C.; de Guise, Hubert

2018-06-01

We obtain coincidence rates for passive optical interferometry by exploiting the permutational symmetries of partially distinguishable input photons, and our approach elucidates qualitative features of multiphoton coincidence landscapes. We treat the interferometer input as a product state of any number of photons in each input mode with photons distinguished by their arrival time. Detectors at the output of the interferometer count photons from each output mode over a long integration time. We generalize and prove the claim of Tillmann et al. [Phys. Rev. X 5, 041015 (2015), 10.1103/PhysRevX.5.041015] that coincidence rates can be elegantly expressed in terms of immanants. Immanants are functions of matrices that exhibit permutational symmetries and the immanants appearing in our coincidence-rate expressions share permutational symmetries with the input state. Our results are obtained by employing representation theory of the symmetric group to analyze systems of an arbitrary number of photons in arbitrarily sized interferometers.

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.

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.

Wave functions of symmetry-protected topological phases from conformal field theories

NASA Astrophysics Data System (ADS)

Scaffidi, Thomas; Ringel, Zohar

2016-03-01

We propose a method for analyzing two-dimensional symmetry-protected topological (SPT) wave functions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the fractional quantum Hall effect wherein the wave-function amplitude is written as a many-operator correlator in the CFT. Adopting a bottom-up approach, we start from various known microscopic wave functions of SPTs with discrete symmetries and show how the CFT description emerges at large scale, thereby revealing a deep connection between group cocycles and critical, sometimes integrable, models. We show that the CFT describing the bulk wave function is often also the one describing the entanglement spectrum, but not always. Using a plasma analogy, we also prove the existence of hidden quasi-long-range order for a large class of SPTs. Finally, we show how response to symmetry fluxes is easily described in terms of the CFT.

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

REHABILITATION FOLLOWING KNEE DISLOCATION WITH LATERAL SIDE INJURY: IMPLEMENTATION OF THE KNEE SYMMETRY MODEL

PubMed Central

Jenkins, Walter; Urch, Scott E.; Shelbourne, K. Donald

2010-01-01

Rehabilitation following lateral side knee ligament repair or reconstruction has traditionally utilized a conservative approach. An article outlining a new concept in rehabilitation following ACL reconstruction called the Knee Symmetry Model was recently published13. The Knee Symmetry Model can also be applied to rehabilitation of other knee pathologies including a knee dislocation with a lateral side injury. This Clinical Commentary describes the rehabilitation procedures used with patients who underwent surgery to repair lateral side ligaments, based upon the Knee Symmetry Model. These procedures were used previously to rehabilitate a group of patients with lateral side ligament repair as reported by Shelbourne et al10. Outcome data and subjective knee scores for these patients were recorded via the International Knee Documentation Committee (IKDC) guidelines and modified Noyes survey scores and are summarized in this paper, as previously published. Rehabilitation following lateral side knee ligament repair using guidelines based upon the Knee Symmetry Model appears to provide patients with excellent long-term stability, normal ROM and strength, and a high level of function. PMID:21589671

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

Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

Are corticosteroids useful in all degrees of severity and rapid recovery of Bell's palsy?

PubMed

Ferreira, Margarida; Firmino, Machado J; Marques, Elisa A; Santos, Paula C; Duarte, José A

2016-07-01

Conclusions The results provide preliminary evidence that corticosteroids were not effective in all grades of dysfunction and for achieving a rapid remission in the early phase of BP, highlighting the need to define standard and rigorous criteria to prescribe corticosteroids in these patients. Objectives The main aim of this study was to investigate whether the use of corticosteroids better associated than paralleled with neuromuscular training (C + FNT) is more effective than facial neuromuscular training (FNT) applied alone, in terms of recovery degree and facial symmetry during the early phase of Bell's palsy (BP). Patients and methods A prospective single-blinded study involved 73 patients: the C + FNT group (n = 42; median age = 37.5 years) and FNT group (n = 31; median age = 49.0 years). Patients were assessed before and 6 weeks after treatment by House-Brackmann (HB-FGS) and Sunnybrook Facial Grading System (SB-FGS). Results Recovery degree and facial symmetry improved significantly in both groups (p < 0.001), without differences between groups (p > 0.05). However, the C + FNT group displayed better outcomes for cheek (p = 0.004) and mouth (p = 0.022) resting symmetry at SB-FGS, instead of compared to the FNT group. The corticosteroids had no significant effect on all recovery degrees (p = 0.992) and rapid remission (p = 0.952). Multiple linear regression analysis showed that the type of intervention was not a significant predictor for recovery degree (p = 0.917).

Very special conformal field theories and their holographic duals

NASA Astrophysics Data System (ADS)

Nakayama, Yu

2018-03-01

Cohen and Glashow introduced the notion of very special relativity as viable space-time symmetry of elementary particle physics. As a natural generalization of their idea, we study the subgroup of the conformal group, dubbed very special conformal symmetry, which is an extension of the very special relativity. We classify all of them and construct field theory examples as well as holographic realization of the very special conformal field theories.

Supertranslations and Superrotations at the Black Hole Horizon.

PubMed

Donnay, Laura; Giribet, Gaston; González, Hernán A; Pino, Miguel

2016-03-04

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

Measuring pictorial balance perception at first glance using Japanese calligraphy

PubMed Central

Gershoni, Sharon; Hochstein, Shaul

2011-01-01

According to art theory, pictorial balance acts to unify picture elements into a cohesive composition. For asymmetrical compositions, balancing elements is thought to be similar to balancing mechanical weights in a framework of symmetry axes. Assessment of preference for balance (APB), based on the symmetry-axes framework suggested in Arnheim R, 1974 Art and Visual Perception: A Psychology of the Creative Eye (Berkeley, CA: University of California Press), successfully matched subject balance ratings of images of geometrical shapes over unlimited viewing time. We now examine pictorial balance perception of Japanese calligraphy during first fixation, isolated from later cognitive processes, comparing APB measures with results from balance-rating and comparison tasks. Results show high between-task correlation, but low correlation with APB. We repeated the rating task, expanding the image set to include five rotations of each image, comparing balance perception of artist and novice participant groups. Rotation has no effect on APB balance computation but dramatically affects balance rating, especially for art experts. We analyze the variety of rotation effects and suggest that, rather than depending on element size and position relative to symmetry axes, first fixation balance processing derives from global processes such as grouping of lines and shapes, object recognition, preference for horizontal and vertical elements, closure, and completion, enhanced by vertical symmetry. PMID:23145242

Phonon-induced topological transition to a type-II Weyl semimetal

DOE PAGES

Wang, Lin-Lin; Jo, Na Hyun; Wu, Yun; ...

2017-04-11

Given the importance of crystal symmetry for the emergence of topological quantum states, we have studied here, as exemplified in NbNiTe 2, the interplay of crystal symmetry, atomic displacements (lattice vibration), band degeneracy, and band topology. For the NbNiTe 2 structure in space-group 53 (Pmna)$-$ having an inversion center arising from two glide planes and one mirror plane with a two-fold rotation and screw axis$-$a full gap opening exists between two band manifolds near the Fermi energy. Upon atomic displacements by optical phonons, the symmetry lowers to space-group 28 (Pma2), eliminating one glide plane along c, the associated rotation andmore » screw axis, and the inversion center. As a result, 20 Weyl points emerge, including four type-IIWeyl points in the Γ-X direction at the boundary between a pair of adjacent electron and hole bands. Thus, optical phonons may offer control of the transition to a Weyl fermion state.« less

High-field Transport in Low Symmetry β-Ga2O3 Crystal

NASA Astrophysics Data System (ADS)

Ghosh, Krishnendu; Singisetti, Uttam

High-field carrier transport plays an important role in many disciplines of electronics. Conventional transport theories work well on high-symmetry materials but lacks insight as the crystal symmetry goes down. Newly emerging materials, many of which possess low symmetry, demand more rigorous treatment of charge transport. We will present a comprehensive study of high-field transport using ab initio electron-phonon interaction (EPI) elements in a full-band Monte Carlo (FBMC) algorithm. We use monoclinic β-Ga2O3 as a benchmark low-symmetry material which is also an emerging wide-bandgap semiconductor. β-Ga2O3 has a C2m space group and a 10 atom primitive cell. In this work the EPIs are calculated under density-functional perturbation theory framework. We will focus on the computational challenges arising from many phonon modes and low crystal symmetry. Significant insights will be presented on the details of energy relaxation by the hot electrons mediated by different phonon modes. We will also show the velocity-field curves of electrons in different crystal directions. The authors acknowledge the support from the National Science Foundation Grant (ECCS 1607833). The authors also acknowledge the computing support provided by the Center for Computational Research at the University at Buffalo.

Generalization of improved step length symmetry from treadmill to overground walking in persons with stroke and hemiparesis†

PubMed Central

Savin, Douglas N.; Morton, Susanne M.; Whitall, Jill

2013-01-01

Objectives Determine whether adaptation to a swing phase perturbation during gait transferred from treadmill to overground walking, the rate of overground deadaptation, and whether overground aftereffects improved step length asymmetry in persons with hemiparetic stroke and gait asymmetry. Methods Ten participants with stroke and hemiparesis and 10 controls walked overground on an instrumented gait mat, adapted gait to a swing phase perturbation on a treadmill, then walked overground on the gait mat again. Outcome measures, primary: overground step length symmetry, rates of treadmill step length symmetry adaptation and overground step length symmetry deadaptation; secondary: overground gait velocity, stride length, and stride cycle duration. Results Step length symmetry aftereffects generalized to overground walking and adapted at a similar rate on the treadmill in both groups. Aftereffects decayed at a slower rate overground in participants with stroke and temporarily improved overground step length asymmetry. Both groups’ overground gait velocity increased post adaptation due to increased stride length and decreased stride duration. Conclusions Stroke and hemiparesis do not impair generalization of step length symmetry changes from adapted treadmill to overground walking, but prolong overground aftereffects. Significance Motor adaptation during treadmill walking may be an effective treatment for improving overground gait asymmetries post-stroke. PMID:24286858

Crystallographic CourseWare

NASA Astrophysics Data System (ADS)

Kastner, Margaret E.; Vasbinder, Eric; Kowalcyzk, Deborah; Jackson, Sean; Giammalvo, Joseph; Braun, James; Dimarco, Keith

2000-09-01

Literature Cited

1. International Tables for Crystallography: Volume A: Space Group Symmetry; Hanh, T., Ed.; D. Reidel: Boston, 1983.
2. International Tables for Crystallography, Brief Teaching Edition of Volume A, Space-Group Symmetry, 3rd ed.; Hanh, T., Ed.; Dordrecht: Boston, 1993.
3. Kastner, M. E. J. Appl. Crystallogr. 1999, 32, 327-331.
4. Macromedia Director, version 6.5; Macromedia, Inc., San Francisco, CA; 1998.
5. QuickTime, version 3.0; Apple Computer: Cupertino, CA, 1998.
6. ToolBook II, Instructor, version 6.0; Asymetrix: Bellevue, WA, 1998.
7. HyperCard 2.3.5; Apple Computer: Cupertino, CA, 1998.

On the elliptic genera of manifolds of Spin(7) holonomy

DOE PAGES

Benjamin, Nathan; Harrison, Sarah M.; Kachru, Shamit; ...

2015-12-16

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The N=1 superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a c = 12 realization of the symmetry group SW(3/2,2). In this paper, we compute the characters of this supergroup and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. Here, we find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

Real weights, bound states and duality orbits

NASA Astrophysics Data System (ADS)

Marrani, Alessio; Riccioni, Fabio; Romano, Luca

2016-01-01

We show that the duality orbits of extremal black holes in supergravity theories with symmetric scalar manifolds can be derived by studying the stabilizing subalgebras of suitable representatives, realized as bound states of specific weight vectors of the corresponding representation of the duality symmetry group. The weight vectors always correspond to weights that are real, where the reality properties are derived from the Tits-Satake diagram that identifies the real form of the Lie algebra of the duality symmetry group. Both 𝒩 = 2 magic Maxwell-Einstein supergravities and the semisimple infinite sequences of 𝒩 = 2 and 𝒩 = 4 theories in D = 4 and 5 are considered, and various results, obtained over the years in the literature using different methods, are retrieved. In particular, we show that the stratification of the orbits of these theories occurs because of very specific properties of the representations: in the case of the theory based on the real numbers, whose symmetry group is maximally noncompact and therefore all the weights are real, the stratification is due to the presence of weights of different lengths, while in the other cases it is due to the presence of complex weights.

Structural Identification of 19 Purified Isomers of the OPV Acceptor Material bisPCBM by 13C NMR and UV-Vis Absorption Spectroscopy and High-Performance Liquid Chromatography.

PubMed

Liu, Tong; Abrahams, Isaac; Dennis, T John S

2018-04-26

The molecular structures of 19 purified isomers of bis-phenyl-C 62 -butyric acid methyl ester were identified by a combination of 13 C NMR and UV-vis absorption spectroscopies and high-performance liquid chromatography (HPLC) retention time analysis. All 19 isomers are dicyclopropafullerenes (none are homofullerenes). There were seven isomers with C 1 molecular point-group symmetry, four with C s , six with C 2 , one with C 2 v , and one with C 2 h symmetry. The C 2 h , C 2 v , and all five nonequatorial C 1 isomers were unambiguously assigned to their respective HPLC fractions. For the other 12 isomers, the 13 C NMR and UV-vis spectra placed them in six groups of two same-symmetry isomers. On the basis of the widely spaced HPLC retention times of the two isomers within each of these six groups, and the empirical inverse correlation between retention time and addend spacing, each isomer was assigned to its corresponding HPLC fraction. In addition, the missing trans-1 isomer was found, purified, and characterized.

Asymptotically Free Gauge Theories. I

DOE R&D Accomplishments Database

Wilczek, Frank; Gross, David J.

1973-07-01

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

Topological crystalline materials: General formulation, module structure, and wallpaper groups

NASA Astrophysics Data System (ADS)

Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori

2017-06-01

We formulate topological crystalline materials on the basis of the twisted equivariant K theory. Basic ideas of the twisted equivariant K theory are explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an application of our formulation, we present a complete classification of topological crystalline surface states, in the absence of time-reversal invariance. The classification works for gapless surface states of three-dimensional insulators, as well as full gapped two-dimensional insulators. Such surface states and two-dimensional insulators are classified in a unified way by 17 wallpaper groups, together with the presence or the absence of (sublattice) chiral symmetry. We identify the topological numbers and their representations under the wallpaper group operation. We also exemplify the usefulness of our formulation in the classification of bulk gapless phases. We present a class of Weyl semimetals and Weyl superconductors that are topologically protected by inversion symmetry.

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

Vibrational Spectra of Tetrahedral Fullerenes.

PubMed

Cheng; Li; Tang

1999-01-01

From the topological structures of the following classes of tetrahedral fullerenes-(1) Cn(h, h; -i, i), Cn(h, 0; -i, 2i), Cn(2h + i, -h + i; i, i), Cn(h - i, h + 2i; -i, 2i), and Cn(h, i; 0, i) for Td symmetry; (2) Cn(h, k; k, h), Cn(h, k; -h - k, k), and Cn(h, k; -h, h + k) for Th symmetry; (3) Cn(h, k; i, j) for T symmetry-we have obtained theoretically the formulas for the numbers of their IR and Raman active modes for all of the tetrahedral fullerenes through the decomposition of their nuclear motions into irreducible representations by means of group theory. Copyright 1999 Academic Press.

Symmetry and conservation laws in semiclassical wave packet dynamics

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

Ohsawa, Tomoki, E-mail: tomoki@utdallas.edu

2015-03-15

We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum asmore » well as naturally corresponds to the quantum picture.« less

A One-group, One-dimensional Transport Benchmark in Cylindrical Geometry

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

Barry Ganapol; Abderrafi M. Ougouag

A 1-D, 1-group computational benchmark in cylndrical geometry is described. This neutron transport benchmark is useful for evaluating reactor concepts that possess azimuthal symmetry such as a pebble-bed reactor.

Finding higher symmetries of differential equations using the MAPLE package DESOLVII

NASA Astrophysics Data System (ADS)

Vu, K. T.; Jefferson, G. F.; Carminati, J.

2012-04-01

We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. Catalogue identifier: ADYZ_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYZ_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 858 No. of bytes in distributed program, including test data, etc.: 112 515 Distribution format: tar.gz Programming language: MAPLE internal language Computer: PCs and workstations Operating system: Linux, Windows XP and Windows 7 RAM: Depends on the type of problem and the complexity of the system (small ≈ MB, large ≈ GB) Classification: 4.3, 5 Catalogue identifier of previous version: ADYZ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 682 Does the new version supersede the previous version?: Yes Nature of problem: There are a number of approaches one may use to find solutions to systems of differential equations. These include numerical, perturbative, and algebraic methods. Unfortunately, approximate or numerical solution methods may be inappropriate in many cases or even impossible due to the nature of the system and hence exact methods are important. In their own right, exact solutions are valuable not only as a yardstick for approximate/numerical solutions but also as a means of elucidating the physical meaning of fundamental quantities in systems. One particular method of finding special exact solutions is afforded by the work of Sophus Lie and the use of continuous transformation groups. The power of Lie's group theoretic method lies in its ability to unify a number of ad hoc integration methods through the use of symmetries, that is, continuous groups of transformations which leave the differential system “unchanged”. These symmetry groups may then be used to find special solutions. Solutions found in this manner are called similarity or invariant solutions. The method of finding symmetry transformations initially requires the generation of a large overdetermined system of linear, homogeneous, coupled PDEs. The integration of this system is usually reasonably straightforward requiring the (often elementary) integration of equations by splitting the system according to dependency on different orders and degrees of the dependent variable/s. Unfortunately, in the case of contact and Lie-Bäcklund symmetries, the integration of the determining system becomes increasingly more difficult as the order of the symmetry is increased. This is because the symmetry generating functions become dependent on higher orders of the derivatives of the dependent variables and this diminishes the overall resulting “separable” differential conditions derived from the main determining system. Furthermore, typical determining systems consist of tens to hundreds of equations and this, combined with standard mechanical solution methods, makes the process well suited to automation using computer algebra systems. The new MAPLE package DESOLVII, which is a major upgrade of DESOLV, now includes routines allowing the determination of higher symmetries (contact and Lie-Bäcklund) for systems of both ordinary and partial differential equations. In addition, significant improvements have been implemented to the algorithm for PDE solution. Finally, we have made some improvements in the overall automated process so as to improve user friendliness by reducing user intervention where possible. Solution method: See “Nature of problem” above. Reasons for new version: New and improved functionality. New functionality - can now compute generalised symmetries. Much improved efficiency (speed and memory use) of existing routines. Restrictions: Sufficient memory may be required for complex systems. Running time: Depends on the type of problem and the complexity of the system (small ≈ seconds, large ≈ hours).

Recent advances in symmetric and network dynamics

NASA Astrophysics Data System (ADS)

Golubitsky, Martin; Stewart, Ian

2015-09-01

We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.

Non-Abelian Gauge Theory in the Lorentz Violating Background

NASA Astrophysics Data System (ADS)

Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais

2018-03-01

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.

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.

Hip Strength in Patients with Quadriceps Strength Deficits after ACL Reconstruction.

PubMed

Bell, David R; Trigsted, Stephanie M; Post, Eric G; Walden, Courtney E

2016-10-01

Quadriceps strength deficits persist for years after anterior cruciate ligament (ACL) reconstruction, and patients with these deficits often shift torque demands away from the knee extensors to the hip during functional tasks. However, it is not clear how quadriceps strength deficits may affect hip strength. Therefore, the purpose of this study was to investigate differences in lower extremity strength in individuals with ACL reconstruction with differing levels of quadriceps strength asymmetry. Isometric strength was recorded bilaterally in 135 participants (73 control and 62 with unilateral ACL reconstruction, time from surgery = 30.9 ± 17.6 months) from the knee extensors and flexors, hip extensors and abductors, and hip internal and external rotator muscle groups. Symmetry indices (limb symmetry index (LSI)) were created based on quadriceps strength, and subjects with ACL reconstruction were subdivided (high quadriceps (LSI ≥ 90%), n = 37; low quadriceps (LSI < 85%), n = 18). Individual group (control vs high quadriceps vs low quadriceps) by limb (reconstructed/nondominant vs healthy/dominant) repeated-measures ANOVA was used to compare strength (%BW) for each of the six joint motions of interest (knee extensors/flexors, hip abductors/extensors/external, and internal rotators) while controlling for time from surgery. An interaction was observed for quadriceps strength (P < 0.001), and the reconstructed limb in the low quadriceps group was weaker than all other limbs. A main effect for group was observed with the low quadriceps group having greater hip extension (P = 0.007) strength in both limbs compared with the other groups. Knee flexion strength was weaker in the reconstructed limb of the high quadriceps group (P = 0.047) compared with all other groups and limbs. Individuals with ACL reconstruction and involved limb quadriceps weakness have greater hip extension strength in both limbs compared with patients with bilateral strength symmetry and controls.

Strength, power output and symmetry of leg muscles: effect of age and history of falling.

PubMed

Perry, Mark C; Carville, Serena F; Smith, I Christopher H; Rutherford, Olga M; Newham, Di J

2007-07-01

Risk factors for medically unexplained falls may include reduced muscle power, strength and asymmetry in the lower limbs. Conflicting reports exist about strength and there is little information about power and symmetry. Forty-four healthy young people (29.3 +/- 0.6 years), 44 older non-fallers (75.9 +/- 0.6 years), and 34 older fallers (76.4 +/- 0.8 years) were studied. Isometric, concentric and eccentric strength of the knee and ankle muscles and leg extension power were measured bilaterally. The younger group was stronger in all muscles and types of contraction than both older groups (P < 0.02-0.0001). Strength differences between the older groups occasionally reached significance in individual muscles and types of contraction but overall the fallers had 85% of the strength and 79% of the power of the non-fallers (P < 0.001). Young subjects generated more power than both older groups (P < 0.0001) and the fallers generated less than the non-fallers (P = 0.03). Strength symmetry showed an inconsistent age effect in some muscles and some contraction types. This was similar overall in the two older groups. Both older groups had greater asymmetry in power than the young (P < 0.02-0.004). Power asymmetry tended to be greater in the fallers than the non-fallers but this did not reach significance. These data do not support the suggestion that asymmetry of strength and power are associated with either increasing age or fall history. Power output showed clear differences between age groups and fall status and appears to be the most relevant measurement of fall risk and highlights the cumulative effects on function of small changes in strength in individual muscle groups.

Critical flavor number of the Thirring model in three dimensions

NASA Astrophysics Data System (ADS)

Wellegehausen, Björn H.; Schmidt, Daniel; Wipf, Andreas

2017-11-01

The Thirring model is a four-fermion theory with a current-current interaction and U (2 N ) chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition, it serves as a toy model to study chiral symmetry breaking. In the limit of flavor number N →1 /2 it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalization group methods, and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavors, but no symmetry breaking for large N . But there is no consensus on the critical flavor number Ncr above which there is no phase transition anymore and on further details of the critical behavior. Values of N found in the literature vary between 2 and 7. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behavior for even and odd flavor numbers is very different: for even flavor numbers, chiral and parity symmetry are always unbroken; for odd flavor numbers, parity symmetry is spontaneously broken below the critical flavor number Nircr=9 , while chiral symmetry is still unbroken.

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 any symmetry.

Using Symmetry to Design Self-Assembling Protein Cages and Nanomaterials on the Mid-Nanometer Scale

NASA Astrophysics Data System (ADS)

Yeates, Todd

Self-assembling molecular structures having diverse cellular functions are widespread in nature. Some of the largest and most sophisticated types are built from many copies of the same or similar protein molecules arranged following principles of symmetry. A long-standing engineering goal has been to design novel protein molecules to self-assemble into geometrically specific structures similar to the extraordinary structures that have evolved in Nature. Practical routes to this goal have been developed by using ideas in symmetry to articulate the minimum design requirements for achieving various types of symmetric architectures, including cages, extended two-dimensional layers, and three-dimensional crystalline materials. The key requirement is that two distinct self-associating interfaces, each conferring one element of rotational symmetry, have to be engineered into the protein molecule (or molecules), following particular geometric specifications. The main principle is that combining two separate symmetry elements into a single molecular entity produces a molecule that necessarily assembles into an architecture dictated by a symmetry group that is the product of the two simpler contributing symmetries. Recent experiments have demonstrated success using a variety of symmetry-based strategies. Strategic variations are emerging that differ from each other with respect to biophysical features such as flexibility vs rigidity in the assembled structures, and with respect to design aspects such as whether the protein interfaces are inherited from natural oligomeric proteins or are designed de novo by advanced computational methods. The success of these strategies has been proven by determining crystal structures of several giant, self-assembling protein cages and clusters (10-25 nm in diameter), created by design. The ability to create sophisticated supramolecular structures from designed protein subunits opens the way to broad applications in synthetic biology and nanotechnology.

Random waves in the brain: Symmetries and defect generation in the visual cortex

NASA Astrophysics Data System (ADS)

Schnabel, M.; Kaschube, M.; Löwel, S.; Wolf, F.

2007-06-01

How orientation maps in the visual cortex of the brain develop is a matter of long standing debate. Experimental and theoretical evidence suggests that their development represents an activity-dependent self-organization process. Theoretical analysis [1] exploring this hypothesis predicted that maps at an early developmental stage are realizations of Gaussian random fields exhibiting a rigorous lower bound for their densities of topological defects, called pinwheels. As a consequence, lower pinwheel densities, if observed in adult animals, are predicted to develop through the motion and annihilation of pinwheel pairs. Despite of being valid for a large class of developmental models this result depends on the symmetries of the models and thus of the predicted random field ensembles. In [1] invariance of the orientation map's statistical properties under independent space rotations and orientation shifts was assumed. However, full rotation symmetry appears to be broken by interactions of cortical neurons, e.g. selective couplings between groups of neurons with collinear orientation preferences [2]. A recently proposed new symmetry, called shift-twist symmetry [3], stating that spatial rotations have to occur together with orientation shifts in order to be an appropriate symmetry transformation, is more consistent with this organization. Here we generalize our random field approach to this important symmetry class. We propose a new class of shift-twist symmetric Gaussian random fields and derive the general correlation functions of this ensemble. It turns out that despite strong effects of the shift-twist symmetry on the structure of the correlation functions and on the map layout the lower bound on the pinwheel densities remains unaffected, predicting pinwheel annihilation in systems with low pinwheel densities.

4d $$ \\mathcal{N} $$=2 theories with disconnected gauge groups

DOE PAGES

Argyres, Philip C.; Martone, Mario

2017-03-28

In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1more » $$ \\mathcal{N} $$ = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $$ \\mathcal{N} $$ = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1) R, low-energy EM duality group SL(2,Z), and the outer automorphism group of the flavor symmetry algebra, Out(F ). The theories that we construct are remarkable in many ways: (i) two of them have exceptional F 4 and G 2 flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 $$ \\mathcal{N} $$ = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged $$ \\mathcal{N} $$ = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. Here, we propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.« less

Heat-induced symmetry breaking in ant (Hymenoptera: Formicidae) escape behavior

PubMed Central

Chung, Yuan-Kai

2017-01-01

The collective egress of social insects is important in dangerous situations such as natural disasters or enemy attacks. Some studies have described the phenomenon of symmetry breaking in ants, with two exits induced by a repellent. However, whether symmetry breaking occurs under high temperature conditions, which are a common abiotic stress, remains unknown. In our study, we deposited a group of Polyrhachis dives ants on a heated platform and counted the number of escaping ants with two identical exits. We discovered that ants asymmetrically escaped through two exits when the temperature of the heated platform was >32.75°C. The degree of asymmetry increased linearly with the temperature of the platform. Furthermore, the higher the temperature of heated platform was, the more ants escaped from the heated platform. However, the number of escaping ants decreased for 3 min when the temperature was higher than the critical thermal limit (39.46°C), which is the threshold for ants to endure high temperature without a loss of performance. Moreover, the ants tended to form small groups to escape from the thermal stress. A preparatory formation of ant grouping was observed before they reached the exit, indicating that the ants actively clustered rather than accidentally gathered at the exits to escape. We suggest that a combination of individual and grouping ants may help to optimize the likelihood of survival during evacuation. PMID:28355235

Intralines of quasi-conical intersections on torsion planes: methylamine as a case study.

PubMed

Levi, C; Halász, G J; Vibók, A; Bar, I; Zeiri, Y; Kosloff, R; Baer, M

2009-06-18

Recently we reported on a novel feature associated with the intersection of the two lowest states (1)A' and (1)A'' of the methylamine (J. Chem. Phys. 2008, 128, 244302). We established the existence of a finite (closed) line of conical intersections (ci), namely, a finite seam, located in the HC-NHH symmetry plane, a line that is formed by moving a single hydrogen on that plane while locking the positions of the (six) other atoms. In the present article, this study is extended to the corresponding torsion planes formed by rotating the methyl group around the CN axis. The torsion planes, in contrast with the HC-NHH symmetry plane, do not satisfy the symmetry feature that enables the seam just mentioned. Nevertheless, the calculated nonadiabatic coupling terms (NACTs) resemble features similar to those encountered in the HC-NHH symmetry plane. Following a tedious numerical study supported by a theoretical model (Section III), it was verified that these NACTs may become similar to those on the symmetry plane, sometimes even to the level of almost no distinction, but lack one basic feature; namely, they are not singular and therefore do not form topological effects.

Symmetry blockade and its breakdown in energy equipartition of square graphene resonators

NASA Astrophysics Data System (ADS)

Wang, Yisen; Zhu, Zhigang; Zhang, Yong; Huang, Liang

2018-03-01

The interaction between flexural modes due to nonlinear potentials is critical to heat conductivity and mechanical vibration of two dimensional materials such as graphene. Much effort has been devoted to understanding the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during the equipartition process. In particular, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes, forming symmetry blockades. As a result, the energy first flows to the modes in the same symmetry class. Breakdown of the symmetry blockade, i.e., inter-class energy flow, starts when the displacement profile becomes complex and the inter-class couplings bear nonneglectable values. The equipartition time follows the stretched exponential law and survives in the thermodynamic limit. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two dimensional systems with complex potentials and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their contribution in high thermal conductivity and mechanism of energy dissipation that may intrinsically limit the quality factor of the resonator.

Fourth-order structural steganalysis and analysis of cover assumptions

NASA Astrophysics Data System (ADS)

Ker, Andrew D.

2006-02-01

We extend our previous work on structural steganalysis of LSB replacement in digital images, building detectors which analyse the effect of LSB operations on pixel groups as large as four. Some of the method previously applied to triplets of pixels carries over straightforwardly. However we discover new complexities in the specification of a cover image model, a key component of the detector. There are many reasonable symmetry assumptions which we can make about parity and structure in natural images, only some of which provide detection of steganography, and the challenge is to identify the symmetries a) completely, and b) concisely. We give a list of possible symmetries and then reduce them to a complete, non-redundant, and approximately independent set. Some experimental results suggest that all useful symmetries are thus described. A weighting is proposed and its approximate variance stabilisation verified empirically. Finally, we apply symmetries to create a novel quadruples detector for LSB replacement steganography. Experimental results show some improvement, in most cases, over other detectors. However the gain in performance is moderate compared with the increased complexity in the detection algorithm, and we suggest that, without new insight, further extension of structural steganalysis may provide diminishing returns.

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.

Development of Xi'an-CI package – applying the hole–particle symmetry in multi-reference electronic correlation calculations

NASA Astrophysics Data System (ADS)

Suo, Bingbing; Lei, Yibo; Han, Huixian; Wang, Yubin

2018-04-01

This mini-review introduces our works on the Xi'an-CI (configuration interaction) package using graphical unitary group approach (GUGA). Taking advantage of the hole-particle symmetry in GUGA, the Galfand states used to span the CI space are classified into CI subspaces according to the number of holes and particles, and the coupling coefficients used to calculate Hamiltonian matrix elements could be factorised into the segment factors in the hole, active and external spaces. An efficient multi-reference CI with single and double excitations (MRCISD) algorithm is thus developed that reduces the storage requirement and increases the number of correlated electrons significantly. The hole-particle symmetry also gives rise to a doubly contracted MRCISD approach. Moreover, the internally contracted Gelfand states are defined within the CI subspace arising from the hole-particle symmetry, which makes the implementation of internally contracted MRCISD in the framework of GUGA possible. In addition to MRCISD, the development of multi-reference second-order perturbation theory (MRPT2) also benefits from the hole-particle symmetry. A configuration-based MRPT2 algorithm is proposed and extended to the multi-state n-electron valence-state second-order perturbation theory.

Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases

NASA Astrophysics Data System (ADS)

von Keyserlingk, C. W.; Sondhi, S. L.

2016-06-01

Recent work suggests that a sharp definition of "phase of matter" can be given for periodically driven "Floquet" quantum systems exhibiting many-body localization. In this work, we propose a classification of the phases of interacting Floquet localized systems with (completely) spontaneously broken symmetries; we focus on the one-dimensional case, but our results appear to generalize to higher dimensions. We find that the different Floquet phases correspond to elements of Z (G ) , the center of the symmetry group in question. In a previous paper [C. W. von Keyserlingk and S. L. Sondhi, preceding paper, Phys. Rev. B 93, 245145 (2016)], 10.1103/PhysRevB.93.245145, we offered a companion classification of unbroken, i.e., paramagnetic phases.

XXIV International Conference on Integrable Systems and Quantum symmetries (ISQS-24)

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Navrátil, Ondřej; Posta, Severin

2017-01-01

The XXIV International Conference on Integrable Systems and Quantum Symmetries (ISQS-24), organized by the Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University Prague and the Bogoliubov Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research, belongs to the successful series of conferences held at the Czech Technical University which began in 1992 and is devoted to problems of mathematical physics related to the theory of integrable systems, quantum groups and quantum symmetries. During the last 5 years, each of the conferences gathered around 110 scientists from all over the world. 43 papers of plenary lectures and contributions presented at ISQS-24 are published in the present issue of Journal of Physics: Conference Series.

Coulomb branches with complex singularities

NASA Astrophysics Data System (ADS)

Argyres, Philip C.; Martone, Mario

2018-06-01

We construct 4d superconformal field theories (SCFTs) whose Coulomb branches have singular complex structures. This implies, in particular, that their Coulomb branch coordinate rings are not freely generated. Our construction also gives examples of distinct SCFTs which have identical moduli space (Coulomb, Higgs, and mixed branch) geometries. These SCFTs thus provide an interesting arena in which to test the relationship between moduli space geometries and conformal field theory data. We construct these SCFTs by gauging certain discrete global symmetries of N = 4 superYang-Mills (sYM) theories. In the simplest cases, these discrete symmetries are outer automorphisms of the sYM gauge group, and so these theories have lagrangian descriptions as N = 4 sYM theories with disconnected gauge groups.

Similarity solutions for systems arising from an Aedes aegypti model

NASA Astrophysics Data System (ADS)

Freire, Igor Leite; Torrisi, Mariano

2014-04-01

In a recent paper a new model for the Aedes aegypti mosquito dispersal dynamics was proposed and its Lie point symmetries were investigated. According to the carried group classification, the maximal symmetry Lie algebra of the nonlinear cases is reached whenever the advection term vanishes. In this work we analyze the family of systems obtained when the wind effects on the proposed model are neglected. Wide new classes of solutions to the systems under consideration are obtained.

Symmetry enhancement of extremal horizons in D  =  5 supergravity

NASA Astrophysics Data System (ADS)

Kayani, U.

2018-06-01

We consider the near-horizon geometry of supersymmetric extremal black holes in un-gauged and gauged 5-dimensional supergravity, coupled to abelian vector multiplets. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a supersymmetry enhancement. This follows from a set of generalized Lichnerowicz-type theorems we establish, together with an index theory argument. As a consequence, these solutions always admit a symmetry group.

A Simplified Approach to the Basis Functions of Symmetry Operations and Terms of Metal Complexes in an Octahedral Field with d[superscript 1] to d[superscript 9] Configurations

ERIC Educational Resources Information Center

Lee, Liangshiu

2010-01-01

The basis sets for symmetry operations of d[superscript 1] to d[superscript 9] complexes in an octahedral field and the resulting terms are derived for the ground states and spin-allowed excited states. The basis sets are of fundamental importance in group theory. This work addresses such a fundamental issue, and the results are pedagogically…

Observation time scale, free-energy landscapes, and molecular symmetry

PubMed Central

Wales, David J.; Salamon, Peter

2014-01-01

When structures that interconvert on a given time scale are lumped together, the corresponding free-energy surface becomes a function of the observation time. This view is equivalent to grouping structures that are connected by free-energy barriers below a certain threshold. We illustrate this time dependence for some benchmark systems, namely atomic clusters and alanine dipeptide, highlighting the connections to broken ergodicity, local equilibrium, and “feasible” symmetry operations of the molecular Hamiltonian. PMID:24374625

Symmetry and defects in rhombohedral single-crystalline Na0.5Bi0.5TiO3

NASA Astrophysics Data System (ADS)

Beanland, Richard; Thomas, Pam A.

2014-05-01

Recent work has indicated that the symmetry of the lead-free piezoelectric perovskite Na0.5Bi0.5TiO3 can be changed from monoclinic to rhombohedral through the application of an electric field, which may have implications for the study and design of piezoelectric materials close to a morphotropic phase boundary. We have examined high-quality, single-crystal Na0.5Bi0.5TiO3 using transmission electron microscopy and have used digital electron diffraction to observe the symmetry of defect-free regions of material on length scales of a few nanometers. This unequivocally demonstrates that the material is rhombohedral with space group R3c on this length scale. We find that a model that allows disordered displacements of Bi atoms from their nominal sites in the R3c symmetry, while retaining this symmetry on average, gives a very significant improvement in fit to simulations. We use conventional transmission electron microscopy to enumerate the different types of defects that are observed in other regions of the crystal and find a complex microstructure of antiphase boundaries, domain walls, and tetragonal platelets. Their interaction leads to the formation of very high densities of nanotwins. We show that these are expected to have a variable monoclinic Cc symmetry that is driven by the constraint of continuity of the crystal across a domain wall.

[Effect of music on gait symmetry of stroke patients on a treadmill].

PubMed

Schauer, M; Steingrüber, W; Mauritz, K H

1996-10-01

The influence of rhythmic music on gait symmetry was investigated in 12 healthy subjects and 12 stroke patients with mild leg paresis walking on the treadmill. For the measurement, new insoles containing air-filled chambers developed by W.O.M were used. Symmetry deviation was determined as the mean signless difference between left and right swing phases of some 100 strides. In 6 patients, the symmetry deviation decreased by more than 1% of the stride duration some 40 steps after switching on the music. The improvement correlated with the initial symmetry (r2 = 0.61) exclusively in the healthy controls. In order to differentiate individual predictors of the improvement in symmetry, such as cognitive performance in terms of recognizing the beat of the music and the motor performance in terms of synchronizing the movements of the legs to the music, we analysed foot tapping with the patient in the seated position. For both patients and healthy subjects, the mean time difference between beat and foot movement was less than +/-1/32 beat. Individual scatter of mean 8% correspond in the case of healthy subjects to the figures found in the literature for finger movements, and the corresponding figures for the patients are more than twice this. The individual synchronisation performance during walking to music correlates to that during foot tapping (r2 = 0.47) exclusively in the group of healthy controls.

Minimal S U ( 3 ) × S U ( 3 ) symmetry breaking patterns

DOE PAGES

Bai, Yang; Dobrescu, Bogdan A.

2018-03-16

Here, we study the vacua of anmore » $$SU(3)\\times SU(3)$$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification extension of the electroweak group. In other contexts, such as chiral symmetry, $$SU(3)\\times SU(3)$$ is a global symmetry. As opposed to more general $$SU(N)\\times SU(N)$$ symmetric models, the $N=3$ case is special due to the presence of a trilinear scalar term in the potential. We find that the most general tree-level potential has only three types of minima: one that preserves the diagonal $SU(3)$ subgroup, one that is $$SU(2)\\times SU(2)\\times U(1)$$ symmetric, and a trivial one where the full symmetry remains unbroken. The phase diagram is complicated, with some regions where there is a unique minimum, and other regions where two minima coexist.« less

Observation of symmetry-protected topological band with ultracold fermions

PubMed Central

Song, Bo; Zhang, Long; He, Chengdong; Poon, Ting Fung Jeffrey; Hajiyev, Elnur; Zhang, Shanchao; Liu, Xiong-Jun; Jo, Gyu-Boong

2018-01-01

Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems. PMID:29492457

Minimal S U ( 3 ) × S U ( 3 ) symmetry breaking patterns

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

Bai, Yang; Dobrescu, Bogdan A.

Here, we study the vacua of anmore » $$SU(3)\\times SU(3)$$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification extension of the electroweak group. In other contexts, such as chiral symmetry, $$SU(3)\\times SU(3)$$ is a global symmetry. As opposed to more general $$SU(N)\\times SU(N)$$ symmetric models, the $N=3$ case is special due to the presence of a trilinear scalar term in the potential. We find that the most general tree-level potential has only three types of minima: one that preserves the diagonal $SU(3)$ subgroup, one that is $$SU(2)\\times SU(2)\\times U(1)$$ symmetric, and a trivial one where the full symmetry remains unbroken. The phase diagram is complicated, with some regions where there is a unique minimum, and other regions where two minima coexist.« less

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 constructing general F-theory compactifications with U(1) x U(1) x U(1) abelian gauge symmetry. In chapter 1 of this dissertation, I proved finiteness of a region of the string landscape in Type IIB compactifications. String compactifications give rise to a collection of effective low energy theories, known as the string landscape. In chapter 3 of this dissertation, I study abelian gauge symmetries in the duality between F-theory and E8 x E8 heterotic string theory. However, how abelian gauge symmetries can arise in the dual heterotic string theory has never been studied. The main goal of this chapter is to study exactly this. We start with F-theory compactifications with abelian gauge symmetry. With the help of a mathematical lemma as well as a computer code that I came up with, I was able to construct a rich list of specialized examples with specific abelian and nonabelian gauge groups on the F-theory side. (Abstract shortened by ProQuest.).

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

Repeated and diverse losses of corolla bilateral symmetry in the Lamiaceae.

PubMed

Zhong, Jinshun; Preston, Jill C; Hileman, Lena C; Kellogg, Elizabeth A

2017-05-01

Independent evolution of derived complex characters provides a unique opportunity to assess whether and how similar genetic changes correlate with morphological convergence. Bilaterally symmetrical corollas have evolved multiple times independently from radially symmetrical ancestors and likely represent adaptations to attract specific pollinators. On the other hand, losses of bilateral corolla symmetry have occurred sporadically in various groups, due to either modification of bilaterally symmetrical corollas in late development or early establishment of radial symmetry. This study integrated phylogenetic, scanning electron microscopy (SEM)-based morphological, and gene expression approaches to assess the possible mechanisms underlying independent evolutionary losses of corolla bilateral symmetry. This work compared three species of Lamiaceae having radially symmetrical mature corollas with a representative sister taxon having bilaterally symmetrical corollas and found that each reaches radial symmetry in a different way. Higher core Lamiales share a common duplication in the CYCLOIDEA (CYC ) 2 gene lineage and show conserved and asymmetrical expression of CYC2 clade and RAD genes along the adaxial-abaxial floral axis in species having bilateral corolla symmetry. In Lycopus americanus , the development and expression pattern of La-CYC2A and La-CYC2B are similar to those of their bilaterally symmetrical relatives, whereas the loss of La-RAD expression correlates with a late switch to radial corolla symmetry. In Mentha longifolia , late radial symmetry may be explained by the loss of Ml-CYC2A , and by altered expression of two Ml-CYC2B and Ml-RAD genes . Finally, expanded expression of Cc-CYC2A and Cc-RAD strongly correlates with the early development of radially symmetrical corollas in Callicarpa cathayana . Repeated losses of mature corolla bilateral symmetry in Lamiaceae are not uncommon, and may be achieved by distinct mechanisms and various changes to symmetry genes, including the loss of a CYC2 clade gene from the genome, and/or contraction, expansion or alteration of CYC2 clade and RAD -like gene expression. © The Author 2017. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oup.com

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.

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

Argyres, Philip C.; Martone, Mario

In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1more » $$ \\mathcal{N} $$ = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $$ \\mathcal{N} $$ = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1) R, low-energy EM duality group SL(2,Z), and the outer automorphism group of the flavor symmetry algebra, Out(F ). The theories that we construct are remarkable in many ways: (i) two of them have exceptional F 4 and G 2 flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 $$ \\mathcal{N} $$ = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged $$ \\mathcal{N} $$ = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. Here, we propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.« less

Mirror symmetry breaking of silicon polymers--from weak bosons to artificial helix.

PubMed

Fujiki, Michiya

2009-01-01

From elemental particles to human beings, matter and living worlds in our universe are dissymmetric with respect to mirror symmetry. Since the early 19th century, the origin of biomolecular handedness has been puzzling scientists. Nature's elegant bottom-up preference, however, sheds light on new concepts of generating, amplifying, and switching artificial polymers, supramolecules, liquid crystals, and organic crystals that can exhibit ambidextrous circular dichroism in the UV/Visible region with efficiency in production under milder ambient conditions. In the 1920s, Kipping, who first synthesized polysilanes with phenyl groups, had much interest in the handedness of inorganic and organic substances from 1898 to 1909 in his early research life. Polysilanes--which are soluble Si-Si bonded chain-like near-UV chromophores that carry a rich variety of organic groups--may become a bridge between animate and inanimate polymer systems. The present account focuses on several mirror symmetry breaking phenomena exemplified in polysilanes carrying chiral and/or achiral side groups, which are in isotropic dilute solution, as polymer particles dispersed in solution, and in a double layer film immobilized at the solid surface, and subtle differences in the helix, by dictating ultimately ultraweak chiral forces at subatomic, atomic, and molecular levels. Copyright 2009 The Japan Chemical Journal Forum and Wiley Periodicals, Inc.

Structure, dielectric and electric properties of diisobutylammonium hydrogen sulfate crystal

NASA Astrophysics Data System (ADS)

Bednarchuk, Tamara J.; Kinzhybalo, Vasyl; Markiewicz, Ewa; Hilczer, Bożena; Pietraszko, Adam

2018-02-01

Diisobutylammonium hydrogen sulfate, a new organic-inorganic hybrid compound, was successfully synthesized and three structural phases in 298-433 K temperature range were revealed by differential scanning calorimetry and X-ray powder diffraction studies. Single crystal X-ray diffraction data were used to describe the crystal structures in each particular case. In phase III (below 336/319 K on heating/cooling) the crystal arrangement appears to be within the triclinic symmetry with P-1 space group. During heating in the 336-339 K region (and 319-337 K on cooling) the crystal exists in the phase II, characterized by monoclinic symmetry with P21/c space group. Consequently, above 339 K (during heating, and 337 K during cooling temperature sequences), i.e. in phase I the crystal exhibits orthorhombic symmetry (Cmce space group). Ferroelastic domain structure was observed in phase III. These phase boundaries (III→II and II→I) were accompanied by the presence of small anomalies, apparent in the dielectric permittivity and electric conductivity experimental data. Fast proton transport with activation energy of 0.23 eV was observed in the high temperature phase I and related to phonon assisted proton diffusion conditioned by disorder of diisobutylammonium (diba) cations, as well as by high thermal displacements of oxygen and sulfur atoms of hydrogen sulfate anion (hs).

Vectorlike particles, Z‧ and Yukawa unification in F-theory inspired E6

NASA Astrophysics Data System (ADS)

Karozas, Athanasios; Leontaris, George K.; Shafi, Qaisar

2018-03-01

We explore the low energy implications of an F-theory inspired E6 model whose breaking yields, in addition to the MSSM gauge symmetry, a Z‧ gauge boson associated with a U (1) symmetry broken at the TeV scale. The zero mode spectrum of the effective low energy theory is derived from the decomposition of the 27 and 27 ‾ representations of E6 and we parametrise their multiplicities in terms of a minimum number of flux parameters. We perform a two-loop renormalisation group analysis of the gauge and Yukawa couplings of the effective theory model and estimate lower bounds on the new vectorlike particles predicted in the model. We compute the third generation Yukawa couplings in an F-theory context assuming an E8 point of enhancement and express our results in terms of the local flux densities associated with the gauge symmetry breaking. We find that their values are compatible with the ones computed by the renormalisation group equations, and we identify points in the parameter space of the flux densities where the t - b - τ Yukawa couplings unify.

Improvements in muscle symmetry in children with cerebral palsy after equine-assisted therapy (hippotherapy).

PubMed

Benda, William; McGibbon, Nancy H; Grant, Kathryn L

2003-12-01

To evaluate the effect of hippotherapy (physical therapy utilizing the movement of a horse) on muscle activity in children with spastic cerebral palsy. Pretest/post-test control group. Therapeutic Riding of Tucson (TROT), Tucson, AZ. Fifteen (15) children ranging from 4 to 12 years of age diagnosed with spastic cerebral palsy. Children meeting inclusion criteria were randomized to either 8 minutes of hippotherapy or 8 minutes astride a stationary barrel. Remote surface electromyography (EMG) was used to measure muscle activity of the trunk and upper legs during sitting, standing, and walking tasks before and after each intervention. After hippotherapy, significant improvement in symmetry of muscle activity was noted in those muscle groups displaying the highest asymmetry prior to hippotherapy. No significant change was noted after sitting astride a barrel. Eight minutes of hippotherapy, but not stationary sitting astride a barrel, resulted in improved symmetry in muscle activity in children with spastic cerebral palsy. These results suggest that the movement of the horse rather than passive stretching accounts for the measured improvements.

Emergent symmetries in the canonical tensor model

NASA Astrophysics Data System (ADS)

Obster, Dennis; Sasakura, Naoki

2018-04-01

The canonical tensor model (CTM) is a tensor model proposing a classically and quantum mechanically consistent description of gravity, formulated as a first-class constraint system with structural similarities to the ADM formalism of general relativity. The classical CTM produces a general relativistic system in a formal continuum limit, the emergence of which should be explained by the quantum CTM. In this paper we study the symmetry properties of a wave function that exactly solves the quantum constraints of the CTM. We have found that it has strong peaks at configurations invariant under some Lie groups, as predicted by a mechanism described in our previous paper. A surprising result is the preference for configurations invariant not only under Lie groups with positive definite signature, but also with Lorentzian signature. Such symmetries could characterize the global structures of spacetimes, and our results are encouraging towards showing spacetime emergence in the CTM. To verify the asymptotic convergence of the wave function we have also analyzed the asymptotic behavior, which for the most part seems to be well under control.

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.

Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

Rui, Wenjuan; Zhang, Xiangzhi

2016-05-01

This paper investigates the invariance properties of the time fractional Derrida-Lebowitz-Speer-Spohn (FDLSS) equation with Riemann-Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.

Theoretical Studies of Lorentz and CPT Symmetry

NASA Technical Reports Server (NTRS)

Kostelecky, V. Alan

2005-01-01

The fundamental symmetries studied here are Lorentz and CPT invariance, which form a cornerstone of the relativistic quantum theories used in modern descriptions of nature. The results obtained during the reporting period focus on the idea, originally suggested by the P.I. and his group in the late 1980s, that observable CPT and Lorentz violation in nature might emerge from the qualitatively new physics expected to hold at the Planck scale. What follows is a summary of results obtained during the period of this grant.

Some More Solutions of Burgers' Equation

NASA Astrophysics Data System (ADS)

Kumar, Mukesh; Kumar, Raj

2015-01-01

In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

Gauge invariance of fractionally charged quasiparticles and hidden topological Zn symmetry

NASA Astrophysics Data System (ADS)

Wu, Yong-Shi; Hatsugai, Yasuhiro; Kohmoto, Mahito

1991-02-01

Using the braid-group formalism we study the consequences of gauge invariance for fractionally charged anyonic quasiparticles in a two-dimensional multiply connected system. It is shown that gauge invariance requires multicomponent wave functions, and leads to the emergence of a hidden topological Zn symmetry with associated quantum number and unavoidable occurrence of level crossings for many-body eigenstates. In certain situations, it relates the fractional charge to anyon statistics. The implications for the fractional quantum Hall effect are also discussed.

Group Theory, Computational Thinking, and Young Mathematicians

ERIC Educational Resources Information Center

Gadanidis, George; Clements, Erin; Yiu, Chris

2018-01-01

In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…

Algorithmic framework for group analysis of differential equations and its application to generalized Zakharov-Kuznetsov equations

NASA Astrophysics Data System (ADS)

Huang, Ding-jiang; Ivanova, Nataliya M.

2016-02-01

In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical Lie algorithm of construction of symmetries of differential equations, describe the group classification algorithm and discuss the process of reduction of (systems of) PDEs to (systems of) equations with smaller number of independent variables in order to construct invariant solutions. The group classification algorithm and reduction process are illustrated by the example of the generalized Zakharov-Kuznetsov (GZK) equations of form ut +(F (u)) xxx +(G (u)) xyy +(H (u)) x = 0. As a result, a complete group classification of the GZK equations is performed and a number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Lie symmetry reductions and exact solutions for two important invariant models, i.e., the classical and modified Zakharov-Kuznetsov equations, are constructed. The algorithmic framework for group analysis of differential equations presented in this paper can also be applied to other nonlinear PDEs.

Cranial molding helmet therapy and establishment of practical criteria for management in Asian infant positional head deformity.

PubMed

Aihara, Yasuo; Komatsu, Kana; Dairoku, Hitoshi; Kubo, Osami; Hori, Tomokatsu; Okada, Yoshikazu

2014-09-01

The growing number of infants with deformational plagiocephaly (DP) has raised clinical questions about which children, at what age, and how molding helmet therapy (MHT) should be performed especially in Japan. A total of 1,011 Japanese pediatric head deformity infants had undergone MHT after being diagnosed with non-synostotic DP. Three ratios of left to right comparison (anterior, posterior, and overall) were created and analyzed comparing age of starting treatment, helmet wearing period, and severity of skull deformity before with after MHT. The averages of head symmetry ratios after treatment in all groups (for the occipital region) showed apparent improvement; t(930) = -60.86, p = 0.000. (t(932) = -57.8, p = 0.000.) In the "severe" deformation group, the earlier the treatment was started, the higher symmetry ratio recovery was obtained. Treatment was especially effective when started in 4-month-old infants. In contrast to the "severe" group, the "mild" deformation group showed that MHT was most effective if treatment started before 6 months of age. Again, the earlier the treatment was started, the higher symmetry ratio was achieved, but compared to the "severe" group, it had a modest effect when treatment was started in infants older than 8 months. This is the first large-scale molding helmet study reporting the method and efficacy in Japanese infants. It demonstrated that despite the structural and physiological differences from infants of other races, molding helmet therapy is effective in Asian-born infants, provided that intervention timing and recognition conditions are met.

How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

PubMed Central

2017-01-01

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and require q vectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C of International Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal. PMID:28808437

Robust d -wave pairing symmetry in multiorbital cobalt high-temperature superconductors

NASA Astrophysics Data System (ADS)

Li, Yinxiang; Han, Xinloong; Qin, Shengshan; Le, Congcong; Wang, Qiang-Hua; Hu, Jiangping

2017-07-01

The pairing symmetry of the cobalt high-temperature (high-Tc) superconductors formed by vertex-shared cation-anion tetrahedral complexes is studied by the methods of mean-field, random phase approximation (RPA), and functional renormalization-group (FRG) analyses. The results of all of these methods show that the dx2-y2 pairing symmetry is robustly favored near half filling. The RPA and FRG methods, which are valid in weak-interaction regions, predict that the superconducting state is also strongly orbital selective, namely, the dx2-y2 orbital that has the largest density near half filling among the three t2 g orbitals dominates superconducting pairing. These results suggest that these materials, if synthesized, can provide an indisputable test of the high-Tc pairing mechanism and the validity of different theoretical methods.

Crystallization and preliminary crystallographic study of 3 alpha, 20 beta-hydroxysteroid dehydrogenase from Streptomyces hydrogenans.

PubMed

Fitzgerald, P M; Duax, W L; Punzi, J S; Orr, J C

1984-05-15

3 alpha, 20 beta-Hydroxysteroid dehydrogenase, an NADH-dependent oxidoreductase isolated from Streptomyces hydrogenans , is a tetramer containing four subunits each of Mr 25,000. The enzyme has been crystallized by the vapor diffusion technique using either phosphate or borate buffered ammonium sulfate (pH between 6.0 and 8.7) as the precipitant. The crystals are hexagonal bipyramids ; they have the symmetry of space group P6(4)22 (or P6(2)22), with unit cell dimensions a = 127.3 A, c = 112.2 A. Volume and density considerations imply that the crystallographic asymmetric unit contains two monomers, and therefore that the tetramer possesses a 2-fold axis of symmetry that is coincident with a crystallographic 2-fold symmetry element.

SU(3) group structure of strange flavor hadrons

NASA Astrophysics Data System (ADS)

Hong, Soon-Tae

2015-01-01

We provide the isoscalar factors of the SU(3) Clebsch-Gordan series 8⊗ 35 which are extensions of the previous works of de Swart, McNamee and Chilton and play practical roles in current ongoing strange flavor hadron physics research. To this end, we pedagogically study the SU(3) Lie algebra, its spin symmetries, and its eigenvalues for irreducible representations. We also evaluate the values of the Wigner D functions related to the isoscalar factors; these functions are immediately applicable to strange flavor hadron phenomenology. Exploiting these SU(3) group properties associated with the spin symmetries, we investigate the decuplet-to-octet transition magnetic moments and the baryon octet and decuplet magnetic moments in the flavor symmetric limit to construct the Coleman-Glashow-type sum rules.

Infrared modification of gravity from conformal symmetry

NASA Astrophysics Data System (ADS)

Gegenberg, Jack; Rahmati, Shohreh; Seahra, Sanjeev S.

2016-03-01

We reconsider a gauge theory of gravity in which the gauge group is the conformal group SO(4,2), and the action is of the Yang-Mills form, quadratic in the curvature. The resulting gravitational theory exhibits local conformal symmetry and reduces to Weyl-squared gravity under certain conditions. When the theory is linearized about flat spacetime, we find that matter which couples to the generators of special conformal transformations reproduces Newton's inverse square law. Conversely, matter which couples to generators of translations induces a constant and possibly repulsive force far from the source, which may be relevant for explaining the late-time acceleration of the Universe. The coupling constant of the theory is dimensionless, which means that it is potentially renormalizable.

Exsolution in clinoamphiboles

USGS Publications Warehouse

Ross, M.; Papike, J.J.; Weiblen, P.W.

1968-01-01

Ten amphibole specimens from a variety of metamorphic rocks such as talc schists, eclogites, and metamorphosed iron formations contain lamellae of a second amphibole oriented parallel to (101) or (100), or both, of the host. Tremolites, actinolites, and hornblendes commonly have lamellae of a calcium-poor clinoamphibole with P21/m space-group symmetry, or lamellae of citmmingtonite with C2/m space-group symmetry. Likewise ciimmingtonites and P21/m clinoamphiboles commonly contain lamellae of calcium-rich C2/m amphiboles such as tremolite. Results of x-ray diffraction, electron-probe, and microscope studies indicate that most lamellae result from unmixing of a homogeneous amphibole. The P21/m clinoampliibole is analogous to the clinopyroxene pigeonite in agreement with the results of M. G. Bown.

SO(32) heterotic line bundle models

NASA Astrophysics Data System (ADS)

Otsuka, Hajime

2018-05-01

We search for the three-generation standard-like and/or Pati-Salam models from the SO(32) heterotic string theory on smooth, quotient complete intersection Calabi-Yau threefolds with multiple line bundles, each with structure group U(1). These models are S- and T-dual to intersecting D-brane models in type IIA string theory. We find that the stable line bundles and Wilson lines lead to the standard model gauge group with an extra U(1) B-L via a Pati-Salam-like symmetry and the obtained spectrum consists of three chiral generations of quarks and leptons, and vector-like particles. Green-Schwarz anomalous U(1) symmetries control not only the Yukawa couplings of the quarks and leptons but also the higher-dimensional operators causing the proton decay.

A monoclinic polymorph of (1E,5E)-1,5-bis-(2-hy-droxy-benzyl-idene)thio-carbono-hydrazide.

PubMed

Schmitt, Bonell; Gerber, Thomas; Hosten, Eric; Betz, Richard

2011-08-01

The title compound, C(15)H(14)N(4)O(2)S, is a derivative of thio-ureadihydrazide. In contrast to the previously reported polymorph (ortho-rhom-bic, space group Pbca, Z = 8), the current study revealed monoclinic symmetry (space group P2(1)/n, Z = 4). The mol-ecule shows non-crystallographic C(2) as well as approximate C(s) symmetry. Intra-molecular bifurcated O-H⋯(N,S) hydrogen bonds, are present. In the crystal, inter-molecular N-H⋯S hydrogen bonds and C-H⋯π contacts connect the mol-ecules into undulating chains along the b axis. The shortest centroid-centroid distance between two aromatic systems is 4.5285 (12) Å.

Three-dimensional organic Dirac-line materials due to nonsymmorphic symmetry: A data mining approach

NASA Astrophysics Data System (ADS)

Geilhufe, R. Matthias; Bouhon, Adrien; Borysov, Stanislav S.; Balatsky, Alexander V.

2017-01-01

A data mining study of electronic Kohn-Sham band structures was performed to identify Dirac materials within the Organic Materials Database. Out of that, the three-dimensional organic crystal 5,6-bis(trifluoromethyl)-2-methoxy-1 H -1,3-diazepine was found to host different Dirac-line nodes within the band structure. From a group theoretical analysis, it is possible to distinguish between Dirac-line nodes occurring due to twofold degenerate energy levels protected by the monoclinic crystalline symmetry and twofold degenerate accidental crossings protected by the topology of the electronic band structure. The obtained results can be generalized to all materials having the space group P 21/c (No. 14, C2h 5) by introducing three distinct topological classes.

Kondo effect in systems with dynamical symmetries

NASA Astrophysics Data System (ADS)

Kuzmenko, T.; Kikoin, K.; Avishai, Y.

2004-05-01

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low-energy spin excitations consist of a few different spin multiplets |SiMi>. Under certain conditions (to be explained below), some of the lowest energy levels ESi are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top, in the sense that beside its spin operator other dot (vector) operators Rn are needed (in order to fully determine its quantum states), which have nonzero matrix elements between states of different spin multiplets ≠0. These Runge-Lenz operators do not appear in the isolated dot Hamiltonian (so in some sense they are “hidden”). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin s with the operators of the dot then contains exchange terms JnsṡRn besides the ubiquitous ones JisṡSi. The operators Si and Rn generate a dynamical group [usually SO(n)]. Remarkably, the value of n can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied, under favorable circumstances the exchange interaction involves solely the Runge-Lenz operators Rn and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in a triple quantum dot with four electrons.

Micropunch blepharopeeling versus blepharoplasty; what is the best procedure for upper eyelid rejuvenation?

PubMed

Asilian, Ali; Bafandeh, Behzad; Shahmoradi, Zabihollah; Faghihi, Gita; Bostakian, Anis; Mozafarpoor, Samaneh; Hosseini, Sayed Mohsen

2018-05-17

Periocular rejuvenation is the most common aesthetic plastic surgery. The aim of this study was to determine effects of micropunch blepharopeeling (MBP) approach vs blepharoplasty (BP) in periocular rejuvenation. This is a clinical trial study on 22 patients who underwent periorbital rejuvenation referred to University Skin Clinics. Patients were randomly divided into two groups of blepharoplasty or micropunch blepharopeeling. After procedure, all patients were followed in 2 weeks and 2 months and were asked about complications. Patients' satisfaction was scored based on 5-grade scale. Physician satisfaction was assessed based on patients' photographs taken before and 2 months after surgery based on 4-grade scale. The mean age of group MBP was 48.45 ± 7.71 and group BP was 45.45 ± 7.20 (P-value = .36) and Fitzpatrick skin type was not significantly different. Scar was significantly different between groups that 4 (36.4%) patients of BP complained from scars, while none of MBP had significant scar (P-value = .04). Patients were statistically more satisfied with MBP in terms of symmetry, pain, and scar (P-value = .048, .040, and<.001, respectively). Also, MBP was significantly more satisfying for physicians in terms of symmetry and scar (P-value = .047 and <.001, respectively). Micropunch blepharopeeling can be considered as an acceptable procedure of upper eyelid rejuvenation mentioned by patients and physicians. Micropunch blepharopeeling causes fewer scars, better symmetry, and less pain. © 2018 Wiley Periodicals, Inc.

Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

NASA Astrophysics Data System (ADS)

Yannouleas, Constantine; Landman, Uzi

2017-10-01

A constructive theoretical platform for the description of quantum space-time crystals uncovers for N interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta Lm. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond the mean-field level can be induced by superpositions of such good-Lm many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied, natural or synthetic, magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons.

A three-dimensional comparison of a morphometric and conventional cephalometric midsagittal planes for craniofacial asymmetry.

PubMed

Damstra, Janalt; Fourie, Zacharias; De Wit, Marnix; Ren, Yijin

2012-02-01

Morphometric methods are used in biology to study object symmetry in living organisms and to determine the true plane of symmetry. The aim of this study was to determine if there are clinical differences between three-dimensional (3D) cephalometric midsagittal planes used to describe craniofacial asymmetry and a true symmetry plane derived from a morphometric method based on visible facial features. The sample consisted of 14 dry skulls (9 symmetric and 5 asymmetric) with metallic markers which were imaged with cone-beam computed tomography. An error study and statistical analysis were performed to validate the morphometric method. The morphometric and conventional cephalometric planes were constructed and compared. The 3D cephalometric planes constructed as perpendiculars to the Frankfort horizontal plane resembled the morphometric plane the most in both the symmetric and asymmetric groups with mean differences of less than 1.00 mm for most variables. However, the standard deviations were often large and clinically significant for these variables. There were clinically relevant differences (>1.00 mm) between the different 3D cephalometric midsagittal planes and the true plane of symmetry determined by the visible facial features. The difference between 3D cephalometric midsagittal planes and the true plane of symmetry determined by the visible facial features were clinically relevant. Care has to be taken using cephalometric midsagittal planes for diagnosis and treatment planning of craniofacial asymmetry as they might differ from the true plane of symmetry as determined by morphometrics.

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.

Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models

DOE PAGES

Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.

2016-04-25

In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark andmore » lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.« less

A minimal model of neutrino flavor

NASA Astrophysics Data System (ADS)

Luhn, Christoph; Parattu, Krishna Mohan; Wingerter, Akın

2012-12-01

Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T 7 and does not require extra {Z} N or U(1) factors in the Yukawa sector, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T 7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9°. Problematic NLO deviations of the other two mixing angles can be controlled in an ultraviolet completion of the model. The vacuum alignment mechanism that we use necessitates the introduction of a hidden flavon sector that transforms under a {Z} 6 symmetry, thereby spoiling the minimality of our model whose flavor symmetry is then T 7 × {Z} 6.

Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).

Morphology and the gradient of a symmetric potential predict gait transitions of dogs.

PubMed

Wilshin, Simon; Haynes, G Clark; Porteous, Jack; Koditschek, Daniel; Revzen, Shai; Spence, Andrew J

2017-08-01

Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a [Formula: see text] increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was [Formula: see text] larger. This shift is related to (linear regression, [Formula: see text], [Formula: see text]) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models.

The use of SymNose for quantitative assessment of lip symmetry following repair of complete bilateral cleft lip and palate.

PubMed

Russell, James H B; Kiddy, Harriet C; Mercer, Nigel S

2014-07-01

The SymNose computer program has been proposed as an objective method for the quantitative assessment of lip symmetry following unilateral cleft lip repair. This study aims to demonstrate the use of SymNose in patients with complete bilateral cleft lip and palate (BCLP), a group previously excluded from computer-based analysis. A retrospective cohort study compared several parameters of lip symmetry between BCLP cases and non-cleft controls. 15 BCLP cases aged 10 (±1 year) who had undergone primary repair were recruited from the patient database at the South West Cleft Unit, Frenchay Hospital. Frontal facial photographs were selected for measurement. 15 age-matched controls were recruited from a local school. Lip symmetry was expressed as: percentage mismatch of left vermillion border and upper lip area over the right, horizontal lip tilt and lateral deviation of the lip. A significant increase in lip asymmetry was found in the BCLP group expressed as upper vermillion border mismatch across computer-defined and user-defined midlines (mean difference was 16.4% (p < 0.01) and 17.5% (p < 0.01) respectively). The results suggest that a significant degree of lip asymmetry remains in BCLP patients even after primary repair. This challenges previous assumptions that those with bilateral defects would be relatively symmetrical. Copyright © 2013 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rights reserved.

On domain symmetry and its use in homogenization

DOE PAGES

Barbarosie, Cristian A.; Tortorelli, Daniel A.; Watts, Seth E.

2017-03-08

The present study focuses on solving partial differential equations in domains exhibiting symmetries and periodic boundary conditions for the purpose of homogenization. We show in a systematic manner how the symmetry can be exploited to significantly reduce the complexity of the problem and the computational burden. This is especially relevant in inverse problems, when one needs to solve the partial differential equation (the primal problem) many times in an optimization algorithm. The main motivation of our study is inverse homogenization used to design architected composite materials with novel properties which are being fabricated at ever increasing rates thanks to recentmore » advances in additive manufacturing. For example, one may optimize the morphology of a two-phase composite unit cell to achieve isotropic homogenized properties with maximal bulk modulus and minimal Poisson ratio. Typically, the isotropy is enforced by applying constraints to the optimization problem. However, in two dimensions, one can alternatively optimize the morphology of an equilateral triangle and then rotate and reflect the triangle to form a space filling D 3 symmetric hexagonal unit cell that necessarily exhibits isotropic homogenized properties. One can further use this D 3 symmetry to reduce the computational expense by performing the “unit strain” periodic boundary condition simulations on the single triangle symmetry sector rather than the six fold larger hexagon. In this paper we use group representation theory to derive the necessary periodic boundary conditions on the symmetry sectors of unit cells. The developments are done in a general setting, and specialized to the two-dimensional dihedral symmetries of the abelian D 2, i.e. orthotropic, square unit cell and nonabelian D 3, i.e. trigonal, hexagon unit cell. We then demonstrate how this theory can be applied by evaluating the homogenized properties of a two-phase planar composite over the triangle symmetry sector of a D 3 symmetric hexagonal unit cell.« less

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

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.

Symmetry-protected topological phases of one-dimensional interacting fermions with spin-charge separation

NASA Astrophysics Data System (ADS)

Montorsi, Arianna; Dolcini, Fabrizio; Iotti, Rita C.; Rossi, Fausto

2017-06-01

The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels. Interaction is known to induce, besides the gapless Luttinger liquid phase, eight possible gapped phases, among which are the Mott, Haldane, charge-/spin-density, and bond-ordered wave insulators, and the Luther Emery liquid. Here we prove that some of these physically distinct phases have nontrivial topological properties, notably the presence of degenerate protected edge modes with fractionalized charge/spin. Moreover, we show that the eight gapped phases are in one-to-one correspondence with the symmetry-protected topological (SPT) phases classified by group cohomology theory in the presence of particle-hole symmetry P. The latter result is also exploited to characterize SPT phases by measurable nonlocal order parameters which follow the system evolution to the quantum phase transition. The implications on the appearance of exotic orders in the class of microscopic Hubbard Hamiltonians, possibly without P symmetry at higher energies, are discussed.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

NASA Astrophysics Data System (ADS)

Bokhari, Ashfaque H.; Mahomed, F. M.; Zaman, F. D.

2010-05-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

Modeling the SHG activities of diverse protein crystals

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

Haupert, Levi M.; DeWalt, Emma L.; Simpson, Garth J.

2012-10-18

A symmetry-additiveab initiomodel for second-harmonic generation (SHG) activity of protein crystals was applied to assess the likely protein-crystal coverage of SHG microscopy. Calculations were performed for 250 proteins in nine point-group symmetries: a total of 2250 crystals. The model suggests that the crystal symmetry and the limit of detection of the instrument are expected to be the strongest predictors of coverage of the factors considered, which also included secondary-structural content and protein size. Much of the diversity in SHG activity is expected to arise primarily from the variability in the intrinsic protein response as well as the orientation within themore » crystal lattice. Two or more orders-of-magnitude variation in intensity are expected even within protein crystals of the same symmetry. SHG measurements of tetragonal lysozyme crystals confirmed detection, from which a protein coverage of ~84% was estimated based on the proportion of proteins calculated to produce SHG responses greater than that of tetragonal lysozyme. Good agreement was observed between the measured and calculated ratios of the SHG intensity from lysozyme in tetragonal and monoclinic lattices.« less

Symmetry mismatch-driven perpendicular magnetic anisotropy for perovskite/brownmillerite heterostructures.

PubMed

Zhang, Jing; Zhong, Zhicheng; Guan, Xiangxiang; Shen, Xi; Zhang, Jine; Han, Furong; Zhang, Hui; Zhang, Hongrui; Yan, Xi; Zhang, Qinghua; Gu, Lin; Hu, Fengxia; Yu, Richeng; Shen, Baogen; Sun, Jirong

2018-05-15

Grouping different transition metal oxides together by interface engineering is an important route toward emergent phenomenon. While most of the previous works focused on the interface effects in perovskite/perovskite heterostructures, here we reported on a symmetry mismatch-driven spin reorientation toward perpendicular magnetic anisotropy in perovskite/brownmillerite heterostructures, which is scarcely seen in tensile perovskite/perovskite heterostructures. We show that alternately stacking perovskite La 2/3 Sr 1/3 MnO 3 and brownmillerite LaCoO 2.5 causes a strong interface reconstruction due to symmetry discontinuity at interface: neighboring MnO 6 octahedra and CoO 4 tetrahedra at the perovskite/brownmillerite interface cooperatively relax in a manner that is unavailable for perovskite/perovskite interface, leading to distinct orbital reconstructions and thus the perpendicular magnetic anisotropy. Moreover, the perpendicular magnetic anisotropy is robust, with an anisotropy constant two orders of magnitude greater than the in-plane anisotropy of the perovskite/perovskite interface. The present work demonstrates the great potential of symmetry engineering in designing artificial materials on demand.

Chern-Simons theory and S-duality

NASA Astrophysics Data System (ADS)

Dimofte, Tudor; Gukov, Sergei

2013-05-01

We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example, the space of flat SL(2 , {C} ) connections on M is identified with the space of supersymmetric vacua in a dual 3d gauge theory. The hidden symmetry [InlineMediaObject not available: see fulltext.] of SL(2) Chern-Simons theory can be identified as the S-duality transformation of {N}=4 super-Yang-Mills theory (obtained by compactifying the five-brane theory on a torus); whereas the mapping class group action in Chern-Simons theory on a three-manifold M with boundary C is realized as S-duality in 4d {N}=2 super-Yang-Mills theory associated with the Riemann surface C. We illustrate these symmetries by considering simple examples of 3-manifolds that include knot complements and punctured torus bundles, on the one hand, and mapping cylinders associated with mapping class group transformations, on the other. A generalization of mapping class group actions further allows us to study the transformations between several distinguished coordinate systems on the phase space of Chern-Simons theory, the SL(2) Hitchin moduli space.

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.

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

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.

Standard Model as a Double Field Theory.

PubMed

Choi, Kang-Sin; Park, Jeong-Hyuck

2015-10-23

We show that, without any extra physical degree introduced, the standard model can be readily reformulated as a double field theory. Consequently, the standard model can couple to an arbitrary stringy gravitational background in an O(4,4) T-duality covariant manner and manifest two independent local Lorentz symmetries, Spin(1,3)×Spin(3,1). While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the standard model more rigid, and also stringy, than it appeared. The CP violating θ term may no longer be allowed by the symmetry, and hence the strong CP problem can be solved. There are now stronger constraints imposed on the possible higher order corrections. We speculate that the quarks and the leptons may belong to the two different spin classes.

De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity

NASA Astrophysics Data System (ADS)

Berra-Montiel, Jasel; Molgado, Alberto; Serrano-Blanco, David

2017-12-01

We analyse the behaviour of the MacDowell-Mansouri action with internal symmetry group SO(4, 1) under the De Donder-Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder-Weyl equations, are obtained by means of the graded Poisson-Gerstenhaber bracket structure present within the De Donder-Weyl formulation. The decomposition of the internal algebra so(4, 1)≃so(3, 1)\\oplus{R}3, 1 allows the symmetry breaking SO(4, 1)\\toSO(3, 1) , which reduces the original action to the Palatini action without the topological term. We demonstrate that, in contrast to the Lagrangian approach, this symmetry breaking can be performed indistinctly in the polysymplectic formalism either before or after the variation of the De Donder-Weyl Hamiltonian has been done, recovering Einstein’s equations via the Poisson-Gerstenhaber bracket.

Z/sub n/ Baxter model: symmetries and the Belavin parametrization

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

Richey, M.P.; Tracy, C.A.

1986-02-01

The Z/sub n/ Baxter model is an exactly solvable lattice model in the special case of the Belavin parametrization. For this parametrization the authors calculate the partition function in an antiferromagnetic region and the order parameter in a ferromagnetic region. They find that the order parameter is expressible in terms of a modular function of level n which for n=2 is the Onsager-Yang-Baxter result. In addition they determine the symmetry group of the finite lattice partition function for the general Z/sub n/ Baxter model.

Symmetry and Circularization in the Damped Kepler Problem

NASA Astrophysics Data System (ADS)

Crescimanno, Michael; Hamilton, Brian

2007-05-01

Generically, a Hamiltonian system to which damping (non-Hamiltonian) forces are added loses its symmetry. It is a non-trivial fact that the eccentricity vector of lightly damped Kepler orbits is a constant for linear damping only. We describe the group theoretic background necessary to understand this fact and to relate it to that analogue of the Landau criterion for superfluidity associated with the general problem of orbit circularization. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.OSS07.C2.4

Negative birefringent polyimide films

NASA Technical Reports Server (NTRS)

Harris, Frank W. (Inventor); Cheng, Stephen Z. D. (Inventor)

1994-01-01

A negative birefringent film, useful in liquid crystal displays, and a method for controlling the negative birefringence of a polyimide film is disclosed which allows the matching of an application to a targeted amount of birefringence by controlling the degree of in-plane orientation of the polyimide by the selection of functional groups within both the diamine and dianhydride segments of the polyimide which affect the polyimide backbone chain rigidity, linearity, and symmetry. The higher the rigidity, linearity and symmetry of the polyimide backbone, the larger the value of the negative birefringence of the polyimide film.

The axion mass in modular invariant supergravity

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

Butter, Daniel; Gaillard, Mary K.

2005-02-09

When supersymmetry is broken by condensates with a single condensing gauge group, there is a nonanomalous R-symmetry that prevents the universal axion from acquiring a mass. It has been argued that, in the context of supergravity, higher dimension operators will break this symmetry and may generate an axion mass too large to allow the identification of the universal axion with the QCD axion. We show that such contributions to the axion mass are highly suppressed in a class of models where the effective Lagrangian for gaugino and matter condensation respects modular invariance (T-duality).

Sigma models with negative curvature

DOE PAGES

Alonso, Rodrigo; Jenkins, Elizabeth E.; Manohar, Aneesh V.

2016-03-16

Here, we construct Higgs Effective Field Theory (HEFT) based on the scalar manifold Hn, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n, 1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.

Area-Preserving Diffeomorphisms, W∞ and { U}q [sl(2)] in Chern-Simons Theory and the Quantum Hall System

NASA Astrophysics Data System (ADS)

Kogan, Ian I.

We discuss a quantum { U}q [sl(2)] symmetry in the Landau problem, which naturally arises due to the relation between { U}q [sl(2)] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern-Simons term and in a quantum Hall system, which are both connected with the Landau problem.

Novel phases and superconductivity of tin sulfide compounds

NASA Astrophysics Data System (ADS)

Gonzalez, Joseph M.; Nguyen-Cong, Kien; Steele, Brad A.; Oleynik, Ivan I.

2018-05-01

Tin sulfides, SnxSy, are an important class of materials that are actively investigated as novel photovoltaic and water splitting materials. A first-principles evolutionary crystal structure search is performed with the goal of constructing the complete phase diagram of SnxSy and discovering new phases as well as new compounds of varying stoichiometry at ambient conditions and pressures up to 100 GPa. The ambient phase of SnS2 with P 3 ¯ m 1 symmetry remains stable up to 28 GPa. Another ambient phase, SnS, experiences a series of phase transformations including α-SnS to β-SnS at 9 GPa, followed by β-SnS to γ-SnS at 40 GPa. γ-SnS is a new high-pressure metallic phase with P m 3 ¯ m space group symmetry stable up to 100 GPa, which becomes a superconductor with a maximum Tc = 9.74 K at 40 GPa. Another new metallic compound, Sn3S4 with I 4 ¯ 3 d space group symmetry, is predicted to be stable at pressures above 15 GPa, which also becomes a superconductor with relatively high Tc = 21.9 K at 30 GPa.

Molecular Eigensolution Symmetry Analysis and Fine Structure

PubMed Central

Harter, William G.; Mitchell, Justin C.

2013-01-01

Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041

Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components

NASA Astrophysics Data System (ADS)

Kuzmiak, Vladimir; Maradudin, Alexei A.

1998-09-01

We study the distribution of the electromagnetic field of the eigenmodes and corresponding group velocities associated with the photonic band structures of two-dimensional periodic systems consisting of an array of infinitely long parallel metallic rods whose intersections with a perpendicular plane form a simple square lattice. We consider both nondissipative and lossy metallic components characterized by a complex frequency-dependent dielectric function. Our analysis is based on the calculation of the complex photonic band structure obtained by using a modified plane-wave method that transforms the problem of solving Maxwell's equations into the problem of diagonalizing an equivalent non-Hermitian matrix. In order to investigate the nature and the symmetry properties of the eigenvectors, which significantly affect the optical properties of the photonic lattices, we evaluate the associated field distribution at the high symmetry points and along high symmetry directions in the two-dimensional first Brillouin zone of the periodic system. By considering both lossless and lossy metallic rods we study the effect of damping on the spatial distribution of the eigenvectors. Then we use the Hellmann-Feynman theorem and the eigenvectors and eigenfrequencies obtained from a photonic band-structure calculation based on a standard plane-wave approach applied to the nondissipative system to calculate the components of the group velocities associated with individual bands as functions of the wave vector in the first Brillouin zone. From the group velocity of each eigenmode the flow of energy is examined. The results obtained indicate a strong directional dependence of the group velocity, and confirm the experimental observation that a photonic crystal is a potentially efficient tool in controlling photon propagation.

Crystal structure of iron(III) perchlorate nona­hydrate

PubMed Central

Hennings, Erik; Schmidt, Horst; Voigt, Wolfgang

2014-01-01

Since the discovery of perchlorate salts on Mars and the known occurrence of ferric salts in the regolith, there is a distinct possibility that the title compound could form on the surface of Mars. [Fe(H2O)6](ClO4)3·3H2O was crystallized from aqueous solutions at low temperatures according to the solid–liquid phase diagram. It consists of Fe(H2O)6 octa­hedra (point group symmetry -3.) and perchlorate anions (point group symmetry .2) as well as non-coordinating water mol­ecules, as part of a second hydrogen-bonded coordination sphere around the cation. The perchlorate appears to be slightly disordered, with major–minor component occupancies of 0.773 (9):0.227 (9). PMID:25552970

Young Athletes With Quadriceps Femoris Strength Asymmetry at Return to Sport After Anterior Cruciate Ligament Reconstruction Demonstrate Asymmetric Single-Leg Drop-Landing Mechanics.

PubMed

Ithurburn, Matthew P; Paterno, Mark V; Ford, Kevin R; Hewett, Timothy E; Schmitt, Laura C

2015-11-01

Young athletes who have had anterior cruciate ligament (ACL) reconstruction demonstrate suboptimal rates of return to sport, high rates of second ACL injuries, and persistent movement asymmetries. Therefore, the influence of musculoskeletal impairments on movement mechanics in this population needs to be further evaluated. The primary hypothesis was that among young athletes who have had ACL reconstruction, those with greater quadriceps strength asymmetry would demonstrate altered single-leg drop-landing mechanics at return to sport compared with individuals with more symmetric quadriceps strength and also compared with healthy controls (ie, those with no ACL reconstruction). A second hypothesis was that quadriceps strength symmetry would predict single-leg drop-landing symmetry in individuals who have undergone ACL reconstruction. Controlled laboratory study. The study entailed a total of 103 participants (age, 17.4 years) at the time of return to sport after ACL reconstruction and 47 control participants (age, 17.0 years). The quadriceps index (QI) was calculated for isometric quadriceps strength, which was then used to divide the ACL reconstruction participants into high-quadriceps (QI ≥90%; n = 52) and low-quadriceps (QI <85%; n = 41) subgroups. Biomechanical data were collected by use of 3-dimensional motion analysis during a single-leg drop-landing task. The LSI was calculated for kinematic and kinetic sagittal-plane variables of interest during landing. Group differences were compared by use of 1-way analysis of variance and linear regression analyses (α < .05). Both the low- and high-quadriceps groups demonstrated greater limb asymmetry during landing compared with the control group in knee flexion excursion (mean LSI ± SD: low quadriceps, 85.8% ± 15.5% [P < .001]; high quadriceps, 94.2% ± 15.6% [P = .019]; control, 102.7% ± 14.1%), peak trunk flexion angle (low quadriceps, 129.2% ± 36.6% [P < .001]; high quadriceps, 110.5% ± 22.6% [P = .03]; control, 95.5% ± 26.2%), and peak knee extension moment (low quadriceps, 79.5% ± 25.2% [P < .001]; high quadriceps, 89.9% ± 19.8% [P = .005]; control, 102.2% ± 10.9%). Compared with the high-quadriceps group, the low-quadriceps group also demonstrated greater asymmetry during landing in knee flexion excursion (P = .026), peak trunk flexion angle (P = .006), and peak knee extension moment (P = .034). In the ACL reconstruction group, quadriceps strength symmetry predicted symmetry in knee flexion excursion, peak trunk flexion, and peak knee extension moment (all P < .001) and predicted symmetry in peak trunk flexion angle (P < .001) after controlling for graft type, knee-related pain, function with activities of daily living, and sport function. At the time of return to sport, athletes who had undergone ACL reconstruction, including those in both the high- and low-quadriceps groups, demonstrated asymmetry during a single-leg drop-landing task compared with controls. Compensations included increased trunk flexion, decreased knee flexion excursion, and decreased knee extension moments on the involved limb. In addition, individuals in the low-quadriceps group demonstrated greater movement asymmetry compared with individuals in the high-quadriceps group. Restoration of symmetric quadriceps strength after ACL reconstruction is associated with more symmetric mechanics during a single-leg drop-landing movement. However, this appears to be multifactorial, as the high-quadriceps group also demonstrated landing asymmetries. Restoration of symmetric quadriceps strength may improve postoperative athletic participation; however, future study is warranted. © 2015 The Author(s).

Numerical solution of modified differential equations based on symmetry preservation.

PubMed

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Using Molecular Modeling in Teaching Group Theory Analysis of the Infrared Spectra of Organometallic Compounds

ERIC Educational Resources Information Center

Wang, Lihua

2012-01-01

A new method is introduced for teaching group theory analysis of the infrared spectra of organometallic compounds using molecular modeling. The main focus of this method is to enhance student understanding of the symmetry properties of vibrational modes and of the group theory analysis of infrared (IR) spectra by using visual aids provided by…

Molecular structure and conformations of para-methylbenzene sulfonamide and ortho-methylbenzene sulfonamide: gas electron diffraction and quantum chemical calculations study.

PubMed

Petrov, Vjacheslav M; Girichev, Georgiy V; Oberhammer, Heinz; Petrova, Valentina N; Giricheva, Nina I; Bardina, Anna V; Ivanov, Sergey N

2008-04-03

The molecular structure and conformational properties of para-methylbenzene sulfonamide (4-MBSA) and ortho-methylbenzene sulfonamide (2-MBSA) have been studied by gas electron diffraction (GED) and quantum chemical methods (B3LYP/6-311+G** and MP2/6-31G**). Quantum chemical calculations predict the existence of two conformers for 4-MBSA with the S-N bond perpendicular to the benzene plane and the NH2 group either eclipsing or staggering the S-O bonds of the SO2 group. Both conformers possess CS symmetry. The eclipsed form is predicted to be favored by DeltaE = 0.63 kcal/mol (B3LYP) or 1.00 kcal/mol (MP2). According to the calculations, the S-N bond in 2-MBSA can possess planar direction opposite the methyl group (phi(C2C1SN) = 180 degrees ) or nonplanar direction (phi(C2C1SN) approximately 60 degrees ). In both cases, the NH2 group can adopt eclipsed or staggered orientation, resulting in a total of four stable conformers. The nonplanar eclipsed conformer (C1 symmetry) and the planar eclipsed form (CS symmetry) are predicted to be favored. According to the GED analysis, the saturated vapor over solid 4-MBSA at T = 151(3) degrees C consists as mixture of the eclipsed (78(19) %) and staggered (22(19) %) forms. The saturated vapor over solid 2-MBSA at T = 157(3) degrees C consists as a mixture of the nonplanar eclipsed (69(11) %) and planar eclipsed (31(11) %) forms.

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-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed 'single-metric truncations' which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.

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 shows that such a theorem is unlikely to hold even under more restrictive assumptions.

Structure symmetry determination and magnetic evolution in Sr 2Ir 1–xRh xO 4

DOE PAGES

Ye, Feng; Wang, Xiaoping; Hoffmann, Christina; ...

2015-11-23

We use single-crystal neutron diffraction to determine the crystal structure symmetry and to study the magnetic evolution in the rhodium doped iridates Sr 2Ir 1–xRh xO 4 (0 ≤ x ≤ 0.16). Throughout this doping range, the crystal structure retains a tetragonal symmetry (space group I4 1/a) with two distinct magnetic Ir sites in the unit cell forming staggered IrO 6 rotation. Upon Rh doping, the magnetic order is suppressed and the magnetic moment of Ir4+ is reduced from 0.21 μ B/Ir for x = 0 to 0.18 μ B/Ir for x = 0.12. As a result, the magnetic structuremore » at x = 0.12 is different from that of the parent compound while the moments remain in the basal plane.« less

Surveying the SO(10) model landscape: The left-right symmetric case

NASA Astrophysics Data System (ADS)

Deppisch, Frank F.; Gonzalo, Tomás E.; Graf, Lukas

2017-09-01

Grand unified theories (GUTs) are a very well motivated extensions of the Standard Model (SM), but the landscape of models and possibilities is overwhelming, and different patterns can lead to rather distinct phenomenologies. In this work we present a way to automatize the model building process, by considering a top to bottom approach that constructs viable and sensible theories from a small and controllable set of inputs at the high scale. By providing a GUT scale symmetry group and the field content, possible symmetry breaking paths are generated and checked for consistency, ensuring anomaly cancellation, SM embedding and gauge coupling unification. We emphasize the usefulness of this approach for the particular case of a nonsupersymmetric SO(10) model with an intermediate left-right symmetry, and we analyze how low-energy observables such as proton decay and lepton flavor violation might affect the generated model landscape.

Dark matter in E 6 Grand unification

NASA Astrophysics Data System (ADS)

Schwichtenberg, Jakob

2018-02-01

We discuss fermionic dark matter in non-supersymmetric E 6 Grand Unification. The fundamental representation of E 6 contains, in addition to the standard model fermions, exotic fermions and we argue that one of them is a viable, interesting dark matter candidate. Its stability is guaranteed by a discrete remnant symmetry, which is an unbroken subgroup of the E 6 gauge symmetry. We compute the symmetry breaking scales and the effect of possible threshold corrections by solving the renormalization group equations numerically after imposing gauge coupling unification. Since the Yukawa couplings of the exotic and the standard model fermions have a common origin, the mass of the dark matter particles is constrained. We find a mass range of 3 · 109 GeV ≲ m DM ≲ 1 · 1013 GeV for our E 6 dark matter candidate, which is within the reach of next-generation direct detection experiments.

Discrete symmetries in the heterotic-string landscape

NASA Astrophysics Data System (ADS)

Athanasopoulos, P.

2015-07-01

We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ2 × ℤ2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories.

Hyper-Raman and Raman scattering from the polar modes of PbMg1/3Nb2/3O3.

PubMed

Hehlen, B; Amouri, A; Al-Zein, A; Khemakhem, H

2014-01-08

Microhyper-Raman spectroscopy of PbMg(1/3)Nb(2/3)O(3) (PMN) single crystal is performed at room temperature. The use of an optical microscope working in backscattering geometry significantly reduces the LO signal, highlighting thereby the weak contributions underneath. We clearly identify the highest frequency transverse optic mode (TO3) in addition to the previously observed soft TO-doublet at low frequency and TO2 at intermediate frequency. TO3 exhibits strong inhomogeneous broadening but perfectly fulfils the hyper-Raman cubic selection rules. The analysis shows that hyper-Raman spectroscopy is sensitive to all the vibrations of the average cubic Pm3¯m symmetry group of PMN, the three polar F1u- and the silent F2u-symmetry modes. All these vibrations can be identified in the Raman spectra alongside other vibrational bands likely arising from symmetry breaking in polar nanoregions.

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

A Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies

NASA Astrophysics Data System (ADS)

Lu, Wei

2017-09-01

We propose a Clifford algebra approach to chiral symmetry breaking and fermion mass hierarchies in the context of composite Higgs bosons. Standard model fermions are represented by algebraic spinors of six-dimensional binary Clifford algebra, while ternary Clifford algebra-related flavor projection operators control allowable flavor-mixing interactions. There are three composite electroweak Higgs bosons resulted from top quark, tau neutrino, and tau lepton condensations. Each of the three condensations gives rise to masses of four different fermions. The fermion mass hierarchies within these three groups are determined by four-fermion condensations, which break two global chiral symmetries. The four-fermion condensations induce axion-like pseudo-Nambu-Goldstone bosons and can be dark matter candidates. In addition to the 125 GeV Higgs boson observed at the Large Hadron Collider, we anticipate detection of tau neutrino composite Higgs boson via the charm quark decay channel.

Instanton operators and symmetry enhancement in 5d supersymmetric quiver gauge theories

NASA Astrophysics Data System (ADS)

Yonekura, Kazuya

2015-07-01

We consider general 5d SU( N ) quiver gauge theories whose nodes form an ADE Dynkin diagram of type G. Each node has SU( N i ) gauge group of general rank, Chern-Simons level κ i and additional w i fundamentals. When the total flavor number at each node is less than or equal to 2 N i - 2| κ i |, we give general rules under which the symmetries associated to instanton currents are enhanced to G × G or a subgroup of it in the UV 5d superconformal theory. When the total flavor number violates that condition at some of the nodes, further enhancement of flavor symmetries occurs. In particular we find a large class of gauge theories interpreted as S 1 compactification of 6d superconformal theories which are waiting for string/F-theory realization. We also consider hypermultiplets in (anti-)symmetric representation.

A Study of Gaugeon Formalism for QED in Lorentz Violating Background

NASA Astrophysics Data System (ADS)

Shah, Mushtaq B.; Ganai, Prince A.

2018-02-01

At the energy regimes close to Planck scales, the usual structure of Lorentz symmetry fails to address certain fundamental issues and eventually breaks down, thus paving the way for an alternative road map. It is thus argued that some subgroup of proper Lorentz group could stand consistent and might possibly help us to circumvent this problem. It is this subgroup that goes by the name of Very Special Relativity (VSR). Apart from violating rotational symmetry, VSR is believed to preserve the very tenets of special relativity. The gaugeon formalism due to type-I Yokoyama and type-II Izawa are found to be invariant under BRST symmetry. In this paper, we analyze the scope of this invariance in the scheme of VSR. Furthermore, we will obtain VSR modified Lagrangian density using path integral derivation. We will explore the consistency of VSR with regard to these theories.

Axion like particles and the inverse seesaw mechanism

DOE PAGES

Carvajal, C. D. R.; Dias, Alex G.; Nishi, C. C.; ...

2015-05-13

Light pseudoscalars known as axion like particles (ALPs) may be behind physical phenomena like the Universe transparency to ultra-energetic photons, the soft -ray excess from the Coma cluster, and the 3.5 keV line. We explore the connection of these particles with the inverse seesaw (ISS) mechanism for neutrino mass generation. We propose a very restrictive setting where the scalar field hosting the ALP is also responsible for generating the ISS mass scales through its vacuum expectation value on gravity induced nonrenormalizable operators. A discrete gauge symmetry protects the theory from the appearance of overly strong gravitational effects and discrete anomalymore » cancellation imposes strong constraints on the order of the group. In conclusion, the anomalous U(1) symmetry leading to the ALP is an extended lepton number and the protective discrete symmetry can be always chosen as a subgroup of a combination of the lepton number and the baryon number.« less

An experimental study of symmetry lowering of analcime

NASA Astrophysics Data System (ADS)

Sugano, Neo; Kyono, Atsushi

2018-04-01

Single crystals of analcime were hydrothermally synthesized from a gel of analcime composition at 200 °C for 24 h. They were grown up to 100 μm in size with typical deltoidal icositetrahedron habit. The chemical composition determined by EPMA and TG analyses was Na0.84(Al0.89Si2.12)O6·1.04H2O. The single-crystal X-ray diffraction method was used to determine the symmetry and crystal structure of analcime. The analcime grown from a gel crystallized in cubic space group Ia3 d with lattice parameter a = 13.713(3) Å. In the cubic analcime, Si and Al cations were totally disordered over the framework T sites with site occupancy of Si:Al = 0.6871:0.3129(14). The single crystals of analcime with cubic symmetry were hydrothermally reheated at 200 °C in ultrapure water. After the hydrothermal treatment for 24 h, forbidden reflections for the cubic Ia3 d symmetry were observed. The reflection conditions led to an orthorhombic space group Ibca with lattice parameters a = 13.727(2) Å, b = 13.707(2) Å, and c = 13.707(2) Å. The unit-cell showed a slight distortion with ( a + b)/2 > c, yielding a flattened cell along c. In the orthorhombic analcime, Al exhibited a site preference for T11 site, which indicates that the Si/Al ordering over the framework T sites lowers the symmetry from cubic Ia3 d to orthorhombic Ibca. After the hydrothermal treatment for 48 h, reflections corresponding to orthorhombic space group Ibca were observed as well. The lattice parameters were a = 13.705(2) Å, b = 13.717(2) Å, and c = 13.706(2) Å, retaining the flattened cell shape with ( a + b)/2 > c. The Si and Al cations were further ordered among the framework T sites than the case of the hydrothermal treatment for 24 h. As a consequence, the Si/Al ordering was slightly but significantly accelerated with increasing the hydrothermal treatment time. During the hydrothermal reaction, however, chemical compositions were almost unchanged. The site occupancies of Na over the extra-framework sites remained unaffected with the heating time; thus, the hydrothermal heating influences the degree of ordering of Si and Al over the framework T sites rather than that of Na among the extra-framework sites.

Super-Group Field Cosmology in Batalin-Vilkovisky Formulation

NASA Astrophysics Data System (ADS)

Upadhyay, Sudhaker

2016-09-01

In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.

Relationships of Muscle Function and Subjective Knee Function in Patients After ACL Reconstruction.

PubMed

Bodkin, Stephan; Goetschius, John; Hertel, Jay; Hart, Joe

2017-07-01

After anterior cruciate ligament reconstruction (ACLR), relationships between objective measures of muscle function and patient-reported outcomes may change over time. Examining these measures at different time frames after surgery may help develop individualized approaches to improve post-ALCR analysis. To examine the associations between subjective knee function and lower-extremity muscle function in individual patients at various time points after ACLR. Descriptive laboratory study. Fifty-one participants who underwent primary, unilateral ACLR (15 males, 36 females; mean age, 22.9 ± 4.5 years; mean height, 172.4 ± 10.1 cm; mean weight, 68.7 ± 13.1 kg) were separated into 3 groups depending on time since surgery (early, <2 years; middle, 2-5 years; late, >5 years). Subjective knee function was quantified using the International Knee Documentation Committee (IKDC) subjective knee form and the Knee injury and Osteoarthritis Outcome Score (KOOS). Isometric knee extension and flexion strength were collected at 90 deg/s. Single-leg hop performance was measured using the single hop, triple hop, cross-over hop, and 6-m timed hop. Coefficient correlations were calculated between subjective knee function and objective measures of muscle function for each group. The early group demonstrated moderate correlations between the KOOS and unilateral measures of flexion peak torque ( r = 0.514, P = .035) and flexion power ( r = 0.54, P = .027). The middle group demonstrated the strongest correlations between the KOOS and symmetry measures of the single hop ( r = 0.69, P = .002) and extension work ( r = 0.71, P = .002) as well as unilateral measures of the triple hop ( r = 0.52, P = .034) and extension work ( r = 0.66, P = .004). The late group demonstrated strong correlations between the 6-m timed hop symmetry and the IKDC ( r = 0.716, P = .001) and KOOS ( r = 0.71, P = .001). Patients with a post-ACLR status of less than 2 years exhibited stronger relationships with unilateral strength measures to subjective function; graft type was found to change these relationships. Patients at 2 to 5 years postsurgery demonstrated relationships with both unilateral and symmetry measures of muscle function to subjective function. Patients who were more than 5 years after ACLR exhibited strong associations between hopping symmetry and subjective function. Future clinical guidelines for patients after ACLR may need to consider time since surgery as a potential factor.

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.

Global SO(3) x SO(3) x U(1) symmetry of the Hubbard model on bipartite lattices

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

Carmelo, J.M.P., E-mail: carmelo@fisica.uminho.p; Ostlund, Stellan; Sampaio, M.J.

2010-08-15

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U {ne} 0 the local SU(2) x SU(2) x U(1) gauge symmetry of the Hubbard model on amore » bipartite lattice with N{sub a}{sup D} sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) x SU(2) x U(1)]/Z{sub 2}{sup 2} = SO(3) x SO(3) x U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N{sub a}a for which D = 1, 2, 3,... in the number N{sub a}{sup D} of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4{sup N}{sub a}{sup D} energy eigenstates refer to representations of the new found global [SU(2) x SU(2) x U(1)]/Z{sub 2}{sup 2} = SO(3) x SO(3) x U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) x SO(3) x U(1) equals the Hilbert-space dimension 4{sup N}{sub a}{sup D}. It is confirmed elsewhere that the new found symmetry has important physical consequences.« less

Affine q-deformed symmetry and the classical Yang-Baxter σ-model

NASA Astrophysics Data System (ADS)

Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.

2017-03-01

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

Non-linear optical probing of strain-enabled ferroelectricity in CaTiO3 thin films

NASA Astrophysics Data System (ADS)

Vlahos, Eftihia; Brooks, Charles; Ecklund, Carl Johan; Biegalski, Mike; Rabe, Karin; Schlom, Darrell; Gopalan, Venkatraman

2010-03-01

First principles calculations predict CaTiO3, under tensile strain, to become ferroelectric with a spontaneous polarization of up to 0.5 C/m^2. Comparative second harmonic generation (SHG) studies of a series of strained CaTiO3 thin films were undertaken in order to determine their transition temperature and point group symmetry. The epitaxial strain ranged from -1.7% to 3.3%. Symmetry analysis of the SHG polar plots confirms that for the samples under tensile strain, the polarization is along the <110>p directions and the point group of the ferroelectric phase is mm2. SHG ``hysteresis'' loops were also obtained; these show clear switching. The experimental results are in excellent agreement with the first principles calculations predictions, and low temperature dielectric measurements that were performed on the same samples.

Old friends in a new light: “SnSb” revisited

NASA Astrophysics Data System (ADS)

Norén, Lasse; Withers, Ray L.; Schmid, Siegbert; Brink, Frank J.; Ting, Valeska

2006-02-01

The binary pnictide 'SnSb' has been re-investigated using a combination of X-ray, synchrotron and electron diffraction as well as electron microprobe analysis. Its structure was found to be incommensurately modulated with an underlying rhombohedral parent structure of space group symmetry R3¯m (No. 166), unit cell parameters a=b=4.3251(4) Å, c=5.3376(6) Å in the hexagonal setting. The incommensurate primary modulation wave vector q=1.3109(9)ch* and the superspace group symmetry is R3¯m (0, 0, ˜1.311) (No. 166.1). The refinement of the incommensurate structure indicates that the satellite reflections arise from displacive shifts of presumably essentially pure Sn and Sb layers along the hexagonal c-axis, with increasing distance between the Sn-layers and decreasing distance between the Sb layers.

Phenomenology of the SU(3)_c⊗ SU(3)_L⊗ U(1)_X model with right-handed neutrinos

NASA Astrophysics Data System (ADS)

Gutiérrez, D. A.; Ponce, W. A.; Sánchez, L. A.

2006-05-01

A phenomenological analysis of the three-family model based on the local gauge group SU(3)_c⊗ SU(3)_L⊗ U(1)_X with right-handed neutrinos is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we introduce an alternative set of four Higgs scalar triplets, which combined with an anomaly-free discrete symmetry, produces a quark mass spectrum without hierarchies in the Yukawa coupling constants. We also embed the structure into a simple gauge group and show some conditions for achieving a low energy gauge coupling unification, avoiding possible conflict with proton decay bounds. By using experimental results from the CERN-LEP, SLAC linear collider, and atomic parity violation data, we update constraints on several parameters of the model.

Phenomenology of the SU(3)c⊗SU(3)L⊗U(1)X model with exotic charged leptons

NASA Astrophysics Data System (ADS)

Salazar, Juan C.; Ponce, William A.; Gutiérrez, Diego A.

2007-04-01

A phenomenological analysis of the three-family model based on the local gauge group SU(3)c⊗SU(3)L⊗U(1)X with exotic charged leptons, is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we introduce an alternative set of four Higgs scalar triplets, which combined with an anomaly-free discrete symmetry, produce quark and charged lepton mass spectrum without hierarchies in the Yukawa coupling constants. We also embed the structure into a simple gauge group and show some conditions to achieve a low energy gauge coupling unification, avoiding possible conflict with proton decay bounds. By using experimental results from the CERN-LEP, SLAC linear collider, and atomic parity violation data, we update constraints on several parameters of the model.

A monoclinic polymorph of (1E,5E)-1,5-bis­(2-hy­droxy­benzyl­idene)thio­carbono­hydrazide

PubMed Central

Schmitt, Bonell; Gerber, Thomas; Hosten, Eric; Betz, Richard

2011-01-01

The title compound, C15H14N4O2S, is a derivative of thio­ureadihydrazide. In contrast to the previously reported polymorph (ortho­rhom­bic, space group Pbca, Z = 8), the current study revealed monoclinic symmetry (space group P21/n, Z = 4). The mol­ecule shows non-crystallographic C 2 as well as approximate C s symmetry. Intra­molecular bifurcated O—H⋯(N,S) hydrogen bonds, are present. In the crystal, inter­molecular N—H⋯S hydrogen bonds and C—H⋯π contacts connect the mol­ecules into undulating chains along the b axis. The shortest centroid–centroid distance between two aromatic systems is 4.5285 (12) Å. PMID:22091213

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.

Non Abelian T-duality in Gauged Linear Sigma Models

NASA Astrophysics Data System (ADS)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

Spinless hourglass nodal-line semimetals

NASA Astrophysics Data System (ADS)

Takahashi, Ryo; Hirayama, Motoaki; Murakami, Shuichi

2017-10-01

Nodal-line semimetals, one of the topological semimetals, have degeneracy along nodal lines where the band gap is closed. In many cases, the nodal lines appear accidentally, and in such cases it is impossible to determine whether the nodal lines appear or not, only from the crystal symmetry and the electron filling. In this paper, for spinless systems, we show that in specific space groups at 4 N +2 fillings (8 N +4 fillings including the spin degree of freedom), presence of the nodal lines is required regardless of the details of the systems. Here, the spinless systems refer to crystals where the spin-orbit coupling is negligible and the spin degree of freedom can be omitted because of the SU(2) spin degeneracy. In this case the shape of the band structure around these nodal lines is like an hourglass, and we call this a spinless hourglass nodal-line semimetal. We construct a model Hamiltonian as an example and we show that it is always in the spinless hourglass nodal-line semimetal phase even when the model parameters are changed without changing the symmetries of the system. We also establish a list of all the centrosymmetric space groups, under which spinless systems always have hourglass nodal lines, and illustrate where the nodal lines are located. We propose that Al3FeSi2 , whose space-group symmetry is Pbcn (No. 60), is one of the nodal-line semimetals arising from this mechanism.

Spin Triplet Nematic Pairing Symmetry and Superconducting Double Transition in U1-xThxBe13

NASA Astrophysics Data System (ADS)

Machida, Kazushige

2018-03-01

Motivated by a recent experiment on U1-xThxBe13 with x = 3%, we develop a theory to narrow down the possible pair symmetry to consistently describe the double transition utilizing various theoretical tools, including group theory and Ginzburg-Landau theory. It is explained in terms of the two-dimensional representation Eu with spin triplet. Symmetry breaking causes the degenerate Tc to split into two. The low-temperature phase is identified as the cyclic p wave: d(k) = \\hat{x}kx + ɛ \\hat{y}ky + ɛ 2\\hat{z}kz with ɛ3 = 1, whereas the biaxial nematic phase: d(k) = √{3} (\\hat{x}kx - \\hat{y}ky) is the high-temperature one. This allows us to simultaneously identify the uniaxial nematic phase: d(k) = 2\\hat{z}kz - \\hat{x}kx - \\hat{y}ky for UBe13, which spontaneously breaks the cubic symmetry of the system. Those pair functions are fully consistent with this description and existing data. We comment on the accidental scenario in addition to this degeneracy scenario and the intriguing topological nature hidden in this long-known material.

On gauge independence for gauge models with soft breaking of BRST symmetry

NASA Astrophysics Data System (ADS)

Reshetnyak, Alexander

2014-12-01

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang-Mills and gravity theories. The Gribov-Zwanziger action and the refined Gribov-Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

Transverse fields to tune an Ising-nematic quantum phase transition

NASA Astrophysics Data System (ADS)

Maharaj, Akash V.; Rosenberg, Elliott W.; Hristov, Alexander T.; Berg, Erez; Fernandes, Rafael M.; Fisher, Ian R.; Kivelson, Steven A.

2017-12-01

The paradigmatic example of a continuous quantum phase transition is the transverse field Ising ferromagnet. In contrast to classical critical systems, whose properties depend only on symmetry and the dimension of space, the nature of a quantum phase transition also depends on the dynamics. In the transverse field Ising model, the order parameter is not conserved, and increasing the transverse field enhances quantum fluctuations until they become strong enough to restore the symmetry of the ground state. Ising pseudospins can represent the order parameter of any system with a twofold degenerate broken-symmetry phase, including electronic nematic order associated with spontaneous point-group symmetry breaking. Here, we show for the representative example of orbital-nematic ordering of a non-Kramers doublet that an orthogonal strain or a perpendicular magnetic field plays the role of the transverse field, thereby providing a practical route for tuning appropriate materials to a quantum critical point. While the transverse fields are conjugate to seemingly unrelated order parameters, their nontrivial commutation relations with the nematic order parameter, which can be represented by a Berry-phase term in an effective field theory, intrinsically intertwine the different order parameters.

Particle-hole symmetry, many-body localization, and topological edge modes

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Friedman, Aaron J.; Parameswaran, S. A.; Potter, Andrew C.

We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are less localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. Supported by the Gordon and Betty Moore Foundation's EPiQS Initiative (Grant GBMF4307 (ACP), the Quantum Materials Program at LBNL (RV), NSF Grant DMR-1455366 and UCOP Research Catalyst Award No. CA-15-327861 (SAP).

Revealing the Topology of Fermi-Surface Wave Functions from Magnetic Quantum Oscillations

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Wang, Chong; Duan, Wenhui; Glazman, Leonid

2018-01-01

The modern semiclassical theory of a Bloch electron in a magnetic field now encompasses the orbital magnetic moment and the geometric phase. These two notions are encoded in the Bohr-Sommerfeld quantization condition as a phase (λ ) that is subleading in powers of the field; λ is measurable in the phase offset of the de Haas-van Alphen oscillation, as well as of fixed-bias oscillations of the differential conductance in tunneling spectroscopy. In some solids and for certain field orientations, λ /π are robustly integer valued, owing to the symmetry of the extremal orbit; i.e., they are the topological invariants of magnetotransport. Our comprehensive symmetry analysis identifies solids in any (magnetic) space group for which λ is a topological invariant, as well as the symmetry-enforced degeneracy of Landau levels. The analysis is simplified by our formulation of ten (and only ten) symmetry classes for closed, Fermi-surface orbits. Case studies are discussed for graphene, transition metal dichalcogenides, 3D Weyl and Dirac metals, and crystalline and Z2 topological insulators. In particular, we point out that a π phase offset in the fundamental oscillation should not be viewed as a smoking gun for a 3D Dirac metal.

Landau-Ginzburg orbifolds and symmetries of K 3 CFTs

DOE PAGES

Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; ...

2017-01-11

Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K 3 string theory. To test and clarify these proposed K 3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K 3 sigma models. We compute K 3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions thatmore » have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M 11 c 2.M 12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Finally, our results provide strong evidence for the relevance of umbral moonshine for K 3 symmetries, as well as new hints for its eventual explanation.« less

Hidden order and flux attachment in symmetry-protected topological phases: A Laughlin-like approach

NASA Astrophysics Data System (ADS)

Ringel, Zohar; Simon, Steven H.

2015-05-01

Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here, we introduce a new approach for generating SPT ground states, based on a generalization of the Laughlin wave function. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wave functions obtained in this manner and group cohomology wave functions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wave function obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.

An algebraic cluster model based on the harmonic oscillator basis

NASA Technical Reports Server (NTRS)

Levai, Geza; Cseh, J.

1995-01-01

We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

Sigma-phase packing of icosahedral clusters in 780-atom tetragonal crystals of Cr5Ni3Si2 and V15Ni10Si that by twinning achieve 8-fold rotational point-group symmetry

PubMed Central

Pauling, Linus

1988-01-01

A 780-atom primitive tetragonal unit with edges 27.3, 27.3, and 12.6 Å is assigned to rapidly solidified Cu5Ni3Si2 and V15Ni10Si by analysis of electron diffraction photographs with the assumption that the crystals contain icosahedral clusters. There are thirty 26-atom clusters at the sigma-phase positions. Apparent 8-fold symmetry results from 45° twinning on the basal plane. PMID:16593915

Sigma-phase packing of icosahedral clusters in 780-atom tetragonal crystals of Cr(5)Ni(3)Si(2) and V(15)Ni(10)Si that by twinning achieve 8-fold rotational point-group symmetry.

PubMed

Pauling, L

1988-04-01

A 780-atom primitive tetragonal unit with edges 27.3, 27.3, and 12.6 A is assigned to rapidly solidified Cu(5)Ni(3)Si(2) and V(15)Ni(10)Si by analysis of electron diffraction photographs with the assumption that the crystals contain icosahedral clusters. There are thirty 26-atom clusters at the sigma-phase positions. Apparent 8-fold symmetry results from 45 degrees twinning on the basal plane.

SU(2)×U(1) gauge invariance and the shape of new physics in rare B decays.

PubMed

Alonso, R; Grinstein, B; Martin Camalich, J

2014-12-12

New physics effects in B decays are routinely modeled through operators invariant under the strong and electromagnetic gauge symmetries. Assuming the scale for new physics is well above the electroweak scale, we further require invariance under the full standard model gauge symmetry group. Retaining up to dimension-six operators, we unveil new constraints between different new physics operators that are assumed to be independent in the standard phenomenological analyses. We illustrate this approach by analyzing the constraints on new physics from rare B(q) (semi-)leptonic decays.

Self-dual monopoles and toda molecules

NASA Astrophysics Data System (ADS)

Ganoulis, N.; Goddard, P.; Olive, D.

1982-07-01

Stable static solutions to a gauge field theory with a Higgs field in the adjoint representation and with vanishing self-coupling are self-dual in the sense of Bogomolny. Leznov and Saveliev showed that a specific form of spherical symmetry reduces these equations to a modified form of the Toda molecule equations associated with the overall gauge symmetry G. Values of the constants of integration are found in terms of the distant Higgs field, guaranteeing regularity of the solution at the origin. The expressions hold for any simple Lie group G, depending on G via its root system.

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

History of electroweak symmetry breaking

NASA Astrophysics Data System (ADS)

Kibble, T. W. B.

2015-07-01

In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.

Power of the Poincaré group: elucidating the hidden symmetries in focal conic domains.

PubMed

Alexander, Gareth P; Chen, Bryan Gin-Ge; Matsumoto, Elisabetta A; Kamien, Randall D

2010-06-25

Focal conic domains are typically the "smoking gun" by which smectic liquid crystalline phases are identified. The geometry of the equally spaced smectic layers is highly generic but, at the same time, difficult to work with. In this Letter we develop an approach to the study of focal sets in smectics which exploits a hidden Poincaré symmetry revealed only by viewing the smectic layers as projections from one-higher dimension. We use this perspective to shed light upon several classic focal conic textures, including the concentric cyclides of Dupin, polygonal textures, and tilt-grain boundaries.

Emergence of chirality in hexagonally packed monolayers of hexapentyloxytriphenylene on Au(111): a joint experimental and theoretical study.

PubMed

Sleczkowski, Piotr; Katsonis, Nathalie; Kapitanchuk, Oleksiy; Marchenko, Alexandr; Mathevet, Fabrice; Croset, Bernard; Lacaze, Emmanuelle

2014-11-11

We investigate the expression of chirality in a monolayer formed spontaneously by 2,3,6,7,10,11-pentyloxytriphenylene (H5T) on Au(111). We resolve its interface morphology by combining scanning tunneling microscopy (STM) with theoretical calculations of intermolecular and interfacial interaction potentials. We observe two commensurate structures. While both of them belong to a hexagonal space group, analogical to the triangular symmetry of the molecule and the hexagonal symmetry of the substrate surface, they surprisingly reveal a 2D chiral character. The corresponding breaking of symmetry arises for two reasons. First it is due to the establishment of a large molecular density on the substrate, which leads to a rotation of the molecules with respect to the molecular network crystallographic axes to avoid steric repulsion between neighboring alkoxy chains. Second it is due to the molecule-substrate interactions, leading to commensurable large crystallographic cells associated with the large size of the molecule. As a consequence, molecular networks disoriented with respect to the high symmetry directions of the substrate are induced. The high simplicity of the intermolecular and molecule-substrate van der Waals interactions leading to these observations suggests a generic character for this kind of symmetry breaking. We demonstrate that, for similar molecular densities, only two kinds of molecular networks are stabilized by the molecule-substrate interactions. The most stable network favors the interfacial interactions between terminal alkoxy tails and Au(111). The metastable one favors a specific orientation of the triphenylene core with its symmetry axes collinear to the Au⟨110⟩. This specific orientation of the triphenylene cores with respect to Au(111) appears associated with an energy advantage larger by at least 0.26 eV with respect to the disoriented core.

Molecular dynamics of 17α- and 21-hydroxy progesterone studied by NMR. Relation between molecule conformation and height of the barrier for methyl group reorientations in steroid compounds

NASA Astrophysics Data System (ADS)

Szyczewski, A.; Hołderna-Natkaniec, K.

2005-01-01

For the two steroid compounds 17αOH-progesterone and 21OH-progesterone, the activation energies of reorientations of the methyl groups have been determined. Their values together with results of the quantum chemical calculations permitted establishment of the sequence of the onset of the methyl group reorientations about the three-fold symmetry axis of the C-C bond. On the basis of the asymmetry parameters, the conformations of the hitherto studied pregnane derivatives and testosterone have been determined. It has been found that the conformation of ring A has dominant effect on the activation energies of the reorientation of C(19)H 3. The reorientation of the methyl group C(18)H 3 significantly depends on the conformation of the side chain 17β (torsional angle C(13)-C(17)-C(20)-O(20)) and the distance between C18 and O20. The study has proved that the 1H NMR method in combination with the quantum chemistry calculations and inelastic incoherent neutron scattering (IINS) are effective for prediction of the sequence of the methyl group reorientations about the three-fold symmetry axis.

Quantum mechanics of Klein-Gordon fields I: Hilbert Space, localized states, and chiral symmetry

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

Mostafazadeh, A.; Zamani, F.

2006-09-15

We derive an explicit manifestly covariant expression for the most general positive-definite and Lorentz-invariant inner product on the space of solutions of the Klein-Gordon equation. This expression involves a one-parameter family of conserved current densities J{sub a}{sup {mu}}, with a-bar (-1,1), that are analogous to the chiral current density for spin half fields. The conservation of J{sub a}{sup {mu}} is related to a global gauge symmetry of the Klein-Gordon fields whose gauge group is U(1) for rational a and the multiplicative group of positive real numbers for irrational a. We show that the associated gauge symmetry is responsible for themore » conservation of the total probability of the localization of the field in space. This provides a simple resolution of the paradoxical situation resulting from the fact that the probability current density for free scalar fields is neither covariant nor conserved. Furthermore, we discuss the implications of our approach for free real scalar fields offering a direct proof of the uniqueness of the relativistically invariant positive-definite inner product on the space of real Klein-Gordon fields. We also explore an extension of our results to scalar fields minimally coupled to an electromagnetic field.« less

Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe.

PubMed

Schoop, Leslie M; Topp, Andreas; Lippmann, Judith; Orlandi, Fabio; Müchler, Lukas; Vergniory, Maia G; Sun, Yan; Rost, Andreas W; Duppel, Viola; Krivenkov, Maxim; Sheoran, Shweta; Manuel, Pascal; Varykhalov, Andrei; Yan, Binghai; Kremer, Reinhard K; Ast, Christian R; Lotsch, Bettina V

2018-02-01

Recent interest in topological semimetals has led to the proposal of many new topological phases that can be realized in real materials. Next to Dirac and Weyl systems, these include more exotic phases based on manifold band degeneracies in the bulk electronic structure. The exotic states in topological semimetals are usually protected by some sort of crystal symmetry, and the introduction of magnetic order can influence these states by breaking time-reversal symmetry. We show that we can realize a rich variety of different topological semimetal states in a single material, CeSbTe. This compound can exhibit different types of magnetic order that can be accessed easily by applying a small field. Therefore, it allows for tuning the electronic structure and can drive it through a manifold of topologically distinct phases, such as the first nonsymmorphic magnetic topological phase with an eightfold band crossing at a high-symmetry point. Our experimental results are backed by a full magnetic group theory analysis and ab initio calculations. This discovery introduces a realistic and promising platform for studying the interplay of magnetism and topology. We also show that we can generally expand the numbers of space groups that allow for high-order band degeneracies by introducing antiferromagnetic order.

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerene and Their Correlation with Three Geometric Properties: Symmetry, Aromaticity, and Size

NASA Technical Reports Server (NTRS)

Moore, C. E.; Cardelino, B. H.; Frazier, D. O.; Niles, J.; Wang, X.-Q.

1998-01-01

The static third-order polarizabilities (gamma) of C60, C70, five isomers of C78 and two isomers of C84 were analyzed in terms of three properties, from a geometric point of view: symmetry, aromaticity and size. The polarizability values were based on the finite field approximation using a semiempirical Hamiltonian (AM1) and applied to molecular structures obtained from density functional theory calculations. Symmetry was characterized by the molecular group order. The selection of 6-member rings as aromatic was determined from an analysis of bond lengths. Maximum interatomic distance and surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear polarizability (alpha) and gamma in these molecules respond differently to geometrical properties: alpha depends almost exclusively on surface area while gamma is affected by a combination of number of aromatic rings, length and group order, in decreasing importance. In the case of alpha, valence electron contributions provide the same information as all-electron estimates. For gamma, the best correlation coefficients are obtained when all-electron estimates are used and when the dependent parameter is ln(gamma) instead of gamma.

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

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

Becker, D., E-mail: BeckerD@thep.physik.uni-mainz.ded; Reuter, M., E-mail: reuter@thep.physik.uni-mainz.de

2014-11-15

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 Averagemore » 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-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type. - Highlights: • The Asymptotic Safety scenario in quantum gravity is explored. • A bi-metric generalization of the Einstein–Hilbert truncation is investigated. • We find that Background Independence can coexist with Asymptotic Safety. • RG trajectories restoring (background-quantum) split-symmetry are constructed. • The degree of validity of single-metric truncations is critically assessed.« less

On the optimal systems of subalgebras for the equations of hydrodynamic stability analysis of smooth shear flows and their group-invariant solutions

NASA Astrophysics Data System (ADS)

Hau, Jan-Niklas; Oberlack, Martin; Chagelishvili, George

2017-04-01

We present a unifying solution framework for the linearized compressible equations for two-dimensional linearly sheared unbounded flows using the Lie symmetry analysis. The full set of symmetries that are admitted by the underlying system of equations is employed to systematically derive the one- and two-dimensional optimal systems of subalgebras, whose connected group reductions lead to three distinct invariant ansatz functions for the governing sets of partial differential equations (PDEs). The purpose of this analysis is threefold and explicitly we show that (i) there are three invariant solutions that stem from the optimal system. These include a general ansatz function with two free parameters, as well as the ansatz functions of the Kelvin mode and the modal approach. Specifically, the first approach unifies these well-known ansatz functions. By considering two limiting cases of the free parameters and related algebraic transformations, the general ansatz function is reduced to either of them. This fact also proves the existence of a link between the Kelvin mode and modal ansatz functions, as these appear to be the limiting cases of the general one. (ii) The Lie algebra associated with the Lie group admitted by the PDEs governing the compressible dynamics is a subalgebra associated with the group admitted by the equations governing the incompressible dynamics, which allows an additional (scaling) symmetry. Hence, any consequences drawn from the compressible case equally hold for the incompressible counterpart. (iii) In any of the systems of ordinary differential equations, derived by the three ansatz functions in the compressible case, the linearized potential vorticity is a conserved quantity that allows us to analyze vortex and wave mode perturbations separately.

Clinic-based assessment of weight-bearing asymmetry during squatting in people with anterior cruciate ligament reconstruction using Nintendo Wii Balance Boards.

PubMed

Clark, Ross A; Howells, Brooke; Feller, Julian; Whitehead, Tim; Webster, Kate E

2014-06-01

To use low-cost Nintendo Wii Balance Boards (NWBB) to assess weight-bearing asymmetry (WBA) in people who have undergone anterior cruciate ligament reconstruction (ACLR), and to compare their results with a matched control group. Quantitative clinical study using a cross-sectional design. Orthopedic clinic of a private hospital. ACLR participants (n=41; mean age ± SD, 26.0 ± 9.8 y; current Cincinnati sports activity level, 75.3 ± 19.8) performed testing in conjunction with their routine 6- or 12-month clinical follow-up, and a control group (n=41) was matched for age, height, body mass, and physical activity level. Participants performed double-limb squats while standing on 2 NWBBs, 1 under each foot. The WBA variables mean mass difference as a percentage of body mass, time favoring a single limb by >5% body mass, absolute symmetry index, and symmetry index relative to the operated or matched control limb were derived. Mann-Whitney U tests were performed to assess between-group differences. Significant (P<.05) increases in asymmetry in the ACLR group were found for all outcome measures except symmetry index relative to the operated limb. People who have undergone ACLR are likely to possess WBA during squats, and this can be assessed using low-cost NWBBs in a clinical setting. Interestingly, the observed asymmetry was not specific to the surgical limb. Future research is needed to assess the relationship between WBA early in the rehabilitation process and long-term outcomes. Copyright © 2014 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

The Motion and Control of a Chaplygin Sleigh with Internal Shape in an Ideal Fluid

NASA Astrophysics Data System (ADS)

Barot, Christopher

In this dissertation we will examine a nonholonomic system with Lie group symmetry: the Chaplygin sleigh coupled to an oscillator moving through a potential fluid in two dimensions. This example is chosen to illustrate several general features. The sleigh system in the plane has SE(2) symmetry. This group symmetry will be used to separate the dynamics of the system into those along the group directions and those not. The oscillator motion is not along the group and so acts as an additional configuration space coordinate that plays the role of internal "shape". The potential fluid serves as an interactive environment for the sleigh. The interaction between the fluid and sleigh depends not only on the sleigh body shape and size but also on its motion. The motion of the sleigh causes motion in the surrounding fluid and vice-versa. Since the sleigh body is coupled to the oscillator, the oscillator will have indirect interaction with the fluid. This oscillator serves as internal shape and interacts with the external environment of the sleigh through its coupling to the sleigh body and the nonholonomic constraint; it will be shown that this interaction can produce a variety of types of motion depending on the sleigh geometry. In particular, when the internal shape of the system is actively controlled, it will be proven that the sleigh can be steered through the plane towards any desired position. In this way the sleigh-fluid-oscillator system will demonstrate how a rigid body can be steered through an interactive environment by controlling things wholly within the body itself and without use of external thrust.

Multidimensional integrable systems and deformations of Lie algebra homomorphisms

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

Dunajski, Maciej; Grant, James D. E.; Strachan, Ian A. B.

We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti-self-dual Yang-Mills equations with a gauge group Diff(S{sup 1})

An Investigation of Bilateral Symmetry During Manual Wheelchair Propulsion.

PubMed

Soltau, Shelby L; Slowik, Jonathan S; Requejo, Philip S; Mulroy, Sara J; Neptune, Richard R

2015-01-01

Studies of manual wheelchair propulsion often assume bilateral symmetry to simplify data collection, processing, and analysis. However, the validity of this assumption is unclear. Most investigations of wheelchair propulsion symmetry have been limited by a relatively small sample size and a focus on a single propulsion condition (e.g., level propulsion at self-selected speed). The purpose of this study was to evaluate bilateral symmetry during manual wheelchair propulsion in a large group of subjects across different propulsion conditions. Three-dimensional kinematics and handrim kinetics along with spatiotemporal variables were collected and processed from 80 subjects with paraplegia while propelling their wheelchairs on a stationary ergometer during three different conditions: level propulsion at their self-selected speed (free), level propulsion at their fastest comfortable speed (fast), and propulsion on an 8% grade at their level, self-selected speed (graded). All kinematic variables had significant side-to-side differences, primarily in the graded condition. Push angle was the only spatiotemporal variable with a significant side-to-side difference, and only during the graded condition. No kinetic variables had significant side-to-side differences. The magnitudes of the kinematic differences were low, with only one difference exceeding 5°. With differences of such small magnitude, the bilateral symmetry assumption appears to be reasonable during manual wheelchair propulsion in subjects without significant upper-extremity pain or impairment. However, larger asymmetries may exist in individuals with secondary injuries and pain in their upper extremity and different etiologies of their neurological impairment.

An Investigation of Bilateral Symmetry During Manual Wheelchair Propulsion

PubMed Central

Soltau, Shelby L.; Slowik, Jonathan S.; Requejo, Philip S.; Mulroy, Sara J.; Neptune, Richard R.

2015-01-01

Studies of manual wheelchair propulsion often assume bilateral symmetry to simplify data collection, processing, and analysis. However, the validity of this assumption is unclear. Most investigations of wheelchair propulsion symmetry have been limited by a relatively small sample size and a focus on a single propulsion condition (e.g., level propulsion at self-selected speed). The purpose of this study was to evaluate bilateral symmetry during manual wheelchair propulsion in a large group of subjects across different propulsion conditions. Three-dimensional kinematics and handrim kinetics along with spatiotemporal variables were collected and processed from 80 subjects with paraplegia while propelling their wheelchairs on a stationary ergometer during three different conditions: level propulsion at their self-selected speed (free), level propulsion at their fastest comfortable speed (fast), and propulsion on an 8% grade at their level, self-selected speed (graded). All kinematic variables had significant side-to-side differences, primarily in the graded condition. Push angle was the only spatiotemporal variable with a significant side-to-side difference, and only during the graded condition. No kinetic variables had significant side-to-side differences. The magnitudes of the kinematic differences were low, with only one difference exceeding 5°. With differences of such small magnitude, the bilateral symmetry assumption appears to be reasonable during manual wheelchair propulsion in subjects without significant upper-extremity pain or impairment. However, larger asymmetries may exist in individuals with secondary injuries and pain in their upper extremity and different etiologies of their neurological impairment. PMID:26125019

Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs

NASA Astrophysics Data System (ADS)

Takane, Daichi; Nakayama, Kosuke; Souma, Seigo; Wada, Taichi; Okamoto, Yoshihiko; Takenaka, Koshi; Yamakawa, Youichi; Yamakage, Ai; Mitsuhashi, Taichi; Horiba, Koji; Kumigashira, Hiroshi; Takahashi, Takashi; Sato, Takafumi

2018-01-01

One of key challenges in current material research is to search for new topological materials with inverted bulk-band structure. In topological insulators, the band inversion caused by strong spin-orbit coupling leads to opening of a band gap in the entire Brillouin zone, whereas an additional crystal symmetry such as point-group and nonsymmorphic symmetries sometimes prohibits the gap opening at/on specific points or line in momentum space, giving rise to topological semimetals. Despite many theoretical predictions of topological insulators/semimetals associated with such crystal symmetries, the experimental realization is still relatively scarce. Here, using angle-resolved photoemission spectroscopy with bulk-sensitive soft-x-ray photons, we experimentally demonstrate that hexagonal pnictide CaAgAs belongs to a new family of topological insulators characterized by the inverted band structure and the mirror reflection symmetry of crystal. We have established the bulk valence-band structure in three-dimensional Brillouin zone, and observed the Dirac-like energy band and ring-torus Fermi surface associated with the line node, where bulk valence and conducting bands cross on a line in the momentum space under negligible spin-orbit coupling. Intriguingly, we found that no other bands cross the Fermi level and therefore the low-energy excitations are solely characterized by the Dirac-like band. CaAgAs provides an excellent platform to study the interplay among low-energy electron dynamics, crystal symmetry, and exotic topological properties.

Grand minima and equatorial symmetry breaking in axisymmetric dynamo models

NASA Astrophysics Data System (ADS)

Brooke, John M.; Pelt, Jaan; Tavakol, Reza; Tworkowski, Andrew

1998-04-01

We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can undergo breaking of equatorial symmetry, i.e. loss of pure dipolar or quadrupolar symmetry. By considering the symmetry group underlying the solutions, we show that the fluctuations responsible for the symmetry-breaking can be constrained such that they are in resonance with the former solution. They can then be amplified until they are comparable in magnitude to the former solution. If the bifurcation is supercritical, the amplitude of the fluctuation is stabilised and a stable mixed parity limit cycle is formed. If it is subcritical it gives rise to a recently identified form of intermittency, called icicle intermittency. This produces episodes in which the original solution and the fluctuation are almost exactly synchronised and the fluctuation grows exponentially in amplitude, interrupted by brief episodes where synchronicity is lost and the amplitude of the fluctuation declines rapidly by several orders of magnitude. During these latter episodes there is a significant dip in the amplitude of the total magnetic field. This model-independent analysis can produce quantitative predictions for the behaviour of this bifurcation and we provide evidence for this behaviour by analysing timeseries from four different mean-field dynamo models, where intermittency is observed without the need for stochastic, or chaotically driven, forcing terms in the dynamo equations. We compare these results with recent work on intermittency in dynamo models and consider their relevance to the intermittency present in solar and stellar cycles.

Comparison between microprocessor-controlled ankle/foot and conventional prosthetic feet during stair negotiation in people with unilateral transtibial amputation.

PubMed

Agrawal, Vibhor; Gailey, Robert S; Gaunaurd, Ignacio A; O'Toole, Christopher; Finnieston, Adam A

2013-01-01

Contrary to stance-phase dorsiflexion of conventional prosthetic feet, the microprocessor-controlled Proprio foot permits swing-phase dorsiflexion on stairs. The purpose of this study was to compare Symmetry in External Work (SEW) between a microprocessor-controlled foot and conventional prosthetic feet in two groups with unilateral transtibial amputation (Medicare Functional Classification Levels K-Level-2 and K-Level-3) during stair ascent and descent. Ten subjects were evaluated while wearing three conventional prosthetic feet- solid ankle cushion heel (SACH), stationary attachment flexible endoskeleton (SAFE), and Talux-and the Proprio foot using a study socket and were given a 10- to 14-day accommodation period with each foot. Ground reaction forces were collected using F-scan sensors during stair ascent and descent. The SEW between the intact and amputated limbs was calculated for each foot. During stair ascent, the Proprio foot resulted in a higher interlimb symmetry than conventional prosthetic feet, with significant differences between the Pro prio and SACH/SAFE feet. The swing-phase dorsiflexion appeared to promote greater interlimb symmetry because it facilitated forward motion of the body, resulting in a heel-to-toe center of pressure trajectory. During stair descent, all feet had low symmetry without significant differences between feet. The movement strategy used when descending stairs, which is to roll over the edge of a step, had a greater influence on symmetry than the dorsiflexion features of prosthetic feet.

Reinventing the Concepts of Group and Isomorphism: The Case of Jessica and Sandra

ERIC Educational Resources Information Center

Larsen, Sean

2009-01-01

The purpose of this paper is to describe the process by which a pair of undergraduate students, participating in a teaching experiment, reinvented (with guidance) the concepts of group and isomorphism beginning with an exploration of the symmetries of an equilateral triangle. The intent of this description is to highlight some important insights…

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

PubMed

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

About crystal lattices and quasilattices in Euclidean space

NASA Astrophysics Data System (ADS)

Prokhoda, A. S.

2017-07-01

Definitions are given, based on which algorithms have been developed for constructing computer models of two-dimensional quasilattices and the corresponding quasiperiodic tilings in plane, the point symmetry groups of which are dihedral groups D m ( m = 5, 7, 8, 9, 10, 12, 14, 18), and the translation subgroups are free Abelian groups of the fourth or sixth rank. The angles at the tile vertices in the constructed tilings are calculated.

Group foliation of finite difference equations

NASA Astrophysics Data System (ADS)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

Dark matter and gauged flavor symmetries

DOE PAGES

Bishara, Fady; Greljo, Admir; Kamenik, Jernej F.; ...

2015-12-21

We investigate the phenomenology of flavored dark matter (DM). DM stability is guaranteed by an accidental Z 3 symmetry, a subgroup of the standard model (SM) flavor group that is not broken by the SM Yukawa interactions. We consider an explicit realization where the quark part of the SM flavor group is fully gauged. If the dominant interactions between DM and visible sector are through flavor gauge bosons, as we show for Dirac fermion flavored DM, then the DM mass is bounded between roughly 0.5 TeV and 5 TeV if the DM multiplet mass is split only radiatively. In general,more » however, no such relation exists. We demonstrate this using scalar flavored DM where the main interaction with the SM is through the Higgs portal. For both cases we derive constraints from flavor, cosmology, direct and indirect DM detection, and collider searches.« less

Ligands of low electronegativity in the vsepr model: molecular pseudohalides

NASA Astrophysics Data System (ADS)

Glidewell, Christopher; Holden, H. Diane

Equilibrium structures and force constants at linearity, for the skeletal bending mode δ(RNX) have been calculated in the MNDO approximation for 67 isocyanates, isothio-cyanates and azides, RNXY (XY = CO, CS or N 2) and the corresponding structures and force constants, δ(RCN), for 12 fulminates RCNO. Fulminates all have linear skeletons, but for RNXY the molecular skeleton is linear at atom X only if it is linear at N also ; otherwise the skeleton RNXY has a trans planar structure. Bending force constants are large and negative for all azides studied, negative for methyl and substituted methyl isocyanates and isothiocyanates and very small and positive for silyl and substituted silyl isothiocyanates: for silyl and substituted silyl isocyanales, the force constant is small and positive when the R group has effective C2v symmetry, but small and negative when the R group has only effective Cs symmetry.

Spin-triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9Mo6O17

NASA Astrophysics Data System (ADS)

Cho, Weejee; Platt, Christian; McKenzie, Ross H.; Raghu, Srinivas

2015-10-01

The purple bronze Li0.9Mo6O17 is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin-triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has more sign changes than required by the point-group symmetry.

Spin triplet superconductivity in a weak-coupling Hubbard model for the quasi-one-dimensional compound Li0.9 Mo6 O17

NASA Astrophysics Data System (ADS)

Platt, Christian; Cho, Weejee; McKenzie, Ross H.; Raghu, Sri

The purple bronze Li0.9Mo6O17 is of interest due to its quasi-one-dimensional electronic structure and the possible Luttinger liquid behavior resulting from it. For sufficiently low temperatures, it is a superconductor with a pairing symmetry that is still to be determined. To shed light on this issue, we analyze a minimal Hubbard model for this material involving four Molybdenum orbitals per unit cell near quarter filling, using asymptotically exact perturbative renormalization group methods. We find that spin triplet odd-parity superconductivity is the dominant instability. Approximate nesting properties of the two quasi-one-dimensional Fermi surfaces enhance certain second-order processes, which play crucial roles in determining the structure of the pairing gap. Notably, we find that the gap has accidental nodes, i.e. it has more sign changes than required by the point-group symmetry.

Dark matter and gauged flavor symmetries

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

Bishara, Fady; Greljo, Admir; Kamenik, Jernej F.

We investigate the phenomenology of flavored dark matter (DM). DM stability is guaranteed by an accidental Z 3 symmetry, a subgroup of the standard model (SM) flavor group that is not broken by the SM Yukawa interactions. We consider an explicit realization where the quark part of the SM flavor group is fully gauged. If the dominant interactions between DM and visible sector are through flavor gauge bosons, as we show for Dirac fermion flavored DM, then the DM mass is bounded between roughly 0.5 TeV and 5 TeV if the DM multiplet mass is split only radiatively. In general,more » however, no such relation exists. We demonstrate this using scalar flavored DM where the main interaction with the SM is through the Higgs portal. For both cases we derive constraints from flavor, cosmology, direct and indirect DM detection, and collider searches.« less

Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Luo, Li-Shi

2007-01-01

In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.

Special relativity in a discrete quantum universe

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-10-01

The hypothesis of a discrete fabric of the universe, the "Planck scale," is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.

Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis

NASA Astrophysics Data System (ADS)

Tsuchiizu, Masahisa; Kawaguchi, Kouki; Yamakawa, Youichi; Kontani, Hiroshi

2018-04-01

Recently, complex rotational symmetry-breaking phenomena have been discovered experimentally in cuprate superconductors. To find the realized order parameters, we study various unconventional charge susceptibilities in an unbiased way by applying the functional-renormalization-group method to the d -p Hubbard model. Without assuming the wave vector of the order parameter, we reveal that the most dominant instability is the uniform (q =0 ) charge modulation on the px and py orbitals, which possesses d symmetry. This uniform nematic order triggers another nematic p -orbital density wave along the axial (Cu-Cu) direction at Qa≈(π /2 ,0 ) . It is predicted that uniform nematic order is driven by the spin fluctuations in the pseudogap region, and another nematic density-wave order at q =Qa is triggered by the uniform order. The predicted multistage nematic transitions are caused by Aslamazov-Larkin-type fluctuation-exchange processes.

Generalized Bloch theorem and topological characterization

NASA Astrophysics Data System (ADS)

Dobardžić, E.; Dimitrijević, M.; Milovanović, M. V.

2015-03-01

The Bloch theorem enables reduction of the eigenvalue problem of the single-particle Hamiltonian that commutes with the translational group. Based on a group theory analysis we present a generalization of the Bloch theorem that incorporates all additional symmetries of a crystal. The generalized Bloch theorem constrains the form of the Hamiltonian which becomes manifestly invariant under additional symmetries. In the case of isotropic interactions the generalized Bloch theorem gives a unique Hamiltonian. This Hamiltonian coincides with the Hamiltonian in the periodic gauge. In the case of anisotropic interactions the generalized Bloch theorem allows a family of Hamiltonians. Due to the continuity argument we expect that even in this case the Hamiltonian in the periodic gauge defines observables, such as Berry curvature, in the inverse space. For both cases we present examples and demonstrate that the average of the Berry curvatures of all possible Hamiltonians in the Bloch gauge is the Berry curvature in the periodic gauge.

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 successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.

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 successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory...

Quantum critical spin-2 chain with emergent SU(3) symmetry.

PubMed

Chen, Pochung; Xue, Zhi-Long; McCulloch, I P; Chung, Ming-Chiang; Huang, Chao-Chun; Yip, S-K

2015-04-10

We study the quantum critical phase of an SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the finite-size energies and entanglement entropy by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectra, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)_{1} Wess-Zumino-Witten model. We find that, while the Hamiltonian is only SU(2) invariant, in this critical phase there is an emergent SU(3) symmetry in the thermodynamic limit.

Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

NASA Astrophysics Data System (ADS)

Rashidi, Saeede; Hejazi, S. Reza

This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

Two-dimensional N = 2 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

August, Daniel; Wellegehausen, Björn; Wipf, Andreas

2018-03-01

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

Separation of variables for the Dirac equation in an extended class of Lorentzian metrics with local rotational symmetry

NASA Astrophysics Data System (ADS)

Iyer, B. R.; Kamran, N.

1991-09-01

The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.

Crystal structure of langbeinite-related Rb0.743K0.845Co0.293Ti1.707(PO4)3.

PubMed

Strutynska, Nataliia Yu; Bondarenko, Marina A; Ogorodnyk, Ivan V; Baumer, Vyacheslav N; Slobodyanik, Nikolay S

2015-03-01

Potassium rubidium cobalt(II)/titanium(IV) tris-(orthophosphate), Rb0.743K0.845Co0.293Ti1.707(PO4)3, has been obtained using a high-temperature crystallization method. The obtained compound has a langbeinite-type structure. The three-dimensional framework is built up from mixed-occupied (Co/Ti(IV))O6 octa-hedra (point group symmetry .3.) and PO4 tetra-hedra. The K(+) and Rb(+) cations are statistically distributed over two distinct sites (both with site symmetry .3.) in the large cavities of the framework. They are surrounded by 12 O atoms.