Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ≥Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator χ ˆ =Rˆy (π) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
Spatial symmetry breaking in rapidly rotating convective spherical shells
NASA Technical Reports Server (NTRS)
Zhang, Keke; Schubert, Gerald
1995-01-01
Many problems in geophysical and astrophysical convection systems are characterized by fast rotation and spherical shell geometry. The combined effects of Coriolis forces and spherical shell geometry produce a unique spatial symmetry for the convection pattern in a rapidly rotating spherical shell. In this paper, we first discuss the general spatial symmetries for rotating spherical shell convection. A special model, a spherical shell heated from below, is then used to illustrate how and when the spatial symmetries are broken. Symmetry breaking occurs via a sequence of spatial transitions from the primary conducting state to the complex multiple-layered columnar structure. It is argued that, because of the dominant effects of rotation, the sequence of spatial transitions identified from this particular model is likely to be generally valid. Applications of the spatial symmetry breaking to planetary convection problems are also discussed.
Necessary symmetry conditions for the rotation of light.
Fernandez-Corbaton, Ivan; Vidal, Xavier; Tischler, Nora; Molina-Terriza, Gabriel
2013-06-01
Two conditions on symmetries are identified as necessary for a linear scattering system to be able to rotate the linear polarization of light: Lack of at least one mirror plane of symmetry and electromagnetic duality symmetry. Duality symmetry is equivalent to the conservation of the helicity of light in the same way that rotational symmetry is equivalent to the conservation of angular momentum. When the system is a solution of a single species of particles, the lack of at least one mirror plane of symmetry leads to the familiar requirement of chirality of the individual particle. With respect to helicity preservation, according to the analytical and numerical evidence presented in this paper, the solution preserves helicity if and only if the individual particle itself preserves helicity. However, only in the particular case of forward scattering the helicity preservation condition on the particle is relaxed: We show that the random orientation of the molecules endows the solution with an effective rotational symmetry; at its turn, this leads to helicity preservation in the forward scattering direction independently of any property of the particle. This is not the case for a general scattering direction. These results advance the current understanding of the phenomena of molecular optical activity and provide insight for the design of polarization control devices at the nanoscale. PMID:23758375
Emergent Rotational Symmetries in Disordered Magnetic Domain Patterns
NASA Astrophysics Data System (ADS)
Su, Run; Seu, Keoki A.; Parks, Daniel; Kan, Jimmy J.; Fullerton, Eric E.; Roy, Sujoy; Kevan, Stephen D.
2011-12-01
Uniaxial systems often form labyrinthine domains that exhibit short-range order but are macroscopically isotropic and would not be expected to exhibit precise symmetries. However, their underlying frustration results in a multitude of metastable configurations of comparable energy, and driving such a system externally might lead to pattern formation. We find that soft x-ray speckle diffraction patterns of the labyrinthine domains in CoPd/IrMn heterostructures reveal a diverse array of hidden rotational symmetries about the magnetization axis, thereby suggesting an unusual form of emergent order in an otherwise disordered system. These symmetries depend on applied magnetic field, magnetization history, and scattering wave vector. Maps of rotational symmetry exhibit intriguing structures that can be controlled by manipulating the applied magnetic field in concert with the exchange bias condition.
Effects of rotational symmetry breaking in polymer-coated nanopores
Osmanović, D.; Hoogenboom, B. W.; Ford, I. J.; Kerr-Winter, M.; Eccleston, R. C.
2015-01-21
The statistical theory of polymers tethered around the inner surface of a cylindrical channel has traditionally employed the assumption that the equilibrium density of the polymers is independent of the azimuthal coordinate. However, simulations have shown that this rotational symmetry can be broken when there are attractive interactions between the polymers. We investigate the phases that emerge in these circumstances, and we quantify the effect of the symmetry assumption on the phase behavior of the system. In the absence of this assumption, one can observe large differences in the equilibrium densities between the rotationally symmetric case and the non-rotationally symmetric case. A simple analytical model is developed that illustrates the driving thermodynamic forces responsible for this symmetry breaking. Our results have implications for the current understanding of the behavior of polymers in cylindrical nanopores.
Geometry of Landau Level without Galilean or Rotational Symmetry
NASA Astrophysics Data System (ADS)
Shen, Yu; Haldane, F. D. M.
The integer quantum Hall effect is usually modeled using Galilean-invariant or rotationally-invariant Landau levels. However, these are not generic symmetries of electrons moving in a crystalline background. We explicitly break both symmetries by considering a inversion-symmetric Hamiltonian with quartic terms. We carry out exact diagonalization numerically with a truncated Hilbert space, and define an emergent metric gabn for each Landau level as the expectation value of a bilinear form in momentum. With an appropriate choice of the guiding center coherent state, the Landau level wavefunctions are holomorphic functions of z* times a Gaussian (this is distinct from a well-known property of rotationally-invariant lowest-Landau-level wavefunctions). We show that the zeroes of the wavefunction define a ``topological spin sn'', with its original definition as an ``intrinsic angular momentum'' no longer valid without rotational symmetry. This is now related to the number of zeroes n encircled by the classical orbit by sn = n +1/2 . Finally we introduce a mass tensor mabn for each Landau level using a Lagrangian formalism. We conclude that topological and geometric information can be extracted without resort to Galilean or Rotational symmetries. This work is partly supported by DOE Grant No. DE-SC0002140 and the W. M. Keck Foundation.
Hidden Symmetries of Higher-Dimensional Rotating Black Holes
NASA Astrophysics Data System (ADS)
Kubiznak, David
2008-09-01
In this thesis we study higher-dimensional rotating black holes. Such black holes are widely discussed in string theory and brane-world models at present. We demonstrate that even the most general known Kerr-NUT-(A)dS spacetime, describing the general rotating higher-dimensional asymptotically (anti) de Sitter black hole with NUT parameters, is in many aspects similar to its four-dimensional counterpart. Namely, we show that it admits a fundamental hidden symmetry associated with the principal conformal Killing-Yano tensor. Such a tensor generates towers of hidden and explicit symmetries. The tower of Killing tensors is responsible for the existence of irreducible, quadratic in momenta, conserved integrals of geodesic motion. These integrals, together with the integrals corresponding to the tower of explicit symmetries, make geodesic equations in the Kerr-NUT-(A)dS spacetime completely integrable. We further demonstrate that in this spacetime the Hamilton-Jacobi, Klein-Gordon, and stationary string equations allow complete separation of variables and the problem of finding parallel-propagated frames reduces to the set of the first order ordinary differential equations. Moreover, we show that the Kerr-NUT-(A)dS spacetime is the most general Einstein space which possesses all these properties. We also explicitly derive the most general (off-shell) canonical metric admitting the principal conformal Killing-Yano tensor and demonstrate that such a metric is necessarily of the special algebraic type D of the higher-dimensional algebraic classification. The results presented in this thesis describe the new and complete picture of the relationship of hidden symmetries and rotating black holes in higher dimensions.
Interactive Visualization of Rotational Symmetry Fields on Surfaces.
Palacios, Jonathan; Zhang, Eugene
2011-07-01
Rotational symmetries (RoSys) have found uses in several computer graphics applications, such as global surface parameterization, geometry remeshing, texture and geometry synthesis, and nonphotorealistic visualization of surfaces. The visualization of N-way rotational symmetry (N-RoSy) fields is a challenging problem due to the ambiguities in the N directions represented by an N-way symmetry. We provide an algorithm that allows faithful and interactive representation of N-RoSy fields in the plane and on surfaces, by adapting the well-known line integral convolution (LIC) technique from vector and second-order tensor fields. Our algorithm captures N directions associated with each point in a given field by decomposing the field into multiple different vector fields, generating LIC images of these fields, and then blending the results. To address the loss of contrast caused by the blending of images, we observe that the pixel values in LIC images closely approximate normally distributed random variables. This allows us to use concepts from probability theory to correct the loss of contrast without the need to perform any image analysis at each frame. PMID:20855918
Ultrashort polarization rotator based on cross-symmetry waveguide
NASA Astrophysics Data System (ADS)
Wang, Xu; Dong, Jianji
2016-05-01
An ultrashort polarization rotator (PR) based on cross-symmetry waveguide is proposed and discussed. At the operating wavelength of 1 . 55 μ m , the presented PR has a small conversion length of 3 . 3 μ m . The polarization conversion efficiency (PCE) is 99 . 8 % (TE-TM) and 99 . 97 % (TM-TE). The PR can achieve rather high conversion efficiency (> 97 %) over a broad bandwidth (1450 - 1700 nm). The cross-symmetry structure can significantly improve the extinction ratio. The extinction ratio is 27 . 7 dB (TE-TM) and 35 . 9 dB (TM-TE) with the insertion loss of 0 . 28 dB . The fabrication tolerances for the waveguide for both transverse and horizontal directions are also studied.
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
NASA Astrophysics Data System (ADS)
Duguet, T.
2015-02-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree-Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.
Magnetic Rotation and Chirality and X(5) Critical Symmetry in Nucleus
Zhu, L. H.; Wu, X. G.; He, C. Y.; Hao, X.; Wang, L. L.; Zheng, Y.; Li, G. S.
2010-05-12
The magnetic and chiral rotation, the critical symmetry are fundamental problems in the study of nuclear structure. Here we report the recent results from the experiments on the magnetic and electric rotations in {sup 106}Ag, the chiral rotation in {sup 130}Cs and the evolution of X(5) symmetry in {sup 176}Os.
Hen, Itay; Karliner, Marek
2008-06-01
We study the phenomenon of spontaneous breaking of rotational symmetry in the rotating solutions of two types of baby Skyrme models. In the first, the domain is a two-sphere, and in the other, the Skyrmions are confined to the interior of a unit disk. Numerical full-field results show that when the angular momentum of the Skyrmions increases above a certain critical value, the rotational symmetry of the solutions is broken and the minimal-energy configurations become less symmetric. We propose a possible mechanism as to why spontaneous breaking of rotational symmetry is present in the rotating solutions of these models, while it is not observed in the 'usual' baby Skyrme model. Our results might be relevant for a qualitative understanding of the nonspherical deformation of excited nucleons with high orbital angular momentum.
Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
NASA Astrophysics Data System (ADS)
Gao, Zihao; Hua, Meng; Zhang, Haijun; Zhang, Xiao
2016-05-01
Three-dimensional (3D) Dirac and Weyl semimetals are novel states of quantum matter. We classify stable 3D Dirac and Weyl semimetals with reflection and rotational symmetry in the presence of time reversal symmetry and spin-orbit coupling, which belong to seventeen different point groups. They have two classes of reflection symmetry, with the mirror plane parallel and perpendicular to rotation axis. In both cases two types of Dirac points, existing through accidental band crossing (ABC) or at a time reversal invariant momentum (TBC), are determined by four different reflection symmetries. We classify those two types of Dirac points with a combination of different reflection and rotational symmetries. We further classify Dirac and Weyl line nodes to show in which types of mirror plane they can exist. Finally we discuss that Weyl line nodes and Dirac points can exist at the same time taking C4 v symmetry as an example.
Scaling symmetry and scalar hairy rotating AdS3 black holes
NASA Astrophysics Data System (ADS)
Ahn, Byoungjoon; Hyun, Seungjoon; Park, Sang-A.; Yi, Sang-Heon
2016-01-01
By using the scaling symmetry in the reduced action formalism, we derive the novel Smarr relation which holds even for the hairy rotating AdS3 black holes. Then, by using the Smarr relation we argue that the hairy rotating AdS3 black holes are stable thermodynamically, compared to the nonhairy ones.
Some consequences of scrPscrT symmetry for optical rotation experiments
NASA Astrophysics Data System (ADS)
Canright, G. S.; Rojo, A. G.
1992-03-01
We perform a general symmetry analysis of optical experiments on samples in the ``scrPscrT state,'' that is, samples for which 3D inversion symmetry scrP and time inversion symmetry scrT are each broken, but which are invariant under the product scrPscrT. We show that scrPscrT symmetry is compatible with all known results on optical rotation in the high-temperature superconductors. We also find a o/Iunique and accessible experimental signature for the scrPscrT state.
Interfacial Octahedral Rotation Mismatch Control of the Symmetry and Properties of SrRuO3.
Gao, Ran; Dong, Yongqi; Xu, Han; Zhou, Hua; Yuan, Yakun; Gopalan, Venkatraman; Gao, Chen; Fong, Dillon D; Chen, Zuhuang; Luo, Zhenlin; Martin, Lane W
2016-06-15
Epitaxial strain can be used to tune the properties of complex oxides with perovskite structure. Beyond just lattice mismatch, the use of octahedral rotation mismatch at heterointerfaces could also provide an effective route to manipulate material properties. Here, we examine the evolution of the structural motif (i.e., lattice parameters, symmetry, and octahedral rotations) of SrRuO3 films grown on substrates engineered to have the same lattice parameters, but different octahedral rotations. SrRuO3 films grown on SrTiO3 (001) (no octahedral rotations) and GdScO3-buffered SrTiO3 (001) (with octahedral rotations) substrates are found to exhibit monoclinic and tetragonal symmetry, respectively. Electrical transport and magnetic measurements reveal that the tetragonal films exhibit higher resistivity, lower magnetic Curie temperatures, and more isotropic magnetism as compared to those with monoclinic structure. Synchrotron-based quantification of the octahedral rotation network reveals that the tilting pattern in both film variants is the same (albeit with slightly different magnitudes of in-plane rotation angles). The abnormal rotation pattern observed in tetragonal SrRuO3 indicates a possible decoupling between the internal octahedral rotation and lattice symmetry, which could provide new opportunities to engineer thin-film structure and properties. PMID:27219026
Rotational directionality via symmetry-breaking in an electrostatic motor
NASA Astrophysics Data System (ADS)
Celestino, A.; Croy, A.; Beims, M. W.; Eisfeld, A.
2016-06-01
We theoretically investigate how one can achieve a preferred rotational direction for the case of a simple electrostatic motor. The motor is composed by a rotor and two electronic reservoirs. Electronic islands on the rotor can exchange electrons with the reservoirs. An electrostatic field exerts a force on the occupied islands. The charge dynamics and the electrostatic field drive rotations of the rotor. Coupling to an environment lead to damping on the rotational degree of freedom. We use two different approaches to the charge dynamics in the electronic islands: hopping process and mean-field. The hopping process approach takes into account charge fluctuations, which can appear along Coulomb blockade effects in nanoscale systems. The mean-field approach neglects the charge fluctuations on the islands, which is typically suitable for larger systems. We show that for a system described by the mean-field equations one can in principle prepare initial conditions to obtain a desired rotational direction. In contrast, this is not possible in the stochastic description. However, for both cases one can achieve rotational directionality by changing the geometry of the rotor. By scanning the space formed by the relevant geometric parameters we find optimal geometries, while fixing the dissipation and driving parameters. Remarkably, in the hopping process approach perfect rotational directionality is possible for a large range of geometries.
Symmetry of extremely floppy molecules: Molecular states beyond rotation-vibration separation.
Schmiedt, Hanno; Schlemmer, Stephan; Jensen, Per
2015-10-21
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 (CH5(+)) [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
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
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
Cooper Pairs with Broken Parity and Spin-Rotational Symmetries in d-Wave Superconductors
NASA Astrophysics Data System (ADS)
Lebed, A. G.
2006-01-01
Paramagnetic effects are shown to result in the appearance of a triplet component of order parameter in a vortex phase of a d-wave superconductor in the absence of impurities. This component, which breaks parity and spin-rotational symmetries of Cooper pairs, is expected to be of the order of unity in a number of modern superconductors such as organic, high Tc, and some others. A generic phase diagram of such type-IV superconductors, which are singlet ones at H=0 and in the Meissner phase, and characterized by singlet-triplet mixed Copper pairs Δs+iΔt with broken symmetries in a vortex phase, is discussed.
Spin-symmetry conversion and internal rotation in high J molecular systems
NASA Astrophysics Data System (ADS)
Mitchell, Justin; Harter, William
2006-05-01
Dynamics and spectra of molecules with internal rotation or rovibrational coupling is approximately modeled by rigid or semi-rigid rotors with attached gyroscopes. Using Rotational Energy (RE)^1 surfaces, high resolution molecular spectra for high angular momentum show two distinct but related phenomena; spin-symmetry conversion and internal rotation. For both cases the high total angular momentum allows for transitions that would otherwise be forbidden. Molecular body-frame J-localization effects associated with tight energy level-clusters dominate the rovibronic spectra of high symmetry molecules, particularly spherical tops at J>10. ^2 The effects include large and widespread spin-symmetry mixing contrary to conventional wisdom^3 about weak nuclear moments. Such effects are discussed showing how RE surface plots may predict them even at low J. Classical dynamics of axially constrained rotors are approximated by intersecting rotational-energy-surfaces (RES) that have (J-S).B.(J-S) forms in the limit of constraints that do no work. Semi-classical eigensolutions are compared to those found by direct diagonalization. ^1 W.G Hater, in Handbook of Atomic, Molecular and Optical Physics, edited by G.W.F Drake (Springer, Germany 2006) ^2 W. G. Harter, Phys. Rev. A24,192-262(1981). ^3 G. Herzberg, Infrared and Raman Spectra (VanNostrand 1945) pp. 458,463.
Relation between perception of vertical axis rotation and vestibulo-ocular reflex symmetry
NASA Technical Reports Server (NTRS)
Peterka, Robert J.; Benolken, Martha S.
1991-01-01
Subjects seated in a vertical axis rotation chair controlled their rotational velocity by adjusting a potentiometer. Their goal was to null out pseudorandom rotational perturbations in order to remain perceptually stationary. Most subjects showed a slow linear drift of velocity (a constant acceleration) to one side when they were deprived of an earth-fixed visual reference. The amplitude and direction of this drift can be considered a measure of a static bias in the subject's perception of rotation. The presence of a perceptual bias is consistent with a small, constant imbalance of vestibular function which could be of either central or peripheral origin. Deviations from perfect vestibulocular reflex (VOR) symmetry are also assumed to be related to imbalances in either peripheral or central vestibular function. Researchers looked for correlations between perceptual bias and various measures of vestibular reflex symmetry that might suggest a common source for both reflective and perceptual imbalances. No correlations were found. Measurement errors could not account for these results since repeated tests on the same subjects of both perceptual bias and VOR symmetry were well correlated.
Relation between perception of vertical axis rotation and vestibulo-ocular reflex symmetry
NASA Technical Reports Server (NTRS)
Peterka, Robert J.; Benolken, Martha S.
1992-01-01
Subjects seated in a vertical axis rotation chair controlled their rotational velocity by adjusting a potentiometer. Their goal was to null out pseudorandom rotational perturbations in order to remain perceptually stationary. Most subjects showed a slow linear drift of velocity (a constant acceleration) to one side when they were deprived of an earth-fixed visual reference. The amplitude and direction of this drift can be considered a measure of a static bias in the subject's perception of rotation. The presence of a perceptual bias is consistent with a small, constant imbalance of vestibular function which could be of either central or peripheral origin. Deviations from perfect vestibulo-ocular reflex (VOR) symmetry are also assumed to be related to imbalances in either peripheral or central vestibular function. Researchers looked for correlations between perceptual bias and various measures of vestibular reflex symmetry that might suggest a common source for both reflective and perceptual imbalances. No correlations were found. Measurement errors could not account for these results since repeated tests on the same subjects of both perceptual bias and VOR symmetry were well correlated.
NASA Astrophysics Data System (ADS)
Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang
2014-05-01
The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.
Rotational symmetry of the C ring and a mechanism for the flagellar rotary motor
Thomas, Dennis R.; Morgan, David Gene; DeRosier, David J.
1999-01-01
FliG, FliM, and FliN, key proteins for torque generation, are located in two rings. The first protein is in the M ring and the last two are in the C ring. The rotational symmetries of the C and M rings have been determined to be about 34 (this paper) and 26 (previous work), respectively. The mechanism proposed here depends on the symmetry mismatch between the rings: the C ring extends 34 levers, of which 26 can bind to the 26 equivalent sites on the M ring. The remaining 8 levers bind to proton–pore complexes (studs) to form 8 torque generators. Movement results from the swapping of stud-bound levers with M ring-bound levers. The model predicts that both the M and C rings rotate in the same direction but at different speeds. PMID:10468575
Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang
2014-01-01
The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved. PMID:24784778
Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang
2014-01-01
The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved. PMID:24784778
On BWR regional oscillations with rotational symmetry line using SIMULATE-3K
Dokhane, A.; Ferroukhi, H.; Pautz, A.
2013-07-01
A new stability analysis methodology is being developed at the Paul Scherrer Institute (PSI) using the best-estimate coupled neutronic/thermal- hydraulics code, SIMULATE-3K (S3K). This methodology has so far been validated against Leibstadt NPP (KKL) stability tests of C10, C13 and C19, which all show global (in-phase) oscillations. However, the methodology has not yet been validated for regional instabilities and to that aim, a special KKL cycle 07 stability test was selected. Indeed, during this test, the core not only showed growing power oscillation amplitudes in an out-of-phase regime but also an oscillating and rotating symmetry line. Thereby, it was selected in order to verify the S3K capability to predict regional instabilities and on that basis, obtain more insights towards understanding the causes for the oscillatory and rotational behaviour of symmetry lines. The results obtained so far are presented in this paper. First, it is found that the S3K results are in good agreement with measurements both qualitatively and quantitatively, although the resonance frequency is slightly over-predicted. Secondly, the excitation of the out-of-phase mode with oscillations as well as rotation of the symmetry line is also well captured i.e. in accordance to the experimental observations. Related to this, an in-depth analysis of LPRM signals indicates that two out-of-phase oscillation modes associated to two azimuthal neutronic modes are simultaneously excited. Furthermore, it is found that a superposition of these two modes will trigger the symmetry line dynamics and that the behaviour will be guided by the dominance ratio between these two modes. More precisely, the oscillatory behaviour is due to the superposition of the two azimuthal modes but with one dominant mode. The rotational behaviour is however due to the superposition of the two modes with comparable strengths. (authors)
Clarification of symmetry breaking mechanism in intrinsic rotation of tokamak plasmas
NASA Astrophysics Data System (ADS)
Yi, S.; Kwon, J. M.; Rhee, T.; Diamond, P. H.; Kim, J. Y.
2010-11-01
Intrinsic rotation of tokamak plasmas is considered to be generated by non-diffusive stress (i.e. residual stress) induced by asymmetric k|| turbulence spectrum. To study the symmetry breaking mechanisms in intrinsic rotation, we have performed numerical simulations of intrinsic rotation by ITG turbulence using the gKPSP code, a delta-f global PIC code for tokamak. It is found that not only distortion of turbulence spectrum by ExB shear but also spatial diffusion of wave momentum driven by turbulence intensity gradient play an important role in the symmetry breaking mechanism, as expected from a theory [1]. It is hard to recognize individual contribution of ExB shear and turbulence intensity gradient to the residual stress because their evolution is strongly coupled with the prey-predator feature [2]. To clarify their role, a comprehensive analysis including their nonlinear coupling is performed. The key symmetry breaking mechanism is identified for various physics situations. [4pt] [1] P.H. Diamond, et al., Phys. of Plasmas 15, 012303 (2008). [0pt] [2] P.H. Diamond, et al., PRL 72, 2565 (1994).
Triangular D3h Symmetry in the Rotation-Vibration Spectrum of 12C
NASA Astrophysics Data System (ADS)
Gai, Moshe
2015-02-01
Our recent measurements of new states in 12C including the second 2+ at 10 MeV and the high spin 5- state at 22.4 MeV allow us to study the Rotation-Vibration spectrum of 12C from which evidence for a new (D3h) geometrical symmetry emerges. The data fit very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4+/-, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed in 12C for the first time in nuclear physics. The triatomic like structure in nuclei is reminiscent of the discovery of diatomic α+14C structure in 18O. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1-) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C.
A subgroup algorithm to identify cross-rotation peaks consistent with non-crystallographic symmetry.
Lilien, Ryan H; Bailey-Kellogg, Chris; Anderson, Amy C; Donald, Bruce R
2004-06-01
Molecular replacement (MR) often plays a prominent role in determining initial phase angles for structure determination by X-ray crystallography. In this paper, an efficient quaternion-based algorithm is presented for analyzing peaks from a cross-rotation function in order to identify model orientations consistent with proper non-crystallographic symmetry (NCS) and to generate proper NCS-consistent orientations missing from the list of cross-rotation peaks. The algorithm, CRANS, analyzes the rotation differences between each pair of cross-rotation peaks to identify finite subgroups. Sets of rotation differences satisfying the subgroup axioms correspond to orientations compatible with the correct proper NCS. The CRANS algorithm was first tested using cross-rotation peaks computed from structure-factor data for three test systems and was then used to assist in the de novo structure determination of dihydrofolate reductase-thymidylate synthase (DHFR-TS) from Cryptosporidium hominis. In every case, the CRANS algorithm runs in seconds to identify orientations consistent with the observed proper NCS and to generate missing orientations not present in the cross-rotation peak list. The CRANS algorithm has application in every molecular-replacement phasing effort with proper NCS. PMID:15159565
Double surface imaging designs with unconstrained object to image mapping under rotational symmetry
NASA Astrophysics Data System (ADS)
Liu, Jiayao; Miñano, Juan C.; Benítez, Pablo
2014-09-01
In this work, we present a novel imaging design formed by two optical surfaces with rotational symmetry. In these designs, both object and image shapes are given but mapping from object to image is obtained through the design process. In the examples considered, the image from a planar object surface is virtual and located at infinity and is seen from a known pupil, which can emulate a human eye. The differential equation method is used to provide single optical surface imaging designs by considering the local properties of the imaging surface and the wavefronts. In the first introductory part, both the rotational symmetrical and the freeform single surface imaging designs are presented using the differential equation method. In these designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the second part, the method is extended to two surface designs with rotational symmetry and the astigmatism of the image has been studied. By adding one more optical surface to the system, the shape of the rotational symmetrical object can be designed while controlling the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a planar object surface have been obtained.
NASA Astrophysics Data System (ADS)
Feng, Chao; Zhao, Yan; Jiang, Yijian
2016-01-01
In this work, on the basis of finite difference time domain simulations and group theory, by employing regular nanosphere trimers as the main examples, we analyse and discuss the polarization-independent surface enhanced Raman scattering (SERS) phenomenon arising from the rotation symmetry of coined metallic nanomultimers. The results demonstrate why the rotationally symmetrical nanomultimers can show polarization-independent SERS performance. Because of the dramatically hybridized polarization-independent SERS performance over the whole 360° range, rotationally symmetrical coined metal nanomultimers, such as regular trimers, regular triangular tetramers and regular pentamers, are reliable and reproducible SERS substrates, which have the potential for convenient and flexible practical SERS detection without the need for optimally incident polarization outside the laboratory setting.
Feng, Chao; Zhao, Yan; Jiang, Yijian
2016-01-29
In this work, on the basis of finite difference time domain simulations and group theory, by employing regular nanosphere trimers as the main examples, we analyse and discuss the polarization-independent surface enhanced Raman scattering (SERS) phenomenon arising from the rotation symmetry of coined metallic nanomultimers. The results demonstrate why the rotationally symmetrical nanomultimers can show polarization-independent SERS performance. Because of the dramatically hybridized polarization-independent SERS performance over the whole 360° range, rotationally symmetrical coined metal nanomultimers, such as regular trimers, regular triangular tetramers and regular pentamers, are reliable and reproducible SERS substrates, which have the potential for convenient and flexible practical SERS detection without the need for optimally incident polarization outside the laboratory setting. PMID:26655083
Coexistence of Epitaxial Lattice Rotation and Twinning Tilt Induced by Surface Symmetry mismatch
Qiao, Liang; Xiao, Hai Yan; Weber, William J.; Biegalski, Michael D.
2014-06-02
Combined x-ray diffraction and first-principles studies of various epitaxial rutile-type metal dioxide films on Al2O3(0001) substrates reveal an unexpected rectangle-on-parallelogram heteroepitaxy. Unique matching of particular lattice spacings and crystal angles between the oxygen sublattices of Al2O3(0001) and the film(100) result in coexisted crystal rotation and lattice twinning inside the film. We demonstrate that, besides symmetry and lattice mismatch, angular mismatch along a specific crystal direction is also an important factor determining epitaxy. A generalized theorem has been proposed to explain epitaxial behaviors for tetragonal metal dioxides on Al2O3(0001).
Hidden conformal symmetry of rotating black holes in minimal five-dimensional gauged supergravity
Setare, M. R.; Kamali, V.
2010-10-15
In the present paper we show that for a low frequency limit the wave equation of a massless scalar field in the background of nonextremal charged rotating black holes in five-dimensional minimal gauged and ungauged supergravity can be written as the Casimir of an SL(2,R) symmetry. Our result shows that the entropy of the black hole is reproduced by the Cardy formula. Also the absorption cross section is consistent with the finite temperature absorption cross section for a two-dimensional conformal field theory.
NASA Astrophysics Data System (ADS)
Liu, Jiayao; Miñano, Juan C.; Benítez, Pablo
2014-05-01
In this work, novel imaging designs with a single freeform optical surface (either refractive or reflective) are presented. In these designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate a human eye. In the first introductory part, 2D designs and 3D designs by rotation using the differential equation method for the limit case of small pupil have been reviewed. Furthermore, the differential equation method is used to provide the freedom to control the tangential rays and sagittal rays simultaneously. In the second part, according to the study of astigmatism of different types of design with rotational symmetry, the differential equation method for 3D rotational design without astigmatism (at the small pupil limit) on a curved object surface has been extended to 3D freeform design. The result of this extended method has been proved to coincide with the former 3D design by rotation which is a special case of 3D freeform design. Finally, the initial condition has been used as an additional freedom to control the shape of the object surface. As a result, a reflective design with a much flatter object surface has been obtained.
Optically isotropic responses induced by discrete rotational symmetry of nanoparticle clusters
NASA Astrophysics Data System (ADS)
Hopkins, Ben; Liu, Wei; Miroshnichenko, Andrey E.; Kivshar, Yuri S.
2013-06-01
Fostered by the recent progress of the fields of plasmonics and metamaterials, the seminal topic of light scattering by clusters of nanoparticles is attracting enormous renewed interest gaining more attention than ever before. Related studies have not only found various new applications in different branches of physics and chemistry, but also spread rapidly into other fields such as biology and medicine. Despite the significant achievements, there still exists unsolved but vitally important challenges of how to obtain robust polarisation-invariant responses of different types of scattering systems. In this paper, we demonstrate polarisation-independent responses of any scattering system with a rotational symmetry with respect to an axis parallel to the propagation direction of the incident wave. We demonstrate that the optical responses such as extinction, scattering, and absorption, can be made independent of the polarisation of the incident wave for all wavelengths. Such polarisation-independent responses are proven to be a robust and generic feature that is purely due to the rotational symmetry of the whole structure. We anticipate our finding will play a significant role in various applications involving light scattering such as sensing, nanoantennas, optical switches, and photovoltaic devices.
Breaking Pseudo-Rotational Symmetry through H_+^2 Metric Deformation in the Eckart Potential Problem
NASA Astrophysics Data System (ADS)
Leija-Martinez, Nehemias; Alvarez-Castillo, David Edwin; Kirchbach, Mariana
2011-12-01
The peculiarity of the Eckart potential problem on H+2 (the upper sheet of the two-sheeted two-dimensional hyperboloid), to preserve the (2l+1)-fold degeneracy of the states typical for the geodesic motion there, is usually explained in casting the respective Hamiltonian in terms of the Casimir invariant of an so(2,1) algebra, referred to as potential algebra. In general, there are many possible similarity transformations of the symmetry algebras of the free motions on curved surfaces towards potential algebras, which are not all necessarily unitary. In the literature, a transformation of the symmetry algebra of the geodesic motion on H+2 towards the potential algebra of Eckart's Hamiltonian has been constructed for the prime purpose to prove that the Eckart interaction belongs to the class of Natanzon potentials. We here take a different path and search for a transformation which connects the (2l+1) dimensional representation space of the pseudo-rotational so(2,1) algebra, spanned by the rank-l pseudo-spherical harmonics, to the representation space of equal dimension of the potential algebra and find a transformation of the scaling type. Our case is that in so doing one is producing a deformed isometry copy to H+2 such that the free motion on the copy is equivalent to a motion on H+2, perturbed by a coth interaction. In this way, we link the so(2,1) potential algebra concept of the Eckart Hamiltonian to a subtle type of pseudo-rotational symmetry breaking through H+2 metric deformation. From a technical point of view, the results reported here are obtained by virtue of certain nonlinear finite expansions of Jacobi polynomials into pseudo-spherical harmonics. In due places, the pseudo-rotational case is paralleled by its so(3) compact analogue, the cotangent perturbed motion on S2. We expect awareness of different so(2,1)/so(3) isomet ry copies to benefit simulation studies on curved manifolds of many-body systems.
NASA Astrophysics Data System (ADS)
McGrann, John V.; Shaw, Gordon L.; Shenoy, Krishna V.; Leng, Xiaodan; Mathews, Robert B.
1994-06-01
Symmetries have long been recognized as a vital component of physical and biological systems. What we propose here is that symmetry operations are an important feature of higher brain function and result from the spatial and temporal modularity of the cortex. These symmetry operations arise naturally in the trion model of the cortex. The trion model is a highly structured mathematical realization of the Mountcastle organizational principle [Mountcastle, in The Mindful Brain (MIT, Cambridge, 1978)] in which the cortical column is the basic neural network of the cortex and is comprised of subunit minicolumns, which are idealized as trions with three levels of firing. A columnar network of a small number of trions has a large repertoire of quasistable, periodic spatial-temporal firing magic patterns (MP's), which can be excited. The MP's are related by specific symmetries: Spatial rotation, parity, ``spin'' reversal, and time reversal as well as other ``global'' symmetry operations in this abstract internal language of the brain. These MP's can be readily enhanced (as well as inherent categories of MP's) by only a small change in connection strengths via a Hebb learning rule. Learning introduces small breaking of the symmetries in the connectivities which enables a symmetry in the patterns to be recognized in the Monte Carlo evolution of the MP's. Examples of the recognition of rotational invariance and of a time-reversed pattern are presented. We propose the possibility of building a logic device from the hardware implementation of a higher level architecture of trion cortical columns.
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. PMID:27544099
Torchinsky, Darius H.; Hsieh, David; Chu, Hao; Qi, Tongfei; Cao, Gang
2014-08-15
Nonlinear optical generation from a crystalline material can reveal the symmetries of both its lattice structure and underlying ordered electronic phases and can therefore be exploited as a complementary technique to diffraction based scattering probes. Although this technique has been successfully used to study the lattice and magnetic structures of systems such as semiconductor surfaces, multiferroic crystals, magnetic thin films, and multilayers, challenging technical requirements have prevented its application to the plethora of complex electronic phases found in strongly correlated electron systems. These requirements include an ability to probe small bulk single crystals at the μm length scale, a need for sensitivity to the entire nonlinear optical susceptibility tensor, oblique light incidence reflection geometry, and incident light frequency tunability among others. These measurements are further complicated by the need for extreme sample environments such as ultra low temperatures, high magnetic fields, or high pressures. In this review we present a novel experimental construction using a rotating light scattering plane that meets all the aforementioned requirements. We demonstrate the efficacy of our scheme by making symmetry measurements on a μm scale facet of a small bulk single crystal of Sr{sub 2}IrO{sub 4} using optical second and third harmonic generation.
Yoneda, S
1997-08-01
One of the most accurate styles of protein simulation is to calculate proteins in crystalline environment without neglect of long-range interactions. The long-range interactions can be accelerated by various methods. However, as a unit cell of a protein crystal is a large molecular assembly, its simulation is still unpractical without high-speed computers. Thus this article is addressed to the reduction of calculational volumes for protein crystal simulation by a further implementation of the rotational symmetry boundary condition method. For protein crystals in P4(3)2(1)2 symmetry, a computational cell and related tables were developed. A 120-ps molecular dynamics simulation was performed for a P4(3)2(1)2 symmetry crystal of glycogen phosphorylase b under rotational symmetry boundary conditions. The computational cell was one-eighth of the unit cell in volume, and less than about one-fourth of the conventional periodic boundary box. Generation of neighbor atom pair lists was greatly accelerated, and thus the simulation was practical even with a personal computer. PMID:9524932
NASA Astrophysics Data System (ADS)
Fyodorov, Yan V.; Sommers, H.-J.
2007-03-01
We provide a detailed discussion of the replica approach to thermodynamics of a single classical particle placed in a random Gaussian N(≫1)-dimensional potential inside a spherical box of a finite radius L=R√{N}. Earlier solutions of R=∞ version of this model were based on applying the Gaussian Variational Ansatz (GVA) to the replicated partition function, and revealed a possibility of glassy phases at low temperatures. For a general R, we show how to utilize instead the underlying rotational symmetry and to arrive to a compact expression for the free energy in the limit N→∞ directly, without any need for intermediate variational approximations. This method reveals a striking similarity with the much-studied spherical model of spin glasses. Depending on the competition between the radius R and the curvature of the parabolic confining potential μ⩾0, as well as on the three types of disorder—short-ranged, long-ranged, and logarithmic—the phase diagram of the system in the (μ,T) plane undergoes considerable modifications. In the limit of infinite confinement radius our analysis confirms all previous results obtained by GVA. The paper has also a considerable pedagogical component by providing an extended presentation of technical details which are not always easy to find in the existing literature.
NASA Astrophysics Data System (ADS)
Higemoto, Wataru; Aoki, Yuji; MacLaughlin, Douglas E.
2016-09-01
Unconventional superconductivity based on the strong correlation of electrons is one of the central issues of solid-state physics. Although many experimental techniques are appropriate for investigating unconventional superconductivity, a complete perspective has not been established yet. The symmetries of electron pairs are crucial properties for understanding the essential state of unconventional superconductivity. In this review, we discuss the investigation of the time-reversal and spin symmetries of superconducting electron pairs using the muon spin rotation and relaxation technique. By detecting a spontaneous magnetic field under zero field and/or the temperature dependence of the muon Knight shift in the superconducting phase, the time-reversal symmetry and spin parity of electron pairs have been determined for several unconventional superconductors.
Szymański, S
2009-12-28
The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra. PMID:20059076
NASA Astrophysics Data System (ADS)
Abbate, Sergio; Gangemi, Roberto; Longhi, Giovanna
2002-10-01
Contact transformation theory up to second order is employed to treat CH-stretching overtone transitions and to calculate dipole and rotational strengths. A general Hamiltonian describing two interacting CH-stretching oscillators is considered, and the Darling-Dennison resonance is appropriately taken into account. The two CH bonds are supposed to be dissymmetrically disposed, so as to represent a chiral HCCH fragment, endowed with C2 symmetry. Analytical expressions of transition moments and dipole and rotational strengths are given in the hypothesis of general electric and magnetic dipole moments with quadratic dependence on coordinates and momenta. Dipole and rotational strengths are then calculated together with frequencies for the fundamental and first three overtone regions in the simplifying hypothesis of the valence optical approach on the coupled-oscillator framework. Simplified analytical expressions thereof in the relevant parameters are presented.
Kimura, Keiji; Takehiro, Shin-ichi; Yamada, Michio
2014-08-15
We investigate properties of convective solutions of the Boussinesq thermal convection in a moderately rotating spherical shell allowing the respective rotation of the inner and outer spheres due to the viscous torque of the fluid. The ratio of the inner and outer radii of the spheres, the Prandtl number, and the Taylor number are fixed to 0.4, 1, and 500{sup 2}, respectively. The Rayleigh number is varied from 2.6 × 10{sup 4} to 3.4 × 10{sup 4}. In this parameter range, the behaviours of obtained asymptotic convective solutions are almost similar to those in the system whose inner and outer spheres are restricted to rotate with the same constant angular velocity, although the difference is found in the transition process to chaotic solutions. The convective solution changes from an equatorially symmetric quasi-periodic one to an equatorially symmetric chaotic one, and further to an equatorially asymmetric chaotic one, as the Rayleigh number is increased. This is in contrast to the transition in the system whose inner and outer spheres are assumed to rotate with the same constant angular velocity, where the convective solution changes from an equatorially symmetric quasi-periodic one, to an equatorially asymmetric quasi-periodic one, and to equatorially asymmetric chaotic one. The inner sphere rotates in the retrograde direction on average in the parameter range; however, it sometimes undergoes the prograde rotation when the convective solution becomes chaotic.
NASA Astrophysics Data System (ADS)
Vrtovec, Tomaž; Likar, Boštjan; Pernuš, Franjo
2007-03-01
Quantitative measurement of vertebral rotation is important in surgical planning, analysis of surgical results, and monitoring of the progression of spinal deformities. However, many established and newly developed techniques for measuring axial vertebral rotation do not exploit three-dimensional (3D) information, which may result in virtual axial rotation because of the sagittal and coronal rotation of vertebrae. We propose a novel automatic approach to the measurement of the location and rotation of vertebrae in 3D without prior volume reformation, identification of appropriate cross-sections or aid by statistical models. The vertebra under investigation is encompassed by a mask in the form of an elliptical cylinder in 3D, defined by its center of rotation and the rotation angles. We exploit the natural symmetry of the vertebral body, vertebral column and vertebral canal by dividing the vertebral mask by its mid-axial, mid-sagittal and mid-coronal plane, so that the obtained volume pairs contain symmetrical parts of the observed anatomy. Mirror volume pairs are then simultaneously registered to each other by robust rigid auto-registration, using the weighted sum of absolute differences between the intensities of the corresponding volume pairs as the similarity measure. The method was evaluated on 50 lumbar vertebrae from normal and scoliotic computed tomography (CT) spinal scans, showing relatively large capture ranges and distinctive maxima at the correct locations and rotation angles. The proposed method may aid the measurement of the dimensions of vertebral pedicles, foraminae and canal, and may be a valuable tool for clinical evaluation of the spinal deformities in 3D.
Pan, Y.; Nikitin, A. M.; Araizi, G. K.; Huang, Y. K.; Matsushita, Y.; Naka, T.; de Visser, A.
2016-01-01
Recently it was demonstrated that Sr intercalation provides a new route to induce superconductivity in the topological insulator Bi2Se3. Topological superconductors are predicted to be unconventional with an odd-parity pairing symmetry. An adequate probe to test for unconventional superconductivity is the upper critical field, Bc2. For a standard BCS layered superconductor Bc2 shows an anisotropy when the magnetic field is applied parallel and perpendicular to the layers, but is isotropic when the field is rotated in the plane of the layers. Here we report measurements of the upper critical field of superconducting SrxBi2Se3 crystals (Tc = 3.0 K). Surprisingly, field-angle dependent magnetotransport measurements reveal a large anisotropy of Bc2 when the magnet field is rotated in the basal plane. The large two-fold anisotropy, while six-fold is anticipated, cannot be explained with the Ginzburg-Landau anisotropic effective mass model or flux flow induced by the Lorentz force. The rotational symmetry breaking of Bc2 indicates unconventional superconductivity with odd-parity spin-triplet Cooper pairs (Δ4-pairing) recently proposed for rhombohedral topological superconductors, or might have a structural nature, such as self-organized stripe ordering of Sr atoms. PMID:27350295
Pan, Y; Nikitin, A M; Araizi, G K; Huang, Y K; Matsushita, Y; Naka, T; de Visser, A
2016-01-01
Recently it was demonstrated that Sr intercalation provides a new route to induce superconductivity in the topological insulator Bi2Se3. Topological superconductors are predicted to be unconventional with an odd-parity pairing symmetry. An adequate probe to test for unconventional superconductivity is the upper critical field, Bc2. For a standard BCS layered superconductor Bc2 shows an anisotropy when the magnetic field is applied parallel and perpendicular to the layers, but is isotropic when the field is rotated in the plane of the layers. Here we report measurements of the upper critical field of superconducting SrxBi2Se3 crystals (Tc = 3.0 K). Surprisingly, field-angle dependent magnetotransport measurements reveal a large anisotropy of Bc2 when the magnet field is rotated in the basal plane. The large two-fold anisotropy, while six-fold is anticipated, cannot be explained with the Ginzburg-Landau anisotropic effective mass model or flux flow induced by the Lorentz force. The rotational symmetry breaking of Bc2 indicates unconventional superconductivity with odd-parity spin-triplet Cooper pairs (Δ4-pairing) recently proposed for rhombohedral topological superconductors, or might have a structural nature, such as self-organized stripe ordering of Sr atoms. PMID:27350295
Symmetry breaking in vortex-induced vibration of a rotating cylinder
NASA Astrophysics Data System (ADS)
Seyed-Aghazadeh, Banafsheh; Modarres-Sadeghi, Yahya
2014-11-01
Vortex-induced vibration (VIV) of a flexibly-mounted circular cylinder, free to oscillate in the crossflow direction with imposed rotation around its axis, is studied experimentally. In particular, the influence of asymmetry that is introduced into the system by the forced rotation of the cylinder is considered. The rotation rate, α, defined as the ratio of the surface velocity and free stream velocity, was varied from 0 to 2.6 in small steps. The amplitudes and frequencies of oscillations as well as the flow forces were measured in a Reynolds number range of Re =350-1000. The maximum amplitude of oscillation was found to be limited to values less than a diameter of the cylinder at high rotation rates. Also the lock-in range was found to become narrower at higher rotation rates and finally the oscillation ceased beyond α = 2.4. Vortex shedding pattern was found to change from 2S and 2P shedding (two single and two pairs of vortices shed per cycle of oscillation) for a non-rotating cylinder to P shedding (one pair of vortices shed in a cycle of oscillations) for the rotating cylinder. Also, the phase difference between the flow forces and displacement of the cylinder in the crossflow direction was influenced as the rotation rate was increased. At high reduced velocities the phase difference decreased from 180 degree for a non-rotating cylinder to values close to 90 degree for a rotating cylinder.
McCollum, Gin; Boyle, Richard
2004-03-01
Organizational structures intrinsic to nervous systems can be more precisely analyzed and compared with other logical structures once they are expressed in mathematical languages. A standard mathematical language for expressing organizational structure is that of groups. Groups are especially well suited to organizational structures involving multiple symmetries such as spatial structures. The vestibular system is widely believed to mediate many neural functions involving spatial structure. The vestibular nuclei receive direct projections from the vestibular endorgans, the semicircular canals and the otolith organs. The near-orthogonal directions of the semicircular canals are embedded in the bone. However, those canal directions are external to the nervous system. This study addresses the way the three-dimensional space of rotations is also embedded in the group structure of neural connectivity. Although we know a great deal about physical rotation, it is not clear that nervous systems organize rotations in the same way as physicists do. It would make sense for nervous systems to organize rotations in such a way as to provide physiologically relevant information about performing or compensating for rotations. The vestibular nuclei, which might be expected to display an organization that binds rotations into a rotation space, do not give a clear organization. This may be because of the multiplicity of spatial functions performed by the vestibular nuclei; rather than one spatial organization, the vestibular nuclei are likely to accommodate multiple, related spatial organizations. This study evaluates one particular data set from the literature that specifies the organization of the disynaptic canal-neck projection; other projections and neuronal populations may have other intrinsic organizations. The data are evaluated directly for their symmetry group. In the symmetry group, the vertebrate requirement that physiology have a right and left is found to be satisfied
NASA Astrophysics Data System (ADS)
Wu, Lian-Ao; Lou, Ji-Zhong; Jing, Xiao-Gong
1995-06-01
In this paper, we first demonstrate the applicability of a phenomenological two-parameter formula, as introduced by Holmberg and Lipas from the Bohr Hamiltonian in a way that is different from Wu and Zeng. Second, for the first time, we show microscopically that Holmberg's two-parameter formula can be applied to diatomic molecules and that it can fit the experimental data of rotational spectra of HCl, HBr, and HF very well when the parameters are determined by two arbitrary experimental levels. Third, we derive a two-parameter formula describing γ-soft rotational spectra which is similar to the Holmberg formula, called Holmberg-like formula in this paper. The experimental yrast lines of nine nuclei in the light rare-earth region are fitted by this formula. For the nuclear γ stiffness, γ softness, and for molecular rotational spectra, all the two-parameter formulas are obtained by making use of a single potential function. It is demonstrated that the reason why one can give a unified description for those three systems is the common rotational features like the widely used harmonic oscillator approximation. More importantly, from the more microscopic nuclear fermion dynamical symmetry model (FDSM), we may derive the variable moment of inertia (VMI) model, and further obtain the Holmberg formula and Holmberg-like formula under a certain approximation, as from the nuclear geometric description within the Bohr-Mottelson model (BM). It is shown that the bridge between the descriptions of the FDSM and of the BM is the effect of stretched alignment (stretching effect). According to another interpretation of the FDSM for the nuclear stretching effect, we also give a simple formula to explain the γ-soft rotational spectra and compare the formula with the above one. Finally, we give a phenomenological generalization to the combination of the Holmberg and Holmberg-like formulas, which may describe a transition from γ-stiff rotations to γ-soft rotations.
A Symmetry Breaking Experiment Aboard Mir and the Stability of Rotating Liquid Films
NASA Technical Reports Server (NTRS)
Concus, P.; Finn, R.; Gomes, D.; McCuan, J.; Weislogel, M.
1999-01-01
We discuss results from two parts of our study on the behavior of liquids under low-gravity conditions. The first concerns the Interface Configuration Experiment (ICE) aboard the Space Station Mir on the Mir-21/NASA-2 mission; for a certain 'exotic' container, distinct asymmetric liquid configurations are found as locally stable ones, even though the container itself is rotationally symmetric, in confirmation of mathematical results and numerical computations. The second investigation concerns the behavior of slowly rotating liquids; it is found that a rotating film instability observed previously in a physical experiment in 1-g, scaled to render gravity effects small, does not correspond to mathematical and computational results obtained for low gravity. These latter results are based on the classical equilibrium theory enhanced with a van der Waals potential of adhesion.
High-efficiency free-form condenser overcoming rotational symmetry limitations.
Miñano, Juan C; Benítez, Pablo; Blen, José; Santamaría, Asunción
2008-12-01
Conventional condensers using rotational symmetric devices perform far from their theoretical limits when transferring optical power from sources such as arc lamps or halogen bulbs to the rectangular entrance of homogenizing prisms (target). We present a free-form condenser design (calculated with the SMS method) that overcomes the limitations inherent to rotational devices and can send to the target 1.8 times the power sent by an equivalent elliptical condenser for a 4:1 target aspect ratio and 1.5 times for 16:9 target and for practical values of target etendue. PMID:19065158
Symmetry breaking and self-consistent rotation of magnetic islands in neoclassical viscous regimes
Lazzaro, E.
2009-09-15
Classical or neoclassical tearing modes (NTMs) perturb the ideal axisymmetry of tokamaks. As a consequence of symmetry breaking a neoclassical toroidal viscosity (NTV) appears, that depends on the island amplitude. This work shows that in the low collisionality regimes NTV has a key role in determining self-consistently the magnetic island velocity and at the same time modifies significantly the ion polarization current effects on NTM instability. This finding can provide a better understanding of the mechanism of onset of NTMs, observed experimentally, and improve the concepts for their control or avoidance.
Exchange bias field induced symmetry-breaking of magnetization rotation in two-dimension
NASA Astrophysics Data System (ADS)
Cui, B.; Song, C.; Sun, Y.; Wang, Y. Y.; Zhao, Y. L.; Li, F.; Wang, G. Y.; Zeng, F.; Pan, F.
2014-10-01
We investigate the effect of strain-induced intrinsic exchange bias field (HEB) on the magnetization rotation process in a nominally "single" layered La2/3Sr1/3MnO3 (LSMO) film. The intrinsic exchange bias appears when the LSMO film is grown on LaAlO3 substrate. The HEB is proved to be an effective approach to tuning the in-plane magnetization rotation, producing a 360° instead of 180° periodicity in the anisotropic magnetoresistance curves measured in a low external magnetic field. The planar Hall effect curves are asymmetric when the in-plane magnetization rotate between two orthogonal axes of LSMO, helped or hindered by the HEB. Our study reveals that the HEB in but not limited to LSMO with phase separation exhibits an unprecedentedly two-dimensional effect rather than merely establishing a reference magnetization direction as achieved in ferromagnetic/antiferromagnetic bilayers, thus furthering the cognition of manipulating the magnetization orientation.
NASA Astrophysics Data System (ADS)
Pfeifer, Tilo; Evertz, Jens; Tutsch, Rainer; Rothe, Hendrik
1993-01-01
Non-rotational aspherics offer new perspectives for the development of new concepts for high power laser resonators (e.g., CO2-laser with unstable resonator). Furthermore, the intensity profile of the laser beam can be adapted to the needs of special working processes (e.g., cutting, welding, surface treatments). At the IPT a variety of mirrors with complex shapes are manufactured with a proprietary fast-tool-servo on a diamond turning lathe. For these mirrors an aspheric testing interferometer with computer generated holograms has been developed. Research work was done on the design of the optical system, the development of algorithms and software for the computation of the holograms, the techniques for manufacturing the computer generated holograms (CGH) and an appropriate strategy for adjustment of the measurement system. The hologram pattern is plotted using a CAD-plotter and photographically reduced in scale. To overcome this time-consuming technique and to improve the precision of the holograms a laser-based direct writing hologram-plotter is under development. We describe the concept of the measurement system, and discuss several systematic error sources. Some recent results are presented.
NASA Astrophysics Data System (ADS)
Bonazzola, S.; Frieben, J.; Gourgoulhon, E.
1998-03-01
An analytical scheme and a numerical method in order to study the effects of general relativity on the viscosity driven secular bar mode instability of rapidly rotating stars are presented. The approach consists in perturbing an axisymmetric and stationary configuration and studying its evolution by constructing a series of triaxial quasi-equilibrium configurations. These are obtained by solution of an approximate set of field equations where only the dominant non-axisymmetric terms are taken into account. The progress with respect to our former investigation consists in a higher relativistic order of the non-axisymmetric terms included into the computation, namely the fully three-dimensional treatment of the vector part of the space-time metric tensor as opposed to the scalar part, solely, in the former case. The scheme is applied to rotating stars built on a polytropic equation of state and compared to our previous results. The 3D-vector part turns out to inhibit the symmetry breaking efficiently. Nevertheless, the bar mode instability is still possible for an astrophysically relevant mass of M_ns=3D1.4M_⊙ when a stiff polytropic equation of state with an adiabatic index of gamma =3D2.5 is employed. Triaxial neutron stars may be efficient emitters of gravitational waves and are thus potentially interesting sources for the forthcoming laser interferometric gravitational wave detectors such as LIGO, VIRGO and GEO600. >From a numerical point of view, the solution of the three-dimensional minimal-distortion shift vector equation in spherical coordinates is an important achievement of our code.
NASA Astrophysics Data System (ADS)
Hofmann, Christoph P.
2016-03-01
The low-temperature properties of systems characterized by a spontaneously broken internal rotation symmetry, O (N) → O (N - 1), are governed by Goldstone bosons and can be derived systematically within effective Lagrangian field theory. In the present study we consider systems living in two spatial dimensions, and evaluate their partition function at low temperatures and weak external fields up to three-loop order. Although our results are valid for any such system, here we use magnetic terminology, i.e., we refer to quantum spin systems. We discuss the sign of the (pseudo-)Goldstone boson interaction in the pressure, staggered magnetization, and susceptibility as a function of an external staggered field for general N. As it turns out, the d = 2 + 1 quantum XY model (N = 2) and the d = 2 + 1 Heisenberg antiferromagnet (N = 3), are rather special, as they represent the only cases where the spin-wave interaction in the pressure is repulsive in the whole parameter regime where the effective expansion applies. Remarkably, the d = 2 + 1 XY model is the only system where the interaction contribution in the staggered magnetization (susceptibility) tends to positive (negative) values at low temperatures and weak external field.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
NASA Astrophysics Data System (ADS)
Soudani, Sarra; Zeller, Matthias; Wenger, Emmanuel; Jelsch, Christian; Lefebvre, Frédéric; Nasr, Cherif Ben
2014-10-01
The structure of the complex [C18H30Cd3Cl6N18S12·2(C18H30Cd2Cl3N18S12)·CdCl4], or [L6Cd3Cl6·2(L6Cd2Cl3)·CdCl4], with L being 2-amino-5-(methylthio)-1,3,4-thiadiazole, C3H5N3S2, crystallizes in the trigonal polar space group R3. The crystal packing features three chemically distinct cadmium complex species with eight crystallographically independent Cd(II) ions distributed over two types of L ligand complexes with two and three Cd(II) centers, respectively, and a tetrachlorocadmate(II) ion. The coordination environment of the cadmium ions in the dinuclear and trinuclear complexes is a distorted octahedron. The tetrachlorocadmate(II) is disordered around a crystallographic threefold rotation axis, which is, in turn, inducing disorder onto the two methyl-thio groups in closest proximity to a CdCl4 anion. The crystal under investigation was found to be twinned by rotational and inversion merohedry. In the higher symmetry setting, the trinuclear complex would feature exact inversion symmetry, and the two binuclear cationic complexes would be inversion counterparts of each other. The R3bar symmetry is broken by a mismatch of less than 1 Å between one pair of ligands L between the dinuclear cations, which feature slightly different rotational angles around the Cd ion in the otherwise symmetry equivalent complexes. This compound is also investigated by FT-IR and solid-state 13CCP-MAS NMR spectroscopies.
ERIC Educational Resources Information Center
Myrick, M. L.; Colavita, P. E.; Greer, A. E.; Long, B.; Andreatta, D.
2004-01-01
The measurement of the infrared rotation-vibration spectrum of HCl(g) is a common experiment in the physical chemistry laboratory, which allows students the opportunity to explore quantization of rotational states in diatomic molecules. It is found that the CO2 vibration-rotation spectrum if used as an addition to the HCl experiment would give the…
Park, G Barratt; Jiang, Jun; Saladrigas, Catherine A; Field, Robert W
2016-04-14
The C̃ (1)B2 state of SO2 has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b2 vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the X̃ state are vibronically forbidden. We use IR-UV double resonance to observe the b2 vibrational levels of the C̃ state below 1600 cm(-1) of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, it allows us to deperturb the strong c-axis Coriolis interactions between levels of a1 and b2 vibrational symmetry and to determine accurately the vibrational dependence of the rotational constants in the distorted C̃ electronic state. PMID:27083725
Park, G. Barratt; Jiang, Jun; Saladrigas, Catherine A.; Field, Robert W.
2016-04-14
Here, the C 1B2 state of SO2 has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b2 vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the X~ state are vibronically forbidden. We use IR-UV double resonance to observe the b2 vibrational levels of the C state below 1600 cm–1 of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, itmore » allows us to deperturb the strong c-axis Coriolis interactions between levels of a1 and b2 vibrational symmetry, and to determine accurately the vibrational dependence of the rotational constants in the distorted C electronic state.« less
NASA Astrophysics Data System (ADS)
Park, G. Barratt; Jiang, Jun; Saladrigas, Catherine A.; Field, Robert W.
2016-04-01
The C ˜ 1B2 state of SO2 has a double-minimum potential in the antisymmetric stretch coordinate, such that the minimum energy geometry has nonequivalent SO bond lengths. However, low-lying levels with odd quanta of antisymmetric stretch (b2 vibrational symmetry) have not previously been observed because transitions into these levels from the zero-point level of the X ˜ state are vibronically forbidden. We use IR-UV double resonance to observe the b2 vibrational levels of the C ˜ state below 1600 cm-1 of vibrational excitation. This enables a direct characterization of the vibrational level staggering that results from the double-minimum potential. In addition, it allows us to deperturb the strong c-axis Coriolis interactions between levels of a1 and b2 vibrational symmetry and to determine accurately the vibrational dependence of the rotational constants in the distorted C ˜ electronic state.
Lazzaro, Enzo
2009-10-08
Established results of neoclassical kinetic theory are used in a fluid model to show that in low collisionality regimes ({nu} and 1/{nu}) the propagation velocity of Neoclassical Tearing Modes (NTM) magnetic islands of sufficient width is determined self-consistently by the Neoclassical Toroidal Viscosity (NTV) appearing because of broken symmetry. The NTV effect on bulk plasma rotation, may also explain recent observations on momentum transport. At the same time this affects the role of the neoclassical ion polarization current on neoclassical tearing modes (NTM) stability.
Nair, K P Rajappan; Jahn, Michaela K; Lesarri, Alberto; Ilyushin, Vadim V; Grabow, Jens-Uwe
2015-10-21
Pure six-fold symmetry (V6) internal rotation poses significant challenges to experimental and theoretical determination, as the very low torsional barriers result in huge tunneling splittings difficult to identify and to model. Here we resolved the methyl group internal rotation dynamics of 2,6- and 3,5-difluorotoluene using a newly developed computer code especially adapted to V6 problems. The jet-cooled rotational spectra of the title molecules in the 5-25 GHz region revealed internal rotation tunneling doublings of up to 3.6 GHz, which translated in methyl group potential barriers of V6 = 0.14872(24) and 0.0856(10) kJ mol(-1), respectively, in the vibrational ground-state. Additional information on Stark effects and carbon isotopic species in natural abundance provided structural data and the electric dipole moments for both molecules. Ab initio calculations at the MP2 level do not reproduce the tiny torsional barriers, calling for experiments on other systems and additional theoretical models. PMID:26393883
Rodríguez-Molina, Braulio; Pérez-Estrada, Salvador
2013-01-01
The synthesis, crystallization, single crystal X-ray structure, and solid state dynamics of molecular rotor 3 provided with a high symmetry order and relatively cylindrical bicyclo[2.2.2]octane (BCO) rotator linked to mestranol fragments were investigated in this work. Using solid state 13C NMR, three rotating fragments were identified within the molecule: the BCO, the C19 methoxy and the C18 methyl groups. To determine the dynamics of the BCO group in crystals of 3 by variable temperature 1H spin-lattice relaxation (VT 1H–T1), we determined the 1H–T1 contributions from the methoxy group C19 by carrying out measurements with the methoxy-deuterated isotopologue rotor 3-d6. The contributions from the quaternary methyl group C18 were estimated by considering the differences between the VT 1H–T1 of mestranol 8 and methoxy-deuterated mestranol 8-d3. From these studies it was determined that the BCO rotator in 3 has an activation energy of only 1.15 kcal mol−1, with a barrier for site exchange that is smaller than those of methyl (Ea = 1.35 kcal mol−1) and methoxy groups (Ea = 1.91 kcal mol−1), despite their smaller moments of inertia and surface areas. PMID:23796326
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…
NASA Astrophysics Data System (ADS)
Lebed, Andrei
2006-03-01
Paramagnetic effects are shown to result in the appearance of a triplet component of order parameter in vortex phases of d- and s-wave singlet superconductors in the absence of impurities. This component, which breaks both parity and spin-rotational symmetries of Cooper pairs, is expected to be of the order of unity in a number of modern superconductors such as high-Tc, organic, MgB2, and some others. A generic phase diagram of such type-IV superconductors [1], which are singlet ones at H=0 and in the Meissner phase and characterized by singlet-triplet mixed Copper pairs, δs+iδt, in a vortex phase, is suggested. [1] A.G. Lebed, Physical Review Letters, accepted (2006).
Park, Jeong Young; Ogletree, D. Frank; Salmeron, Miquel; Ribeiro,R.A.; Canfield, P.C.; Jenks, C.J.; Thiel, P.A.
2005-11-14
Decagonal quasicrystals are made of pairs of atomic planes with pentagonal symmetry periodically stacked along a 10-fold axis. We have investigated the atomic structure of the 2-fold surface of a decagonal Al-Ni-Co quasicrystal using scanning tunneling microscopy (STM). The surface consists of terraces separated by steps of heights 1.9, 4.7, 7.8, and 12.6{angstrom} containing rows of atoms parallel to the 10-fold direction with an internal periodicity of 4{angstrom}. The rows are arranged aperiodically, with separations that follow a Fibonacci sequence and inflation symmetry. The results indicate that the surfaces are preferentially Al-terminated and in general agreement with bulk models.
NASA Technical Reports Server (NTRS)
Ma, Q.; Boulet, C.
2016-01-01
The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of selfbroadened NH3. The half-widths and shifts in the ?1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).
NASA Astrophysics Data System (ADS)
Ma, Q.; Boulet, C.
2016-06-01
The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II).
Ma, Q; Boulet, C
2016-06-14
The Robert-Bonamy formalism has been commonly used to calculate half-widths and shifts of spectral lines for decades. This formalism is based on several approximations. Among them, two have not been fully addressed: the isolated line approximation and the neglect of coupling between the translational and internal motions. Recently, we have shown that the isolated line approximation is not necessary in developing semi-classical line shape theories. Based on this progress, we have been able to develop a new formalism that enables not only to reduce uncertainties on calculated half-widths and shifts, but also to model line mixing effects on spectra starting from the knowledge of the intermolecular potential. In our previous studies, the new formalism had been applied to linear and asymmetric-top molecules. In the present study, the method has been extended to symmetric-top molecules with inversion symmetry. As expected, the inversion splitting induces a complete failure of the isolated line approximation. We have calculated the complex relaxation matrices of self-broadened NH3. The half-widths and shifts in the ν1 and the pure rotational bands are reported in the present paper. When compared with measurements, the calculated half-widths match the experimental data very well, since the inapplicable isolated line approximation has been removed. With respect to the shifts, only qualitative results are obtained and discussed. Calculated off-diagonal elements of the relaxation matrix and a comparison with the observed line mixing effects are reported in the companion paper (Paper II). PMID:27306003
Molecular symmetry with quaternions.
Fritzer, H P
2001-09-01
A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry. PMID:11666072
NASA Astrophysics Data System (ADS)
Mallick, Ritam; Bhattacharyya, Abhijit; Ghosh, Sanjay K.; Raha, Sibaji
2013-02-01
The estimate of the energy deposition rate (EDR) for neutrino pair annihilation has been carried out. The EDR for the neutrinos coming from the equatorial plane of a rotating neutron star is calculated along the rotation axis using the Cook-Shapiro-Teukolsky metric. The neutrino trajectories and hence the neutrinos emitted from the disk are affected by the redshift due to disk rotation and gravitation. The EDR is very sensitive to the value of the temperature and its variation along the disk. The rotation of the star has a negative effect on the EDR; it decreases with increase in rotational velocity.
Evidence for tetrahedral symmetry in (16)O.
Bijker, R; Iachello, F
2014-04-18
We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band. PMID:24785032
None
2011-10-06
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ?renormalizable?. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged ?vector? particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of ?massless? modes
Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…
Superalgebra and fermion-boson symmetry
Miyazawa, Hironari
2010-01-01
Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617
Start2Fold: a database of hydrogen/deuterium exchange data on protein folding and stability
Pancsa, Rita; Varadi, Mihaly; Tompa, Peter; Vranken, Wim F.
2016-01-01
Proteins fulfil a wide range of tasks in cells; understanding how they fold into complex three-dimensional (3D) structures and how these structures remain stable while retaining sufficient dynamics for functionality is essential for the interpretation of overall protein behaviour. Since the 1950's, solvent exchange-based methods have been the most powerful experimental means to obtain information on the folding and stability of proteins. Considerable expertise and care were required to obtain the resulting datasets, which, despite their importance and intrinsic value, have never been collected, curated and classified. Start2Fold is an openly accessible database (http://start2fold.eu) of carefully curated hydrogen/deuterium exchange (HDX) data extracted from the literature that is open for new submissions from the community. The database entries contain (i) information on the proteins investigated and the underlying experimental procedures and (ii) the classification of the residues based on their exchange protection levels, also allowing for the instant visualization of the relevant residue groups on the 3D structures of the corresponding proteins. By providing a clear hierarchical framework for the easy sharing, comparison and (re-)interpretation of HDX data, Start2Fold intends to promote a better understanding of how the protein sequence encodes folding and structure as well as the development of new computational methods predicting protein folding and stability. PMID:26582925
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction. PMID:26086581
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would
NASA Astrophysics Data System (ADS)
D'Yachkov, P. N.; Makaev, D. V.
2007-11-01
Every carbon single-walled nanotube (SWNT) can be generated by first mapping only two nearest-neighbor C atoms onto a surface of a cylinder and then using the rotational and helical symmetry operators to determine the remainder of the tubule [C. T. White , Phys. Rev. B 47, 5485 (1993)]. With account of these symmetries, we developed a symmetry-adapted version of a linear augmented cylindrical wave method. In this case, the cells contain only two carbon atoms, and the ab initio theory becomes applicable to any SWNT independent of the number of atoms in a translational unit cell. The approximations are made in the sense of muffin-tin (MT) potentials and local-density-functional theory only. An electronic potential is suggested to be spherically symmetrical in the regions of atoms and constant in an interspherical region up to the two essentially impenetrable cylinder-shaped potential barriers. To construct the basis wave functions, the solutions of the Schrödinger equation for the interspherical and MT regions of the tubule were sewn together using a theorem of addition for cylindrical functions, the resulting basis functions being continuous and differentiable anywhere in the system. With account of analytical equations for these functions, the overlap and Hamiltonian integrals are calculated, which permits determination of electronic structure of nanotube. We have calculated the total band structures and densities of states of the chiral and achiral, semiconducting, semimetallic, and metallic carbon SWNTs (13, 0), (12, 2), (11, 3), (10, 5), (9, 6), (8, 7), (7, 7), (12, 4), and (100, 99) containing up to the 118 804 atoms per translational unit cell. Even for the (100, 99) system with huge unit cell, the band structure can be easily calculated and the results can be presented in the standard form of four curves for the valence band plus one curve for the low-energy states of conduction band. About 150 functions produce convergence of the band structures better then
Symmetry-protected topological phases in noninteracting fermion systems
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2012-02-01
Symmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion systems with time reversal (T̂), charge conjugation (Ĉ), and/or U(1) (N̂) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T̂N̂T̂-1=N̂ or T̂N̂T̂-1=-N̂. As a result, the SPT phases of those fermion systems with different symmetry groups have different classifications. In this paper, we use Kitaev's K-theory approach to classify the gapped free-fermion phases for those possible symmetry groups. In particular, we can view the U(1) as a spin rotation. We find that superconductors with the Sz spin-rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the Sz spin-rotation symmetries are classified by Z in odd dimensions. We show that all 10 classes of gapped free-fermion phases can be realized by electron systems with certain symmetries. We also point out that, to properly describe the symmetry of a fermionic system, we need to specify its full symmetry group that includes the fermion number parity transformation (-)N̂. The full symmetry group is actually a projective symmetry group.
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Symmetry measures of the electron density.
Casanova, David; Alemany, Pere; Alvarez, Santiago
2010-10-01
In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983
Sarai, A; Takeda, Y
1989-01-01
Results of systematic base-substitution experiments suggest that the lambda repressor dimer, made of identical subunits, recognizes the "pseudo(2-fold)symmetric" operator sequence asymmetrically. Base substitutions within the consensus half of the operator affect binding more than base substitutions within the nonconsensus half of the operator. Furthermore, changing the nonconsensus base pairs to the consensus base pairs does not increase, but decreases, binding. Evidently, the two subunits of the lambda repressor dimer bind to the two halves of the operator differently. This is consistent with the recently determined crystal structure of the complex, which shows that the relative positioning of the amino acids to the DNA bases are slightly different in the two halves of the operator. The sequence-specific interactions indicated by the systematic base-substitution experiments correlate well with the locations of the specific contacts found in the complex. Thus, the amino acids of lambda repressor, mainly of alpha 3-helix and the N-terminus arm, seem to directly read-out the DNA sequence by forming specific hydrogen bonds and hydrophobic contacts to the DNA bases. The observed asymmetric recognition suggests that no recognition code governs amino acids and DNA bases in protein-DNA interactions. PMID:2771938
Matrix Representation of Symmetry Operators in Elementary Crystallography
ERIC Educational Resources Information Center
Cody, R. D.
1972-01-01
Presents the derivation of rotation and reflection matrix representation of symmetry operators as used in the initial discussion of crystal symmetry in elementary mineralogy at Iowa State University. Includes references and an appended list of matrix representations of the important crystallographic symmetry operators, excluding the trigonal and…
Search for primordial symmetry breakings in CMB
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke
2016-06-01
There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Symmetries, currents and conservation laws of self-dual gravity
NASA Astrophysics Data System (ADS)
Popov, A. D.; Bordemann, M.; Römer, H.
1996-02-01
We describe an infinite-dimensional algebra of hidden symmetries for the self-dual gravity equations. Besides the known diffeomorphism-type symmetries (affine extension of w∞ algebra), this algebra contains new hidden symmetries, which are an affine extension of the Lorentz rotations. The full symmetry algebra has both Kac-Moody and Virasoro-like generators, whose exponentiation maps solutions of the field equations to other solutions. Relations to problems of string theories are briefly discussed.
Symmetries in geometrical optics: theory
NASA Astrophysics Data System (ADS)
Szilagyi, M.; Mui, P. H.
1995-12-01
A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
Garcia-March, Miguel-Angel; Zacares, Mario; Sahu, Sarira; Ceballos-Herrera, Daniel E.
2009-05-15
We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.
Rotational dynamics of confined C60 from near-infrared Raman studies under high pressure
Zou, Y.; Liu, B.; Wang, L.; Liu, D.; Yu, S.; Wang, P.; Wang, T.; Yao, M.; Li, Q.; Zou, B.; Cui, T.; Zou, G.; Wagberg, T.; Sundqvist, B.; Mao, H.-K.
2009-12-29
Peapods present a model system for studying the properties of dimensionally constrained crystal structures, whose dynamical properties are very important. We have recently studied the rotational dynamics of C_{60} molecules confined inside single walled carbon nanotube (SWNT) by analyzing the intermediate frequency mode lattice vibrations using near-infrared Raman spectroscopy. The rotation of C_{60} was tuned to a known state by applying high pressure, at which condition C_{60} first forms dimers at low pressure and then forms a single-chain, nonrotating, polymer structure at high pressure. In the latter state the molecules form chains with a 2-fold symmetry. We propose that the C_{60} molecules in SWNT exhibit an unusual type of ratcheted rotation due to the interaction between C_{60} and SWNT in the “hexagon orientation,” and the characteristic vibrations of ratcheted rotation becomes more obvious with decreasing temperature.
Liu, Jinjun; Miller, Terry A
2014-12-26
The rotational structure of the previously observed B̃(2)A' ← X̃(2)A″ and B̃(2)A' ← Ã(2)A' laser-induced fluorescence spectra of jet-cooled cyclohexoxy radical (c-C6H11O) [ Zu, L.; Liu, J.; Tarczay, G.; Dupré, P; Miller, T. A. Jet-cooled laser spectroscopy of the cyclohexoxy radical. J. Chem. Phys. 2004 , 120 , 10579 ] has been analyzed and simulated using a spectroscopic model that includes the coupling between the nearly degenerate X̃ and Ã states separated by ΔE. The rotational and fine structure of these two states is reproduced by a 2-fold model using one set of molecular constants including rotational constants, spin-rotation constants (ε's), the Coriolis constant (Aζt), the quenched spin-orbit constant (aζed), and the vibronic energy separation between the two states (ΔE0). The energy level structure of both states can also be reproduced using an isolated-state asymmetric top model with rotational constants and effective spin-rotation constants (ε's) and without involving Coriolis and spin-orbit constants. However, the spin-orbit interaction introduces transitions that have no intensity using the isolated-state model but appear in the observed spectra. The line intensities are well simulated using the 2-fold model with an out-of-plane (b-) transition dipole moment for the B̃ ← X̃ transitions and in-plane (a and c) transition dipole moment for the B̃ ← Ã transitions, requiring the symmetry for the X̃ (Ã) state to be A″ (A'), which is consistent with a previous determination and opposite to that of isopropoxy, the smallest secondary alkoxy radical. The experimentally determined Ã-X̃ separation and the energy level ordering of these two states with different (A' and A″) symmetries are consistent with quantum chemical calculations. The 2-fold model also enables the independent determination of the two contributions to the Ã-X̃ separation: the relativistic spin-orbit interaction (magnetic effect) and the nonrelativistic
Symmetry-selective third-harmonic generation from plasmonic metacrystals.
Chen, Shumei; Li, Guixin; Zeuner, Franziska; Wong, Wing Han; Pun, Edwin Yue Bun; Zentgraf, Thomas; Cheah, Kok Wai; Zhang, Shuang
2014-07-18
Nonlinear processes are often governed by selection rules imposed by the symmetries of the molecular configurations. The most well-known examples include the role of centrosymmetry breaking for the generation of even harmonics, and the selection rule related to the rotational symmetry in harmonic generation for fundamental beams with circular polarizations. While the role of centrosymmetry breaking in second harmonic generation has been extensively studied in plasmonic systems, the investigation of selection rules pertaining to circular polarization states of harmonic generation is limited to crystals, i.e., symmetries at the atomic level. In this Letter we demonstrate the rotational symmetry dependent third harmonic generation from nonlinear plasmonic metacrystals. We show that the selection rule can be imposed by the rotational symmetry of metacrystals embedded into an isotropic organic nonlinear thin film. The results presented here may open new avenues for designing symmetry-dependent nonlinear optical responses with tailored plasmonic nanostructures. PMID:25083645
Rotations of the Regular Polyhedra
ERIC Educational Resources Information Center
Jones, MaryClara; Soto-Johnson, Hortensia
2006-01-01
The study of the rotational symmetries of the regular polyhedra is important in the classroom for many reasons. Besides giving the students an opportunity to visualize in three dimensions, it is also an opportunity to relate two-dimensional and three-dimensional concepts. For example, rotations in R[superscript 2] require a point and an angle of…
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…
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
NASA Technical Reports Server (NTRS)
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
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
Inversion symmetry protected topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Lee, Dung-Hai; Lu, Yuan-Ming
2015-03-01
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry. In this work we systematically study another class of topological phases of weakly interacting electrons protected by spatial inversion symmetry, which generally don't support stable gapless boundary states. We classify these inversion-symmetric topological insulators and superconductors in the framework of K-theory, and construct their lattice models. We also discuss quantized response functions of these inversion-protected topological phases, which serve as their experimental signatures.
Symmetry detection of auxetic behaviour in 2D frameworks
NASA Astrophysics Data System (ADS)
Mitschke, H.; Schröder-Turk, G. E.; Mecke, K.; Fowler, P. W.; Guest, S. D.
2013-06-01
A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio -1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic.
Multistability in rotating spherical shell convection.
Feudel, F; Seehafer, N; Tuckerman, L S; Gellert, M
2013-02-01
The multiplicity of stable convection patterns in a rotating spherical fluid shell heated from the inner boundary and driven by a central gravity field is presented. These solution branches that arise as rotating waves (RWs) are traced for varying Rayleigh number while their symmetry, stability, and bifurcations are studied. At increased Rayleigh numbers all the RWs undergo transitions to modulated rotating waves (MRWs) which are classified by their spatiotemporal symmetry. The generation of a third frequency for some of the MRWs is accompanied by a further loss of symmetry. Eventually a variety of MRWs, three-frequency solutions, and chaotic saddles and attractors control the dynamics for higher Rayleigh numbers. PMID:23496624
Finding the Finite Groups of Symmetries of the Sphere.
ERIC Educational Resources Information Center
Senechal, Marjorie
1990-01-01
Presented is a way of extending the list of rotation groups to include all finite subgroups of symmetries of the sphere, up to conjugation in its full group. Included is Klein's method for enumeration of the finite subgroups. (KR)
Conformal symmetry breaking and degeneracy of high-lying unflavored mesons
NASA Astrophysics Data System (ADS)
Kirchbach, Mariana; Pallares-Rivera, Adrian; Compean, Cliffor; Raya, Alfredo
2012-08-01
We show that though conformal symmetry can be broken by the dilaton, such can happen without breaking the conformal degeneracy patterns in the spectra. Our argumentation goes as follows: We departure from the gauge-gravity duality which predicts on the boundaries of the AdS5 geometry a conformal theory, associated with QCD at high temperatures, and consider S1 × S3 slicing. The inverse radius, R, of S3 relates to the temperature of the deconfinement phase transition and has to satisfy, hslashc/R gg ΛQCD. On S3, whose isometry group is SO(4), we then focus on the eigenvalue problem of the conformal Laplacian there, given by , with standing for the Casimir invariant of the so(4) algebra. This eigenvalue problem describes the spectrum of a scalar particle, to be associated with a qbar q system. Such a spectrum is characterized by a (K + l)2-fold degeneracy of its levels, with K in [0, ∞). We then break the conformal S3 metric, ds2 = dχ2 + sin2 χ(dθ2 + sin2θdvarphi2) -in polar chi,θ, and azimuthal varphi coordinates- according to, ds~2 = e-bχ((1 + b2/4)dχ2 + sin2 chi(dθ2 + sin2θdvarphi2)), and attribute the symmetry breaking scale bhslash2c2/R2 to the dilaton. Next we show that the above metric deformation is equivalent to a breaking of the conformal curvature of S3 by a term proportional to b cot χ, and that the perturbed conformal Laplacian is equivalent to , with cκ a representation constant, and being again an so(4) Casimir invariant, but this time in a representation unitarily nonequivalent to the 4D rotational one. As long as the spectra before and after the symmetry breaking happen to be determined each by eigenvalues of a Casimir invariant of an so(4), no matter whether or not in a representation that generates the orthogonal group SO(4) as a subgroup of the conformal group SO(2,4), the degeneracy patterns remain unaltered though the conformal symmetry breaks at the level of the representation of the algebra. We fit the S3 radius and the hslash2c
Lorentz symmetry breaking effects on relativistic EPR correlations
NASA Astrophysics Data System (ADS)
Belich, H.; Furtado, C.; Bakke, K.
2015-09-01
Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB (Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.
The symmetry properties of planetary magnetic fields
Raedler, K.H. ); Ness, N.F. )
1990-03-01
This paper provides a comparative study of the geometrical structures of the magnetic fields of Earth, Jupiter, Saturn, and Uranus, starting from the traditional multipolar representations of these fields. For Earth, Jupiter, and Saturn the centered dipole, quadrupole, and octupole contributions are included, while at Uranus, only the dipole and quadrupole contributoins are considered. The magnetic fields are analyzed by decomposing them into those parts which have simple symmetry properties with respect to the rotation axis and the equatorial plane. It is found that there are a number of common features of the magnetic fields of Earth and Jupiter. Compared to Earth and Jupiter, the Saturnian field exhibits not only a high degree of symmetry about the rotation axis, by now rather well known, but also a high degree of antisymmetry about the equatorial plane. The Uranian field shows strong deviations from both such symmetries. Nevertheless, there remain features common to all four planets. The implications of these results for dynamo models are discussed. With a vgiew to Cowling's theorem the symmetry of the fields is investigated with respect to not only the rotation axis but also to other axes intersecting the plaentary center. Surprisingly, the high degree of asymmetry of the Uranian field that is observed with respect to the rotation axis reduces considerably to being compare to that for Earth or Jupiter when the appropriate axis is employed.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
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…
Universal features of spin transport and breaking of unitary symmetries
NASA Astrophysics Data System (ADS)
Jacquod, Ph.; Adagideli, İ.
2013-07-01
When time-reversal symmetry is broken, quantum coherent systems with and without spin rotational symmetry exhibit the same universal behavior in their electric transport properties. We show that spin transport discriminates between these two cases. In systems with large charge conductance, spin transport is essentially insensitive to the breaking of time-reversal symmetry. However, in the opposite limit of a single exit channel, spin currents vanish identically in the presence of time-reversal symmetry, but are turned on by breaking it with an orbital magnetic field.
Template-free wavelet-based detection of local symmetries.
Puspoki, Zsuzsanna; Unser, Michael
2015-10-01
Our goal is to detect and group different kinds of local symmetries in images in a scale- and rotation-invariant way. We propose an efficient wavelet-based method to determine the order of local symmetry at each location. Our algorithm relies on circular harmonic wavelets which are used to generate steerable wavelet channels corresponding to different symmetry orders. To give a measure of local symmetry, we use the F-test to examine the distribution of the energy across different channels. We provide experimental results on synthetic images, biological micrographs, and electron-microscopy images to demonstrate the performance of the algorithm. PMID:26011883
Weak Lie symmetry and extended Lie algebra
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).
NASA Astrophysics Data System (ADS)
Walker, A. R. Hight; Suenram, R. D.; Samuels, Alan; Jensen, James; Ellzy, Michael W.; Lochner, J. Michael; Zeroka, Daniel
2001-05-01
As part of an effort to examine the possibility of using molecular-beam Fourier-transform microwave spectroscopy to unambiguously detect and monitor chemical warfare agents, we report the first observation and assignment of the rotational spectrum of the nerve agent Sarin (GB) (Methylphosphonofluoridic acid 1-methyl-ethyl ester, CAS #107-44-8) at frequencies between 10 and 22 GHz. Only one of the two low-energy conformers of this organophosphorus compound (C4H10FO2P) was observed in the rotationally cold (Trot<2 K) molecular beam. The experimental asymmetric-rotor ground-state rotational constants of this conformer are A=2874.0710(9) MHz, B=1168.5776(4) MHz, C=1056.3363(4) MHz (Type A standard uncertainties are given, i.e., 1σ), as obtained from a least-squares analysis of 74 a-, b-, and c-type rotational transitions. Several of the transitions are split into doublets due to the internal rotation of the methyl group attached to the phosphorus. The three-fold-symmetry barrier to internal rotation estimated from these splittings is 677.0(4) cm-1. Ab initio electronic structure calculations using Hartree-Fock, density functional, and Moller-Plesset perturbation theories have also been made. The structure of the lowest-energy conformer determined from a structural optimization at the MP2/6-311G** level of theory is consistent with our experimental findings.
Rotations in a Vertebrate Setting
NASA Astrophysics Data System (ADS)
McCollum, Gin
2003-05-01
Rotational movements of the head are often considered to be measured in a single three dimensional coordinate system implemented by the semicircular canals of the vestibular system of the inner ear. However, the vertebrate body -- including the nervous system -- obeys rectangular symmetries alien to rotation groups. At best, nervous systems mimic the physical rotation group in a fragmented way, only partially reintegrating physical movements in whole organism responses. The vestibular canal reference frame is widely used in nervous systems, for example by eye movements. It is used to some extent even in the cerebrum, as evidenced by the remission of hemineglect -- in which half of space is ignored -- when the vestibular system is stimulated. However, reintegration of space by the organism remains incomplete. For example, compensatory eye movements (which in most cases aid visual fixation) may disagree with conscious self-motion perception. In addition, movement-induced nausea, illusions, and cue-free perceptions demonstrate symmetry breaking or incomplete spatial symmetries. As part of a long-term project to investigate rotation groups in nervous systems, we have analyzed the symmetry group of a primary vestibulo-spinal projection.
Sekhar Chivukula
2010-01-08
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level. Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter.
Gray, J E; Vogt, A
1997-01-01
Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation. PMID:9224554
NASA Astrophysics Data System (ADS)
Carr, Lincoln D.; Garcia-March, Miguel Angel; Vijande, Javier; Ferrando, Albert
2015-05-01
We explore the nonequilibrium quantum dynamics of partial symmetry-breaking in ring Bose-Einstein condensates described by the Bose-Hubbard Hamiltonian with an external potential. Using exact diagonalization and group theory for small systems, we establish three new concepts to predict and characterize the dynamics after a quantum quench: symmetry memory, critical symmetry-breaking strength, and the symmetry gap. Critical symmetry breaking can manifest in current reversals, but is most clearly observed in the symmetry memory operator, based on unitary rotations. Funded by NSF, AFOSR, AvH Foundation, and MINECO.
Rotational partition functions for symmetric-top molecules
NASA Astrophysics Data System (ADS)
McDowell, Robin S.
1990-08-01
An improved expression is found for the rotational partition functions of symmetric-top molecules. The expression includes the effect of nuclear spin for molecules of C(3v) symmetry. The effect that centrifugal distortion of the rotating molecules has on these rigid-rotator formulations is considered. The nuclear-spin correction is generalized to symmetric-top molecules of other symmetries. The treatment is extended to nonplanar molecules that exhibit inversion doubling, with particular attention given to NH3.
Acoustic streaming flows and sample rotation control
NASA Astrophysics Data System (ADS)
Trinh, Eugene
1998-11-01
Levitated drops in a gas can be driven into rotation by altering their surrounding convective environment. When these drops are placed in an acoustic resonant chamber, the symmetry characteristics of the steady streaming flows in the vicinity of the drops determine the rotational motion of the freely suspended fluid particles. Using ultrasonic standing waves around 22 kHz and millimeter-size electrostatically levitated drops, we have investigated the correlation between the convective flow characteristics and their rotational behavior. The results show that accurate control of the drop rotation axis and rate can be obtained by carefully modifying the symmetry characteristics of the chamber, and that the dominant mechanism for rotation drive is the drag exerted by the air flow over the drop surface. In addition, we found that the rotational acceleration depends on the drop viscosity, suggesting that this torque is initially strongly influenced by differential flows within the drop itself. [Work sponsored by NASA].
Facial symmetry assessment based on geometric features
NASA Astrophysics Data System (ADS)
Xu, Guoping; Cao, Hanqiang
2015-12-01
Face image symmetry is an important factor affecting the accuracy of automatic face recognition. Selecting high symmetrical face image could improve the performance of the recognition. In this paper, we proposed a novel facial symmetry evaluation scheme based on geometric features, including centroid, singular value, in-plane rotation angle of face and the structural similarity index (SSIM). First, we calculate the value of the four features according to the corresponding formula. Then, we use fuzzy logic algorithm to integrate the value of the four features into a single number which represents the facial symmetry. The proposed method is efficient and can adapt to different recognition methods. Experimental results demonstrate its effectiveness in improving the robustness of face detection and recognition.
Breaking the Symmetry in Molecular Nanorings
2016-01-01
Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
Electric-magnetic symmetry and Noether's theorem
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Barnett, Stephen M.
2012-12-01
In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.
Breaking the Symmetry in Molecular Nanorings.
Gong, Juliane Q; Favereau, Ludovic; Anderson, Harry L; Herz, Laura M
2016-01-21
Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
Demonstrating lattice symmetry protection in topological crystalline superconductors
NASA Astrophysics Data System (ADS)
Liu, Xiong-Jun; He, James J.; Law, K. T.
2014-12-01
We propose to study the lattice symmetry protection of Majorana zero bound modes in topological crystalline superconductors (SCs). With an induced s -wave superconductivity in the (001 ) surface of the topological crystalline insulator Pb1 -xSnxTe , which has a C4 rotational symmetry, we show a class of two-dimensional topological SCs with four Majorana modes obtained in each vortex core, while only two of them are protected by the cyclic symmetry. Furthermore, applying an in-plane external field can break the fourfold symmetry and lifts the Majorana modes to finite energy states in general. Surprisingly, we show that even the C4 symmetry is broken; two Majorana modes are restored exactly one time whenever the in-plane field varies π /2 , i.e., 1 /4 -cycle in the direction. This phenomenon has a profound connection to the fourfold cyclic symmetry of the original crystalline SC and uniquely demonstrates the lattice-symmetry protection of the Majorana modes. We further generalize these results to the system with generic C2 N symmetry, and show that the symmetry class of the topological crystalline SC can be demonstrated by the 2 N times of restoration of two Majorana modes when the direction of the external symmetry-breaking field varies one cycle.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries of Spectral Problems
NASA Astrophysics Data System (ADS)
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Translational Symmetry-Breaking for Spiral Waves
NASA Astrophysics Data System (ADS)
LeBlanc, V. G.; Wulff, C.
2000-10-01
Spiral waves are observed in numerous physical situations, ranging from Belousov-Zhabotinsky (BZ) chemical reactions, to cardiac tissue, to slime-mold aggregates. Mathematical models with Euclidean symmetry have recently been developed to describe the dynamic behavior (for example, meandering) of spiral waves in excitable media. However, no physical experiment is ever infinite in spatial extent, so the Euclidean symmetry is only approximate. Experiments on spiral waves show that inhomogeneities can anchor spirals and that boundary effects (for example, boundary drifting) become very important when the size of the spiral core is comparable to the size of the reacting medium. Spiral anchoring and boundary drifting cannot be explained by the Euclidean model alone. In this paper, we investigate the effects on spiral wave dynamics of breaking the translation symmetry while keeping the rotation symmetry. This is accomplished by introducing a small perturbation in the five-dimensional center bundle equations (describing Hopf bifurcation from one-armed spiral waves) which is SO(2)-equivariant but not equivariant under translations. We then study the effects of this perturbation on rigid spiral rotation, on quasi-periodic meandering and on drifting.
Crawford, R J; Kearns, M P
2003-10-01
Rotational moulding promises designers attractive economics and a low-pressure process. The benefits of rotational moulding are compared here with other manufacturing methods such as injection and blow moulding. PMID:14603714
Astronomers combined 146 exposures taken by NASA's Hubble SpaceTelescope to make this 73-frame movie of the asteroid Vesta's rotation.Vesta completes a rotation every 5.34 hours.âº Asteroid and...
Symmetry Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
Boyer, K.; Hammel, J.E.; Longmire, C.L.; Nagle, D.E.; Ribe, F.L.; Tuck, J.L.
1961-10-24
ABS>A method and device are described for obtaining fusion reactions. The basic concept is that of using crossed electric and magnetic fields to induce a plasma rotation in which the ionized particles follow a circumferential drift orbit on wldch a cyclotron mode of motion is superimposed, the net result being a cycloidal motion about the axis of symmetry. The discharge tube has a radial electric field and a longitudinal magnetic field. Mirror machine geometry is utilized. The device avoids reliance on the pinch effect and its associated instability problems. (AEC)
Spin-stabilized magnetic levitation without vertical axis of rotation
Romero, Louis; Christenson, Todd; Aaronson, Gene
2009-06-09
The symmetry properties of a magnetic levitation arrangement are exploited to produce spin-stabilized magnetic levitation without aligning the rotational axis of the rotor with the direction of the force of gravity. The rotation of the rotor stabilizes perturbations directed parallel to the rotational axis.
Aspects of emergent symmetries
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.
2016-03-01
These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
An Exact SU(2) Symmetry and Persistent Spin Helix ina Spin-orbit Coupled System
Bernevig, B.A.; Orenstein, J.; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2007-01-22
Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.
An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
Bernevig, Andrei
2010-02-10
Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the [110] Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.
New symmetry of the cluster model
NASA Astrophysics Data System (ADS)
Gai, Moshe
2015-10-01
A new approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts rotation-vibration structure with rotational band of an oblate equilateral triangular spinning top with a 𝒟3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Our measurement of the new 22+ and the measured of the new 5- state in 12C fit very well to the predicted (ground state) rotational band structure with the sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a 𝒟3h symmetry was observed in triatomic molecules, and it is observed in 12C for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1-) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C.
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
Statistical palaeomagnetic field modelling and symmetry considerations
NASA Astrophysics Data System (ADS)
Hulot, G.; Bouligand, C.
2005-06-01
In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has
Symmetry, Equivalence and Self-Assembly
NASA Astrophysics Data System (ADS)
Douglas, Jack
2006-03-01
Molecular self-assembly at equilibrium is central to the formation of many biological structures and the emulation of this process through the creation of synthetic counterparts offers great promise for nanofabrication. The central problems in this field are an understanding of how the symmetry of the interacting particles encodes the geometrical structure of the organized structure and the nature of the thermodynamic transitions involved. Our approach is inspired by the self-assembly of actin, tubulin and icosahedral structures of plant and animal viruses. We observe chain, membrane,`nanotube' and hollow icosahedron structures using `equivalent' particles exhibiting an interplay between directional (dipolar and multi-polar) interactions and short-range (van der Waals) interactions. Specifically, a dipolar potential (continuous rotational symmetry) gives rise to chain formation, while potentials having discrete rotational symmetries (e.g., square quadrupole or triangular ring of dipoles) led to the self-organization of nanotube and icosahedral structures with some resemblance to tubulin and icosahedral viruses. The simulations are compared to theoretical models of molecular self-assembly, especially in the case of dipolar fluids where the corresponding analytic theory of equilibrium polymerization is well developed. These computations give insights into the design elements required for the development of synthetic systems exhibiting this type of organization.
Symmetry protected topological orders and the group cohomology of their symmetry group
NASA Astrophysics Data System (ADS)
Chen, Xie; Gu, Zheng-Cheng; Liu, Zheng-Xin; Wen, Xiao-Gang
2013-04-01
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain is the first example of SPT phases which is protected by SO(3) spin rotation symmetry. The topological insulator is another example of SPT phases which are protected by U(1) and time-reversal symmetries. In this paper, we show that interacting bosonic SPT phases can be systematically described by group cohomology theory: Distinct d-dimensional bosonic SPT phases with on-site symmetry G (which may contain antiunitary time-reversal symmetry) can be labeled by the elements in H1+d[G,UT(1)], the Borel (1+d)-group-cohomology classes of G over the G module UT(1). Our theory, which leads to explicit ground-state wave functions and commuting projector Hamiltonians, is based on a new type of topological term that generalizes the topological θ term in continuous nonlinear σ models to lattice nonlinear σ models. The boundary excitations of the nontrivial SPT phases are described by lattice nonlinear σ models with a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear σ models. As a result, the symmetry G must be realized as a non-on-site symmetry for the low-energy boundary excitations, and those boundary states must be gapless or degenerate. As an application of our result, we can use H1+d[U(1)⋊Z2T,UT(1)] to obtain interacting bosonic topological insulators (protected by time reversal Z2T and boson number conservation), which contain one nontrivial phase in one-dimensional (1D) or 2D and three in 3D. We also obtain interacting bosonic topological superconductors (protected by time-reversal symmetry only), in term of H1+d[Z2T,UT(1)], which contain one nontrivial phase in odd spatial dimensions and none for even dimensions. Our result is much more general than the above two examples, since it
Radial Symmetry in a Chimaeric Glutamate Receptor Pore
Wilding, Timothy J; Lopez, Melany N.; Huettner, James E.
2014-01-01
Ionotropic glutamate receptors comprise two conformationally different A/C and B/D subunit pairs. Closed channels exhibit 4-fold radial symmetry in the transmembrane domain (TMD) but transition to 2-fold dimer-of-dimers symmetry for extracellular ligand binding and N-terminal domains. Here, to evaluate symmetry in open pores we analyzed interaction between the Q/R editing site near the pore loop apex and the transmembrane M3 helix of kainate receptor subunit GluK2. Chimaeric subunits that combined the GluK2 TMD with extracellular segments from NMDA receptors, which are obligate heteromers, yielded channels made up of A/C and B/D subunit pairs with distinct substitutions along M3 and/or Q/R site editing status, in an otherwise identical homotetrameric TMD. Our results indicate that Q/R site interaction with M3 occurs within individual subunits and is essentially the same for both A/C and B/D subunit conformations, suggesting that 4-fold pore symmetry persists in the open state. PMID:24561802
ERIC Educational Resources Information Center
Lekner, John
2008-01-01
Any free-particle wavepacket solution of Schrodinger's equation can be converted by differentiations to wavepackets rotating about the original direction of motion. The angular momentum component along the motion associated with this rotation is an integral multiple of [h-bar]. It is an "intrinsic" angular momentum: independent of origin and…
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
Stability of the rotating SU(3) Skyrmion
Akiyama, Satoru; Kawabata, Masahiro
2007-11-01
The profile functions of the SU(3) Skyrme soliton are investigated for the octet, decuplet, and antidecuplet baryons by the mean field approach. In this approach, the profile functions are affected by the spatial rotation, the flavor rotation, and the flavor symmetry breaking. The solitons are stable only in the restricted areas of the parameter space for each multiplet. When the flavor symmetry breaking is large, the area for the antidecuplet is narrow compared to those for the octet and decuplet. The parameters are determined by the baryon mass spectrum, and the deformation of the soliton has sizable effects on the masses.
Test of Lorentz symmetry with trapped ions
NASA Astrophysics Data System (ADS)
Pruttivarasin, Thaned
2016-05-01
The outcome of an experiment should not depend on the orientation of the apparatus in space. This important cornerstone of physics is deeply engrained into the Standard Model of Physics by requiring that all fields must be Lorentz invariant. However, it is well-known that the Standard Model is incomplete. Some theories conjecture that at the Planck scale Lorentz symmetry might be broken and measurable at experimentally accessible energy scales. Therefore, a search for violation of Lorentz symmetry directly probes physics beyond the Standard model. We present a novel experiment utilizing trapped calcium ions as a direct probe of Lorentz-violation in the electron-photon sector. We monitor the energy between atomic states with different orientations of the electronic wave-functions as they rotate together with the motion of the Earth. This is analogous to the famous Michelson-Morley experiment. To remove magnetic field noise, we perform the experiment with the ions prepared in the decoherence-free states. Our result improves on the most stringent bounds on Lorentz symmetry for electrons by 100 times. The experimental scheme is readily applicable to many ion species, hence opening up paths toward much improved test of Lorentz symmetry in the future. (Ph. D. Advisor: Hartmut Haeffner, University of California, Berkeley).
NASA Astrophysics Data System (ADS)
Fang, Yi-Nan; Dong, Guo-Hui; Zhou, Duan-Lu; Sun, Chang-Pu
2016-04-01
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking. Supported by the National Natural Science Foundation of China under Grant Nos. 11421063, 11534002, 11475254 and the National 973 Program under Grant Nos. 2014CB921403, 2012CB922104, and 2014CB921202
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Ismael, Jenann Tareq
1997-04-01
Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.
NASA Astrophysics Data System (ADS)
West, Carl T.; Kottos, Tsampikos; Prosen, Tomaz
2010-03-01
We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time PT symmetry. For a value γPT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT-phase. Our results will have applications to the design of optical elements with PT-symmetry.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
NASA Astrophysics Data System (ADS)
Moore, Gregory
The vanishing of the one-loop string cosmological constant in nontrivial non supersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions. For special backgrounds the string theory has an extra symmetry, expressed as a transformation on moduli space. When left- and right-moving wave functions transform in different representations of this symmetry the cosmological constant must vanish. Specific examples of the mechanism are given at one loop for theories in two and four dimensions. Various suggestions are made for the higher loop extension of this idea.
The symmetry properties of planetary magnetic fields
NASA Technical Reports Server (NTRS)
Raedler, Karl-Heinz; Ness, Norman F.
1990-01-01
This paper provides a comparative study of the geometrical structures of the magnetic fields of earth, Jupiter, Saturn, and Uranus, starting from the traditional multipolar representations of these fields. For earth, Jupiter, and Saturn, the centered dipole, quadrupole, and octupole contributions are included, while at Uranus only the dipole and quadrupole contributions are considered. It is found that there are a number of common features of the magnetic fields of earth and Jupiter. Compared to earth and Jupiter, the Saturnian field exhibits not only a high degree of symmetry about the rotation axis but also a high degree of antisymmetry about the equatorial plane. The Uranian field shows strong deviations from both such symmetries. Nevertheless, there remain features common to all four planets.
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2016-03-01
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "nonsymmorphic"-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M -point ordering vectors are worked out in detail. To show that our results generally apply to 2 D hexagonal lattices, we develop a general low-energy SU(3 ) theory of (spinless) saddle-point electrons.
NASA Astrophysics Data System (ADS)
Schou, Jesper; Beck, John G.
2001-01-01
Simple convection models estimate the depth of supergranulation at approximately 15,000 km which suggests that supergranules should rotate at the rate of the plasma in the outer 2% of the Sun by radius. Previous measurements (Snodgrass & Ulrich, 1990; Beck & Schou, 2000) found that supergranules rotate significantly faster than this, with a size-dependent rotation rate. We expand on previous work and show that the torsional oscillation signal seen in the supergranules tracks that obtained for normal modes. We also find that the amplitudes and lifetimes of the supergranulation are size dependent.
NASA Astrophysics Data System (ADS)
Dziembowski, W.
Sunspot observations made by Johannes Hevelius in 1642 - 1644 are the first ones providing significant information about the solar differential rotation. In modern astronomy the determination of the rotation rate is done in a routine way by measuring positions of various structures on the solar surface as well as by studying the Doppler shifts of spectral lines. In recent years a progress in helioseismology enabled determination of the rotation rate in the layers inaccessible for direct observations. There are still uncertainties concerning, especially, the temporal variations of the rotation rate and its behaviour in the radiative interior. We are far from understanding the observations. Theoretical works have not yet resulted in a satisfactory model for the angular momentum transport in the convective zone.
NASA Astrophysics Data System (ADS)
Fletcher, N. H.; Tarnopolsky, A. Z.; Lai, J. C. S.
2002-03-01
Free rotational aerophones such as the bullroarer, which consists of a wooden slat whirled around on the end of a string, and which emits a loud pulsating roar, have been used in many ancient and traditional societies for ceremonial purposes. This article presents an experimental and theoretical investigation of this instrument. The aerodynamics of rotational behavior is elucidated, and relates slat rotation frequency to slat width and velocity through the air. Analysis shows that sound production is due to generation of an oscillating-rotating dipole across the slat, the role of the vortices shed by the slat being relatively minor. Apparent discrepancies between the behavior of a bullroarer slat and a slat mounted on an axle in a wind tunnel are shown to be due to viscous friction in the bearings of the wind-tunnel experiment.
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
NASA Astrophysics Data System (ADS)
Maes, Christian; Salazar, Alberto
2014-01-01
In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary-driven particle systems such as the open Kawasaki lattice gas and the zero-range model. As a measure of time-symmetric dynamical activity over time T we count the difference (Nℓ - Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo-type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.
ERIC Educational Resources Information Center
McGehe, Carol
1991-01-01
Presents math activities, problems, and games for teaching elementary students to recognize the world's natural symmetry and understand the mathematical qualities it represents; suggests activities with construction paper, blocks, and calculators. Instructions for using the calculator to create palindromes are included. (SM)
Asymmetric error field interaction with rotating conducting walls
Paz-Soldan, C.; Brookhart, M. I.; Hegna, C. C.; Forest, C. B.
2012-07-15
The interaction of error fields with a system of differentially rotating conducting walls is studied analytically and compared to experimental data. Wall rotation causes eddy currents to persist indefinitely, attenuating and rotating the original error field. Superposition of error fields from external coils and plasma currents are found to break the symmetry in wall rotation direction. The vacuum and plasma eigenmodes are modified by wall rotation, with the error field penetration time decreased and the kink instability stabilized, respectively. Wall rotation is also predicted to reduce error field amplification by the marginally stable plasma.
Gauging without initial symmetry
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Σ, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Σ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ∼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
Spontaneous chiral symmetry breaking by hydromagnetic buoyancy
NASA Astrophysics Data System (ADS)
Chatterjee, Piyali; Mitra, Dhrubaditya; Brandenburg, Axel; Rheinhardt, Matthias
2011-08-01
Evidence for the parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the nonhelical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of this magnetohydrodynamic instability appears to be the first of its kind and has properties similar to those in chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are discussed.
Hydrodynamic interactions between rotating helices.
Kim, MunJu; Powers, Thomas R
2004-06-01
Escherichia coli bacteria use rotating helical flagella to swim. At this scale, viscous effects dominate inertia, and there are significant hydrodynamic interactions between nearby helices. These interactions cause the flagella to bundle during the "runs" of bacterial chemotaxis. Here we use slender-body theory to solve for the flow fields generated by rigid helices rotated by stationary motors. We determine how the hydrodynamic forces and torques depend on phase and phase difference, show that rigid helices driven at constant torque do not synchronize, and solve for the flows. We also use symmetry arguments based on kinematic reversibility to show that for two rigid helices rotating with zero phase difference, there is no time-averaged attractive or repulsive force between the helices. PMID:15244620
Gravity from Lorentz Symmetry Violation
Potting, Robertus
2006-06-19
In general relativity, the masslessness of gravitons can be traced to symmetry under diffeomorphisms. In this talk, we consider another possibility, whereby the masslessness arises from spontaneous violation of Lorentz symmetry.
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.
Chivukula, R. Sekhar; Simmons, Elizabeth H.; Di Chiara, Stefano; Foadi, Roshan
2009-11-01
We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zb{sub L}b{sub L} coupling from large corrections. This 'doublet-extended standard model' adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4)xU(1){sub X}{approx}SU(2){sub L}xSU(2){sub R}xP{sub LR}xU(1){sub X} symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2){sub L}xU(1){sub Y} electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M{yields}0) and standard-model-like (M{yields}{infinity}) limits. In this simple model, we find that the experimental limits on the Zb{sub L}b{sub L} coupling favor smaller M while the presence of a potentially sizable negative contribution to {alpha}T strongly favors large M. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to {alpha}T, {alpha}S, and the Zb{sub L}b{sub L} coupling in this model arise from an effective operator coupling right-handed top quarks to the Z boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to {alpha}T and the Zb{sub L}b{sub L} coupling, while leaving the standard model contributions essentially unchanged.
Surface Broken Symmetry on Orthorhombic Double-layer Sr3(Ru1-xMnx)2 O7
NASA Astrophysics Data System (ADS)
Chen, Chen; Nascimento, V. B.; Diao, Zhenyu; Zhang, Jiandi; Jin, Rongying; Plummer, E. W.
The surface of double-layered ruthenate Sr3Ru2O7 exhibits octahedra tilt distortion and an enhanced rotational distortion caused by the broken symmetry. Previous LEED IV calculation reveals that the tilt angle is (2.5+/-1.7)°at 80 K (B. Hu et. al., Physical Review B 81, 184104 (2010). A glideline symmetry and a mirror symmetry along this direction are both broken. Results from LEED IV simulations show that both broken symmetries originate from the emergence of surface tilt. The degree of broken symmetry is more sensitive to the tilt angle, thus producing a smaller error than from conventional LEED IV calculation. When Mn doping is induced into the compound, the tilt is removed and the symmetry of the LEED pattern returns to what is expected for rotation, two glide planes and four-fold symmetry. Supported by NSF DMR-1002622.
Dynamical Symmetries in Classical Mechanics
ERIC Educational Resources Information Center
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
Reflections on Symmetry and Proof
ERIC Educational Resources Information Center
Merrotsy, Peter
2008-01-01
The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…
The Platonic Solids from Their Rotation Groups
ERIC Educational Resources Information Center
Grovei, Larry
2005-01-01
The five Platonic solids are constructed (as graphs) from their rotational symmetry groups. The constructions are based on an idea of Bertram Kostant and are quite simple; conjugacy classes in the group are the vertices of the graphs and products determine adjacency.
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Chiral symmetry and pentaquarks
Dmitri Diakonov
2004-07-01
Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
NASA Technical Reports Server (NTRS)
Dickey, Jean O.
1995-01-01
The study of the Earth's rotation in space (encompassing Universal Time (UT1), length of day, polar motion, and the phenomena of precession and nutation) addresses the complex nature of Earth orientation changes, the mechanisms of excitation of these changes and their geophysical implications in a broad variety of areas. In the absence of internal sources of energy or interactions with astronomical objects, the Earth would move as a rigid body with its various parts (the crust, mantle, inner and outer cores, atmosphere and oceans) rotating together at a constant fixed rate. In reality, the world is considerably more complicated, as is schematically illustrated. The rotation rate of the Earth's crust is not constant, but exhibits complicated fluctuations in speed amounting to several parts in 10(exp 8) [corresponding to a variation of several milliseconds (ms) in the Length Of the Day (LOD) and about one part in 10(exp 6) in the orientation of the rotation axis relative to the solid Earth's axis of figure (polar motion). These changes occur over a broad spectrum of time scales, ranging from hours to centuries and longer, reflecting the fact that they are produced by a wide variety of geophysical and astronomical processes. Geodetic observations of Earth rotation changes thus provide insights into the geophysical processes illustrated, which are often difficult to obtain by other means. In addition, these measurements are required for engineering purposes. Theoretical studies of Earth rotation variations are based on the application of Euler's dynamical equations to the problem of finding the response of slightly deformable solid Earth to variety of surface and internal stresses.
NASA Astrophysics Data System (ADS)
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
NASA Technical Reports Server (NTRS)
1979-01-01
In aircraft turbine engine research, certain investigations require extremely precise measurement of the position of a rotating part, such as the rotor, a disc-like part of the engine's compressor which revolves around a shaft at extremely high speeds. For example, in studies of airflow velocity within a compressor, researchers need to know-for data correlation the instantaneous position of a given spot on the rotor each time a velocity measurement is made. Earlier methods of measuring rotor shaft angle required a physical connection to the shaft, which limited the velocity of the rotating object.
Finite element forced vibration analysis of rotating cyclic structures
NASA Technical Reports Server (NTRS)
Elchuri, V.; Smith, G. C. C.
1981-01-01
A capability was added to the general purpose finite element program NASTRAN Level 17.7 to conduct forced vibration analysis of tuned cyclic structures rotating about their axes of symmetry. The effects of Coriolis and centripetal accelerations together with those due to linear acceleration of the axis of rotation were included. The theoretical development of this capability is presented.
Rotational Energy Transfer in N2
NASA Technical Reports Server (NTRS)
Huo, Winifred M.
1994-01-01
Using the N2-N2 intermolecular potential of van der Avoird et al. rotational energy transfer cross sections have been calculated using both the coupled state (CS) and infinite order sudden (IOS) approximations. The rotational energy transfer rate constants at 300 K, calculated in the CS approximation, are in reasonable agreement with the measurements of Sitz and Farrow. The IOS approximation qualitatively reproduces the dependence of the rate constants on the rotational quantum numbers, but consistently overestimates their magnitudes. The treatment of exchange symmetry will be discussed.
Symmetries in laminated composite plates
NASA Technical Reports Server (NTRS)
Noor, A. K.
1976-01-01
The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.
Polarization properties of optical metasurfaces of different symmetries
NASA Astrophysics Data System (ADS)
Kruk, Sergey S.; Poddubny, Alexander N.; Powell, David A.; Helgert, Christian; Decker, Manuel; Pertsch, Thomas; Neshev, Dragomir N.; Kivshar, Yuri S.
2015-05-01
Optical metasurfaces have become a new paradigm for creating flat optical devices. While being typically an order of magnitude thinner than the wavelength of light, metasurfaces allow control of the phase of propagating light waves across the full 2 π range and therefore enable the realization of optical elements such as lenses, waveplates, and beam converters. Currently one of the limiting factors of functional metasurfaces is their small range of operational angles. Here we demonstrate both theoretically and experimentally that the angular range can be broadened by increasing the rotational symmetry of metasurfaces. We develop an analytical model based on the discrete dipole approximation that quantitatively describes the response of metasurfaces under oblique excitation. It shows that the effective optical symmetry is doubled for structures with odd rotational symmetry, increasing the angular range correspondingly. We apply and experimentally verify our model for metasurfaces consisting of identical meta-atoms, arranged into square lattices, hexagonal lattices, and on the vertices of a Penrose tiling. The results demonstrate the increasing angular performance with increasing rotational symmetry.
A vault ribonucleoprotein particle exhibiting 39-fold dihedral symmetry
Kato, Koji; Tanaka, Hideaki; Sumizawa, Tomoyuki; Yoshimura, Masato; Yamashita, Eiki; Iwasaki, Kenji; Tsukihara, Tomitake
2008-05-01
A vault from rat liver was crystallized in space group C2. Rotational symmetry searches indicated that the particle has 39-fold dihedral symmetry. Vault is a 12.9 MDa ribonucleoprotein particle with a barrel-like shape, two protruding caps and an invaginated waist structure that is highly conserved in a wide variety of eukaryotes. Multimerization of the major vault protein (MVP) is sufficient to assemble the entire exterior shell of the barrel-shaped vault particle. Multiple copies of two additional proteins, vault poly(ADP-ribose) polymerase (VPARP) and telomerase-associated protein 1 (TEP1), as well as a small vault RNA (vRNA), are also associated with vault. Here, the crystallization of vault particles is reported. The crystals belong to space group C2, with unit-cell parameters a = 708.0, b = 385.0, c = 602.9 Å, β = 124.8°. Rotational symmetry searches based on the R factor and correlation coefficient from noncrystallographic symmetry (NCS) averaging indicated that the particle has 39-fold dihedral symmetry.
Performance improvements of symmetry-breaking reflector structures in nonimaging devices
Winston, Roland
2004-01-13
A structure and method for providing a broken symmetry reflector structure for a solar concentrator device. The component of the optical direction vector along the symmetry axis is conserved for all rays propagated through a translationally symmetric optical device. This quantity, referred to as the translational skew invariant, is conserved in rotationally symmetric optical systems. Performance limits for translationally symmetric nonimaging optical devices are derived from the distributions of the translational skew invariant for the optical source and for the target to which flux is to be transferred. A numerically optimized non-tracking solar concentrator utilizing symmetry-breaking reflector structures can overcome the performance limits associated with translational symmetry.
Maximal acceleration is non-rotating
NASA Astrophysics Data System (ADS)
Page, Don N.
1998-06-01
In a stationary axisymmetric spacetime, the angular velocity of a stationary observer whose acceleration vector is Fermi-Walker transported is also the angular velocity that locally extremizes the magnitude of the acceleration of such an observer. The converse is also true if the spacetime is symmetric under reversing both t and 0264-9381/15/6/020/img1 together. Thus a congruence of non-rotating acceleration worldlines (NAW) is equivalent to a stationary congruence accelerating locally extremely (SCALE). These congruences are defined completely locally, unlike the case of zero angular momentum observers (ZAMOs), which requires knowledge around a symmetry axis. The SCALE subcase of a stationary congruence accelerating maximally (SCAM) is made up of stationary worldlines that may be considered to be locally most nearly at rest in a stationary axisymmetric gravitational field. Formulae for the angular velocity and other properties of the SCALEs are given explicitly on a generalization of an equatorial plane, infinitesimally near a symmetry axis, and in a slowly rotating gravitational field, including the far-field limit, where the SCAM is shown to be counter-rotating relative to infinity. These formulae are evaluated in particular detail for the Kerr-Newman metric. Various other congruences are also defined, such as a stationary congruence rotating at minimum (SCRAM), and stationary worldlines accelerating radially maximally (SWARM), both of which coincide with a SCAM on an equatorial plane of reflection symmetry. Applications are also made to the gravitational fields of maximally rotating stars, the Sun and the Solar System.
Kohn's theorem and Newton-Hooke symmetry for Hill's equations
NASA Astrophysics Data System (ADS)
Zhang, P. M.; Gibbons, G. W.; Horvathy, P. A.
2012-02-01
Hill’s equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows us to extend Kohn’s theorem about the center-of-mass decomposition. Particular light is shed on the problem using Duval’s “Bargmann” framework. The separation of the center-of-mass motion into that of a guiding center and relative motion is derived by a generalized chiral decomposition.
Flavor symmetry breaking effects on the SU(3) Skyrmion
NASA Astrophysics Data System (ADS)
Hong, Soon-Tae; Park, Young-Jai
2001-03-01
We study the massive SU(3) Skyrmion model to investigate the flavor symmetry breaking (FSB) effects on the static properties of the strange baryons in the framework of the rigid rotator quantization scheme combined with the improved Dirac quantization one. Both the chiral symmetry breaking pion mass and FSB kinetic terms are shown to improve c, the ratio of the strange-light to light-light interaction strengths, and c¯, that of the strange-strange to light-light interaction strengths.
Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in
Sun, K.
2010-05-26
We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux {-+}2{pi}, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak shortrange repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.
Intrinsic rotation with gyrokinetic models
Parra, Felix I.; Barnes, Michael; Catto, Peter J.; Calvo, Ivan
2012-05-15
The generation of intrinsic rotation by turbulence and neoclassical effects in tokamaks is considered. To obtain the complex dependences observed in experiments, it is necessary to have a model of the radial flux of momentum that redistributes the momentum within the tokamak in the absence of a preexisting velocity. When the lowest order gyrokinetic formulation is used, a symmetry of the model precludes this possibility, making small effects in the gyroradius over scale length expansion necessary. These effects that are usually small become important for momentum transport because the symmetry of the lowest order gyrokinetic formulation leads to the cancellation of the lowest order momentum flux. The accuracy to which the gyrokinetic equation needs to be obtained to retain all the physically relevant effects is discussed.
Equilibrium, multistability, and chiral asymmetry in rotated mirror plasmas
Valanju, P.M.; Mahajan, S.M.; Quevedo, H.J.
2006-06-15
The Hall term in two-fluid magnetohydrodynamics is shown to be necessary to balance the curl of the ion inertial force in a rotating plasma with spatially nonuniform crossed electric and magnetic fields. Two-fluid solutions are obtained that qualitatively explain the multistable rotational response observed in magneto-Bernoulli experiment, imply chiral symmetry breaking, i.e., handedness, and yield new dynamo-like electromotive terms in the effective circuit equation for externally rotated mirror plasma equilibria.
Thermal symmetry in isoscaling
Escudero, C. R.; Lopez, J. A.; Dorso, C. O.
2007-02-12
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks
Parra, Felix I.; Barnes, Michael
2011-06-15
Two symmetries of the local nonlinear {delta}f gyrokinetic system of equations in tokamaks in the high flow regime are presented. The turbulent transport of toroidal angular momentum changes sign under an up-down reflection of the tokamak and a sign change of both the rotation and the rotation shear. Thus, the turbulent transport of toroidal angular momentum must vanish for up-down symmetric tokamaks in the absence of both rotation and rotation shear. This has important implications for the modeling of spontaneous rotation.
Observability and Controllability of Nonlinear Networks: The Role of Symmetry
NASA Astrophysics Data System (ADS)
Schiff, Steven; Whalen, Andrew; Brennan, Sean; Sauer, Timothy
2015-03-01
Observability and controllability are essential concepts to the design of predictive observer models and feedback controllers of networked systems. For example, noncontrollable mathematical models of real systems may have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces are difficult to determine in complex nonlinear networks. Since most of the present theory was developed for linear networks without symmetries, here 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 measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. We find that the presence of symmetry in a network may decrease observability and controllability, although networks containing only rotational symmetries remain controllable and observable. These results alter our view of the nature of observability and controllability in complex networks, change our understanding of structural controllability, and affect the design of mathematical models to observe and control such networks. National Academies - Keck Futures Initiative, NSF grant DMS 1216568, and Collaborative Research in Computational Neuroscience NIH Grant 1R01EB014641.
Origami Optimization: Role of Symmetry in Accelerating Design
NASA Astrophysics Data System (ADS)
Buskohl, Philip; Fuchi, Kazuko; Bazzan, Giorgio; Durstock, Michael; Reich, Gregory; Joo, James; Vaia, Richard
Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form, function and mobility of the structure. Design optimization tools have recently been developed to predict optimal fold patterns with mechanics-based metrics, such as the maximal energy storage, auxetic response and actuation. Origami actuator design problems possess inherent symmetries associated with the grid, mechanical boundary conditions and the objective function, which are often exploited to reduce the design space and computational cost of optimization. However, enforcing symmetry eliminates the prediction of potentially better performing asymmetric designs, which are more likely to exist given the discrete nature of fold line optimization. To better understand this effect, actuator design problems with different combinations of rotation and reflection symmetries were optimized while varying the number of folds allowed in the final design. In each case, the optimal origami patterns transitioned between symmetric and asymmetric solutions depended on the number of folds available for the design, with fewer symmetries present with more fold lines allowed. This study investigates the interplay of symmetry and discrete vs continuous optimization in origami actuators and provides insight into how the symmetries of the reference grid regulate the performance landscape. This work was supported by the Air Force Office of Scientific Research.
Applications of chiral symmetry
Pisarski, R.D.
1995-03-01
The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.
Symmetry in halo displays and symmetry in halo-making crystals.
Können, Gunther P
2003-01-20
The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L-R) symmetric if the crystals are formed from the surrounding vapor. L-R symmetry of a halo display implies here that the cross sections for formation of a halo arc on the left-hand side of the solar vertical and its right-hand side mirror image are equal. This property leaves room for two types of halo display only: a full symmetric one (mmm-symmetric), and a partial symmetric one (mm2-symmetric) in which halo constituents lack their counterparts on the other side of the parhelic circle. A partial symmetric display can occur only for point halos. Its occurrence implies that a number of symmetry elements are not present in the shape of the halo-making crystals. These elements are a center of inversion, any rotatory-inversion axis that is parallel to the crystal spin axis P, a mirror plane perpendicular to the P axis, and a twofold rotation axis perpendicular to the P axis. A simple conceptual method is presented to reconstruct possible shapes of the halo-generating crystals from the halos in the display. The method is illustrated in two examples. Halos that may occur on the Saturnian satellite Titan are discussed. The possibilities for the Huygens probe to detect these halos during its descent through the Titan clouds in 2005 are detailed. PMID:12570252
Ostwald, Julia; Berssenbrügge, Philipp; Dirksen, Dieter; Runte, Christoph; Wermker, Kai; Kleinheinz, Johannes; Jung, Susanne
2015-05-01
One aim of cranio-maxillo-facial surgery is to strive for an esthetical appearance. Do facial symmetry and attractiveness correlate? How are they affected by surgery? Within this study faces of patients with orthognathic surgery were captured and analyzed regarding their symmetry. A total of 25 faces of patients were measured three-dimensionally by an optical sensor using the fringe projection technique before and after orthognathic surgery. Based upon this data an asymmetry index was calculated for each case. In order to gather subjective ratings each face was presented to 100 independent test subjects in a 3D rotation sequence. Those were asked to rate the symmetry and the attractiveness of the faces. It was analyzed to what extend the ratings correlate with the measured asymmetry indices and whether pre- and post-surgical data differ. The measured asymmetry indices correlate significantly with the subjective ratings of both items. The measured symmetry as well as the rated symmetry and attractiveness increased on average after surgery. The increase of the ratings was even statistically significant. A larger enhancement of symmetry is achieved in pre-surgical strongly asymmetric faces than in rather symmetric faces. PMID:25841308
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Symmetry fractionalization and twist defects
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
Symmetry of Magnetically Ordered Quasicrystals
NASA Astrophysics Data System (ADS)
Lifshitz, Ron
1998-03-01
The notion of magnetic symmetry is reexamined in light of the recent observation of long-range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals, is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.
Aydemir, Fikret; Salganik, Maxim; Resztak, Justyna; Singh, Jasbir; Bennett, Antonette; Agbandje-McKenna, Mavis
2016-01-01
ABSTRACT We previously reported that an amino acid substitution, Y704A, near the 2-fold interface of adeno-associated virus (AAV) was defective for transcription of the packaged genome (M. Salganik, F. Aydemir, H. J. Nam, R. McKenna, M. Agbandje-McKenna, and N. Muzyczka, J Virol 88:1071–1079, 2013, doi: http://dx.doi.org/10.1128/JVI.02093-13). In this report, we have characterized the defect in 6 additional capsid mutants located in a region ∼30 Å in diameter on the surface of the AAV type 2 (AAV2) capsid near the 2-fold interface. These mutants, which are highly conserved among primate serotypes, displayed a severe defect (3 to 6 logs) in infectivity. All of the mutants accumulated significant levels of uncoated DNA in the nucleus, but none of the mutants were able to accumulate significant amounts of genomic mRNA postinfection. In addition, wild-type (wt) capsids that were bound to the conformational antibody A20, which is known to bind the capsid surface in the region of the mutants, were also defective for transcription. In all cases, the mutant virus particles, as well as the antibody-bound wild-type capsids, were able to enter the cell, travel to the nucleus, uncoat, and synthesize a second strand but were unable to transcribe their genomes. Taken together, the phenotype of these mutants provides compelling evidence that the AAV capsid plays a role in the transcription of its genome, and the mutants map this functional region on the surface of the capsid near the 2-fold interface. This appears to be the first example of a viral structural protein that is also involved in the transcription of the viral genome that it delivers to the nucleus. IMPORTANCE Many viruses package enzymes within their capsids that assist in expressing their genomes postinfection, e.g., retroviruses. A number of nonenveloped viruses, including AAV, carry proteases that are needed for capsid maturation or for capsid modification during infection. We describe here what appears to
Structure of the N-terminal domain of the protein Expansion: an ‘Expansion’ to the Smad MH2 fold
Beich-Frandsen, Mads; Aragón, Eric; Llimargas, Marta; Benach, Jordi; Riera, Antoni; Pous, Joan; Macias, Maria J.
2015-04-01
Expansion is a modular protein that is conserved in protostomes. The first structure of the N-terminal domain of Expansion has been determined at 1.6 Å resolution and the new Nα-MH2 domain was found to belong to the Smad/FHA superfamily of structures. Gene-expression changes observed in Drosophila embryos after inducing the transcription factor Tramtrack led to the identification of the protein Expansion. Expansion contains an N-terminal domain similar in sequence to the MH2 domain characteristic of Smad proteins, which are the central mediators of the effects of the TGF-β signalling pathway. Apart from Smads and Expansion, no other type of protein belonging to the known kingdoms of life contains MH2 domains. To compare the Expansion and Smad MH2 domains, the crystal structure of the Expansion domain was determined at 1.6 Å resolution, the first structure of a non-Smad MH2 domain to be characterized to date. The structure displays the main features of the canonical MH2 fold with two main differences: the addition of an α-helical region and the remodelling of a protein-interaction site that is conserved in the MH2 domain of Smads. Owing to these differences, to the new domain was referred to as Nα-MH2. Despite the presence of the Nα-MH2 domain, Expansion does not participate in TGF-β signalling; instead, it is required for other activities specific to the protostome phyla. Based on the structural similarities to the MH2 fold, it is proposed that the Nα-MH2 domain should be classified as a new member of the Smad/FHA superfamily.
Chu Wenjuan; He Yong; Zhao Qinghuan; Fan Yaoting; Hou Hongwei
2010-10-15
Two novel inorganic-organic 3D network, namely{l_brace}[Ln(L){sub 1.5}(H{sub 2}O){sub 2}].5H{sub 2}O{r_brace}n [Ln=Y (1), Ce (2); Ln(L){sub 1.5}(H{sub 2}O){sub 2}].5H{sub 2}O [Ln=Y (1), Ce (2)], have been prepared through the assembly of the ligand 1,2-bis[3-(1,2,4-triazolyl)-4-amino-5-carboxylmethylthio]ethane (H{sub 2}L) and lanthanide (III) salts under hydrothermal condition and structurally characterized by single-crystal X-ray diffractions. In complexes 1 and 2, the L{sup 2-} anions adopt three different coordination fashions (bidentate chelate, bidentate bridging and bidentate chelate bridging) connecting Ln(III) ions via the oxygen atoms from carboxylate moieties. Both 1 and 2 exhibit 3D network structures with 2-fold interpenetration. Interestingly, the reversible desorption-adsorption behavior of lattice water is significantly observed in the two compounds. The result shows their potential application as late-model water absorbent in the field of adsorption material. - Graphical abstract: Two inorganic-organic 3D network, namely {l_brace}[Ln(L){sub 1.5}(H{sub 2}O){sub 2}].5H{sub 2}O{r_brace}n [Ln=Y (1), Ce (2)], have been prepared under hydrothermal condition and structurally characterized by single-crystal X-ray diffractions. Both 1 and 2 exhibit 3D network structures with 2-fold interpenetration. Interestingly, the reversible desorption-adsorption behavior of lattice water is significantly observed in the two compounds. The result shows their potential application as late-model water absorbent in the field of adsorption material.
Pairing in hot rotating nuclei
Hung, N. Quang; Dang, N. Dinh
2008-12-15
Nuclear pairing properties are studied within an approach that includes the quasiparticle-number fluctuation (QNF) and coupling to the quasiparticle-pair vibrations at finite temperature and angular momentum. The formalism is developed to describe noncollective rotations about the symmetry axis. The numerical calculations are performed within a doubly folded equidistant multilevel model as well as several realistic nuclei. The results obtained for the pairing gap, total energy, and heat capacity show that the QNF smoothes out the sharp SN phase transition and leads to the appearance of a thermally assisted pairing gap in rotating nuclei at finite temperature. The corrections due to the dynamic coupling to SCQRPA vibrations and particle-number projection are analyzed. The effect of backbending of the momentum of inertia as a function of squared angular velocity is also discussed.
NASA Astrophysics Data System (ADS)
Weber, S. V.; Casey, D. T.; Pino, J. E.; Rowley, D. P.; Smalyuk, V. A.; Spears, B. K.; Tipton, R. E.
2013-10-01
NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Topological classification of crystalline insulators with space group symmetry
Jadaun, Priyamvada; Xiao, Di; Niu, Q.; Banerjee, Sanjay K.
2013-01-01
We show that in crystalline insulators, space group symmetry alone gives rise to a topological classification based on the discretization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is discretized into three distinct classes, i.e., it can only take three inequivalent values. We then prove that these classes are topologically distinct. Therefore, a Z3 topological classification exists, with polarization as a topological class index. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on a BN substrate as a possible candidate to realize these Z3 topological states. To complete our analysis, we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry-conserved topological phases and also elucidate topological properties of graphenelike systems.
Symmetries and deformations in the spherical shell model
NASA Astrophysics Data System (ADS)
Van Isacker, P.; Pittel, S.
2016-02-01
We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott’s model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott’s SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells N-1 and N, leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells, N\\to ∞ , the algebraic octupole interaction tends to that of the geometric collective model.
Symmetry and stability in Taylor-Couette flow
NASA Technical Reports Server (NTRS)
Golubitsky, M.; Stewart, I.
1986-01-01
The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.
Kumar, Mohit
2013-01-01
Minor group human rhinoviruses bind low-density lipoprotein (LDL) receptors for endocytosis. Once they are inside endosomes, the acidic pH triggers their dissociation from the receptors and conversion into hydrophobic subviral A particles; these attach to the membrane and transfer their single-strand, positive-sense RNA genome into the cytosol. Here, we allowed human rhinovirus 2 (HRV2) A particles, produced in vitro by incubation at pH 5.4, to attach to liposomes; cryo-electron microscopy 3-dimensional single-particle image reconstruction revealed that they bind to the membrane around a 2-fold icosahedral symmetry axis. PMID:23946453
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
Generalized Atkin-Lehner symmetry
NASA Astrophysics Data System (ADS)
Dienes, Keith R.
1990-09-01
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner ``selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Generalized Atkin-Lehner symmetry
Dienes, K.R. )
1990-09-15
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Ultraviolet completion without symmetry restoration
NASA Astrophysics Data System (ADS)
Endlich, Solomon; Nicolis, Alberto; Penco, Riccardo
2014-03-01
We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Nulling interferometry: symmetry requirements and experimental results
NASA Astrophysics Data System (ADS)
Serabyn, Eugene
2000-07-01
This paper provides a derivation from first principles of the stringent symmetry and stability requirements which deep stellar nulling demands, and also includes a brief status report on recent nulling results obtained with the Jet Propulsion Laboratory's fiber-coupled rotational-shearing interferometer. To date, the deepest transient nulls obtained (at red wavelengths) are 2 X 10-6 with a laser diode source, and 1.4 X 10-5 with a single- polarization thermal white-light source filtered to provide an 18% passband. In addition, both the laser and white light nulls have been stabilized to the 10-4 level. This visible wavelength laboratory nuller thus meets essentially all of the performance goals for the planned nulling experiment on board NASA's Space Interferometer Mission, with the sole exception of dual-polarization operation.
Second moments and rotational spectroscopy
NASA Astrophysics Data System (ADS)
Bohn, Robert K.; Montgomery, John A.; Michels, H. Harvey; Fournier, Joseph A.
2016-07-01
Although determining molecular structure using microwave spectroscopy is a mature technique, there are still simple but powerful insights to analysis of the data which are not generally appreciated. This paper summarizes three applications of second (or planar) moments which quickly and easily provide insights and conclusions about a molecule's structure not easily obtained from the molecule's rotational constants. If the molecule has a plane of symmetry, group second moments can verify that property and determine which groups are located on that plane. Common groups contribute predictable values to second moments. This study examines the contribution and transferability of CH2/CH3, CF2/CF3, isopropyl, and phenyl groups to molecular constants. Structures of related molecules can be critically compared using their second moments. A third application to any molecule, even those whose structures have only the identity symmetry element, determines bond lengths and angles which exactly reproduce experimentally determined 2nd moments, rotational constants, and moments of inertia. Approximate least squares methods are not needed.
NASA Technical Reports Server (NTRS)
1988-01-01
The NASA Bioreactor provides a low turbulence culture environment which promotes the formation of large, three-dimensional cell clusters. Due to their high level of cellular organization and specialization, samples constructed in the bioreactor more closely resemble the original tumor or tissue found in the body. NASA-sponsored bioreactor research has been instrumental in helping scientists to better understand normal and cancerous tissue development. In cooperation with the medical community, the bioreactor design is being used to prepare better models of human colon, prostate, breast and ovarian tumors. Cartilage, bone marrow, heart muscle, skeletal muscle, pancreatic islet cells, liver and kidney are just a few of the normal tissues currently being cultured in rotating bioreactors by investigators.
Singularities and symmetry breaking in swarms.
Li, Wei; Zhang, Hai-Tao; Chen, Michael Zhi Qiang; Zhou, Tao
2008-02-01
A large-scale system consisting of self-propelled particles, moving under the directional alignment rule (DAR), can often self-organize to an ordered state that emerges from an initially rotationally symmetric configuration. It is commonly accepted that the DAR, which leads to effective long-range interactions, is the underlying mechanism contributing to the collective motion. However, in this paper, we demonstrate that a swarm under the DAR has unperceived and inherent singularities. Furthermore, we show that the compelled symmetry-breaking effects at or near the singularities, as well as the topological connectivity of the swarm in the evolution process, contribute fundamentally to the emergence of the collective behavior; and the elimination or weakening of singularities in the DAR will induce an unexpected sharp transition from coherent movement to isotropic dispersion. These results provide some insights into the fundamental issue of collective dynamics: What is the underlying mechanism causing the spontaneous symmetry breaking and leading to eventual coherent motion? PMID:18352064
Spontaneous Planar Chiral Symmetry Breaking in Cells
NASA Astrophysics Data System (ADS)
Hadidjojo, Jeremy; Lubensky, David
Recent progress in animal development has highlighted the central role played by planar cell polarity (PCP) in epithelial tissue morphogenesis. Through PCP, cells have the ability to collectively polarize in the plane of the epithelium by localizing morphogenetic proteins along a certain axis. This allows direction-dependent modulation of tissue mechanical properties that can translate into the formation of complex, non-rotationally invariant shapes. Recent experimental observations[1] show that cells, in addition to being planar-polarized, can also spontaneously develop planar chirality, perhaps in the effort of making yet more complex shapes that are reflection non-invariant. In this talk we will present our work in characterizing general mechanisms that can lead to spontaneous chiral symmetry breaking in cells. We decompose interfacial concentration of polarity proteins in a hexagonal cell packing into irreducible representations. We find that in the case of polar concentration distributions, a chiral state can only be reached from a secondary instability after the cells are polarized. However in the case of nematic distributions, we show that a finite-amplitude (subcritical, or ``first-order'') nematic transition can send the system from disorder directly to a chiral state. In addition, we find that perturbing the system by stretching the hexagonal packing enables direct (supercritical, or ``second-order'') chiral transition in the nematic case. Finally, we do a Landau expansion to study competition between stretch-induced chirality and the tendency towards a non-chiral state in packings that have retained the full 6-fold symmetry.
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
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.
Standard Model Gauge Couplings from Gauge-Dilatation Symmetry Breaking
NASA Astrophysics Data System (ADS)
Odagiri, Kosuke
2014-09-01
It is well known that the self-energy of the gauge bosons is quadratically divergent in the Standard Model when a simple cutoff is imposed. We demonstrate phenomenologically that the quadratic divergences in fact unify. The unification occurs at a surprisingly low scale, GeV. Suppose now that there is a spontaneously broken rotational symmetry between the space-time coordinates and gauge theoretical phases. The symmetry-breaking pattern is such that the gauge bosons arise as the massless Goldstone bosons, whereas the dilatonic mode acts as the massive (Higgs) boson, whose vacuum expectation value determines the gauge couplings. In this case, the quadratic divergences or the tadpoles of the gauge boson self-energy should indeed unify because these divergences need to be cancelled by a universal dilatonic contribution, assuming dynamical symmetry breaking. If there is dynamical symmetry breaking, we are in principle able to calculate the value of the gauge couplings as well as the scale hierarchy . We perform this calculation by adopting a naive quartic symmetry-breaking potential which unfortunately violates local gauge invariance. Using tadpole-cancellation and dilatonic self-energy conditions, the value of is then found to be approximately GeV in the Feynman gauge and GeV in the Landau gauge. The cancellation of an anomaly in the dilaton self-energy requires that the number of fermionic generations equals three. The symmetry-breaking needs to be driven by some other mass-generating mechanism such as electroweak symmetry breaking. Our estimation for is of the correct order if GeV.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Hidden symmetries and black holes
NASA Astrophysics Data System (ADS)
Frolov, Valeri P.
2009-10-01
The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.
The rotationally improved Skyrmion, or RISKY
Dorey, N.; Mattis, M.P.
1995-05-01
The perceived inability of the Skyrme model to reproduce pseudovector pion-baryon coupling has come to be known as the ``Yukawa problem.`` In this talk, we review the complete solution to this problem. The solution involves a new configuration known as the rotationally improved Skyrmion, or ``RISKY,`` in which the hedgehog structure is modified by a small quadrupole distortion. We illustrate our ideas both in the Skyrme model and in a simpler model with a global U(l) symmetry.
NASA Astrophysics Data System (ADS)
Armitage, N. P.
2014-07-01
Optical spectroscopies are most often used to probe dynamical correlations in materials, but they are also a probe of symmetry. Polarization anisotropies are of course sensitive to structural anisotropies, but have been much less used as a probe of more exotic symmetry breakings in ordered states. In this paper, a Jones transfer matrix formalism is discussed to infer the existence of exotic broken symmetry states of matter from their electrodynamic response for a full complement of possible broken symmetries including reflection, rotation, rotation reflection, inversion, and time reversal. A specific condition to distinguish the case of macroscopic time-reversal symmetry breaking is particularly important as in a dynamical experiment like optics, one must distinguish reciprocity from time-reversal symmetry as dissipation violates strict time-reversal symmetry of an experiment. Different forms of reciprocity can be distinguished, but only one is a sufficient (but not necessary) condition for macroscopic time-reversal symmetry breaking. I show the constraints that a Jones matrix develops under the presence or absence of such symmetries. These constraints typically appear in the form of an algebra relating matrix elements or overall constraints (transposition, unitarity, hermiticity, normality, etc.) on the form of the Jones matrix. I work out a number of examples including the trivial case of a ferromagnet and the less trivial cases of magnetoelectrics and vector and scalar spin "chiral" states. I show that the formalism can be used to demonstrate that Kerr rotation must be absent in time-reversal symmetric chiral materials. The formalism here is discussed with an eye towards its use in time-domain terahetrz spectroscopy in transmission, but with small modifications it is more generally applicable.
Combining Flavour and CP Symmetries
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio
2013-07-01
I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.
Liu, Y.; Keller, J.
1996-09-01
It is proved that there exists an additional intrinsic symmetry in the left-handed and right-handed fermions (and other fields). The corresponding group of transformations is induced by the Poincar{acute e} translations in the space{endash}time manifold. This symmetry predicts an additional intrinsic energy-momentum for fermions. Considering this symmetry as local leads to introduction of a gauge field and of a nonintegrable phase angle, the corresponding Berry-type phase depends on the topology of the Riemannian space{endash}time manifold as determined by the vierbein. This additional symmetry provides us with the possibility of considering the fermions as gauge fields on the nonvector bundle. {copyright} {ital 1996 American Institute of Physics.}
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
Higher-dimensional black holes: hidden symmetries and separation of variables
NASA Astrophysics Data System (ADS)
Frolov, Valeri P.; Kubizňák, David
2008-08-01
In this paper, we discuss hidden symmetries in rotating black hole spacetimes. We start with an extended introduction which mainly summarizes results on hidden symmetries in four dimensions and introduces Killing and Killing Yano tensors, objects responsible for hidden symmetries. We also demonstrate how starting with a principal CKY tensor (that is a closed non-degenerate conformal Killing Yano 2-form) in 4D flat spacetime one can 'generate' the 4D Kerr NUT (A)dS solution and its hidden symmetries. After this we consider higher-dimensional Kerr NUT (A)dS metrics and demonstrate that they possess a principal CKY tensor which allows one to generate the whole tower of Killing Yano and Killing tensors. These symmetries imply complete integrability of geodesic equations and complete separation of variables for the Hamilton Jacobi, Klein Gordon and Dirac equations in the general Kerr NUT (A)dS metrics.
Momentum dependence of symmetry energy
NASA Astrophysics Data System (ADS)
Coupland, Daniel D.; Youngs, Michael; Chajecki, Zbigniew; Lynch, William; Tsang, Betty; Zhang, Yingxun; Famiano, Michael; Ghosh, Tilak; Giacherio, B.; Kilburn, Micha; Lee, Jenny; Lu, Fei; Russotto, Paulo; Sanetullaev, Alisher; Showalter, Rachel; Verde, Giuseppe; Winkelbauer, Jack
2014-09-01
One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn +124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn+124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. PHY-1102511.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; Rodríguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
/SU(3) symmetry and scissors mode vibrations in nuclei
NASA Astrophysics Data System (ADS)
Sun, Yang; Wu, Cheng-Li; Bhatt, Kumar; Guidry, Mike
2002-05-01
We show that a nearly perfect SU(3) symmetry emerges from an extended projected shell model. Starting from a deformed potential we construct separate bases for neutron and proton collective rotational states by exact angular momentum projection. These rotational states are then coupled by diagonalizing a residual pairing plus quadrupole interaction. The states obtained exhibit a one-to-one correspondence with an SU(3) spectrum up to high angular momentum and excitation, and their wave functions have a near-maximal overlap with the SU(3) states. They can also be classified as rotational bands built on spin-1ℏ phonon excitations, which correspond to a geometrical scissors mode and its generalizations. This work is a direct demonstration that numerical angular momentum projection theory extends the Elliott's original idea to heavy nuclear systems.
Stellar Rotation Effects in Polarimetric Microlensing
NASA Astrophysics Data System (ADS)
Sajadian, Sedighe
2016-07-01
It is well known that the polarization signal in microlensing events of hot stars is larger than that of main-sequence stars. Most hot stars rotate rapidly around their stellar axes. The stellar rotation creates ellipticity and gravity-darkening effects that break the spherical symmetry of the source's shape and the circular symmetry of the source's surface brightness respectively. Hence, it causes a net polarization signal for the source star. This polarization signal should be considered in polarimetric microlensing of fast rotating stars. For moderately rotating stars, lensing can magnify or even characterize small polarization signals due to the stellar rotation through polarimetric observations. The gravity-darkening effect due to a rotating source star creates asymmetric perturbations in polarimetric and photometric microlensing curves whose maximum occurs when the lens trajectory crosses the projected position of the rotation pole on the sky plane. The stellar ellipticity creates a time shift (i) in the position of the second peak of the polarimetric curves in transit microlensing events and (ii) in the peak position of the polarimetric curves with respect to the photometric peak position in bypass microlensing events. By measuring this time shift via polarimetric observations of microlensing events, we can evaluate the ellipticity of the projected source surface on the sky plane. Given the characterizations of the FOcal Reducer and low dispersion Spectrograph (FORS2) polarimeter at the Very Large Telescope, the probability of observing this time shift is very small. The more accurate polarimeters of the next generation may well measure these time shifts and evaluate the ellipticity of microlensing source stars.
... doctors because of a rotator cuﬀ problem. A torn rotator cuﬀ will weaken your shoulder. This means ... or more of the rotator cuﬀ tendons is torn, the tendon no longer fully attaches to the ...
... others can be very painful. Treatment for a torn rotator cuff depends on age, health, how severe ... is, and how long you've had the torn rotator cuff. Treatment for torn rotator cuff includes: ...
... days, such as in painting and carpentry Poor posture over many years Aging Rotator cuff tears TEARS ... also help prevent rotator cuff problems. Practice good posture to keep your rotator cuff tendons and muscles ...
Forced vibration analysis of rotating cyclic structures in NASTRAN
NASA Technical Reports Server (NTRS)
Elchuri, V.; Gallo, A. M.; Skalski, S. C.
1981-01-01
A new capability was added to the general purpose finite element program NASTRAN Level 17.7 to conduct forced vibration analysis of tuned cyclic structures rotating about their axis of symmetry. The effects of Coriolis and centripetal accelerations together with those due to linear acceleration of the axis of rotation were included. The theoretical, user's, programmer's and demonstration manuals for this new capability are presented.
A quantum reduction to spherical symmetry in loop quantum gravity
NASA Astrophysics Data System (ADS)
Bodendorfer, N.; Lewandowski, J.; Świeżewski, J.
2015-07-01
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3 + 1-dimensional loop quantum gravity. The construction of observables corresponds to using the radial gauge for the spatial metric and allows to identify rotations around a central observer as unitary transformations in the quantum theory. Group averaging over these rotations yields our first proposal for spherical symmetry. Hamiltonians of the full theory with angle-independent lapse preserve this spherically symmetric subsector of the full Hilbert space. A second proposal consists in implementing the vanishing of a certain vector field in spherical symmetry as a constraint on the full Hilbert space, leading to a close analogue of diffeomorphisms invariant states. While this second set of spherically symmetric states does not allow for using the full Hamiltonian, it is naturally suited to implement the spherically symmetric midisuperspace Hamiltonian, as an operator in the full theory, on it. Due to the canonical structure of the reduced variables, the holonomy-flux algebra behaves effectively as a one parameter family of 2 + 1-dimensional algebras along the radial coordinate, leading to a diagonal non-vanishing volume operator on 3-valent vertices. The quantum dynamics thus becomes tractable, including scenarios like spherically symmetric dust collapse.
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Cao, N.; Chen, S.; Jin, S.; Martinez, D.
1997-01-01
The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}
Symmetry in finite phase plane
NASA Astrophysics Data System (ADS)
Zak, J.
2010-03-01
The known symmetries in one-dimensional systems are inversion and translations. These symmetries persist in finite phase plane, but a novel symmetry arises in view of the discrete nature of the coordinate xi and the momentum pi : xi and pi can undergo permutations. Thus, if xi assumes M discrete values, i = 0, 1,2,..., M - 1, a permutation will change the order of the set x0,x1,..., xM-1 into a new ordered set. Such a symmetry element does not exist for a continuous x-coordinate in an infinite phase plane. Thus, in a finite phase plane, translations can be replaced by permutations. This is also true for the inversion operator. The new permutation symmetry has been used for the construction of conjugate representations and for the splitting of the M-dimensional vector space into independent subspaces. This splitting is exhaustive in the sense that if M = iMi with Mi being prime numbers, the M-dimensional space splits into M1,M2,...Mn-dimensional independent subspaces. It is shown that following this splitting one can design new potentials with appropriate constants of motion. A related problem is the Weyl-Heisenberg group in the M-dimensional space which turns into a direct product of its subgroups in the Mi-dimensional subspaces. As an example we consider the case of M = 8.
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
Symmetry Guide to Ferroaxial Transitions
NASA Astrophysics Data System (ADS)
Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.
2016-04-01
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .
Non-Newtonian rotational swimming: experiments
NASA Astrophysics Data System (ADS)
Gomez, S.; Godinez, F. A.; Zenit, R.; Lauga, E.
2013-11-01
Recently Pak et al. (PoF, 2012) showed that a device composed of two unequal spheres (snowman) could swim in a viscoelastic fluid under a rotational actuation. By symmetry such device isn't able to move in a Newtonian fluid but because of its geometrical asymmetry is able to generate asymmetric elastic response and generate a purely viscoelastic thrust. We implemented this swimmer experimentally using a magnetic snowman driven by an external rotating magnetic field. We demonstrate that the snowman swims solely as a result of fluid elasticity. We conduct tests in Newtonian and Boger fluids, varying the sphere size ratio and rotation speed. We also conducted measurements in a confined environment, which showed an improved swimming performance.
Flow-induced vibrations of a rotating cylinder
NASA Astrophysics Data System (ADS)
Bourguet, Remi; Lo Jacono, David
2013-11-01
The flow-induced vibrations of a circular cylinder, free to oscillate in the cross-flow direction and subjected to a forced rotation about its axis, are studied by means of two- and three-dimensional numerical simulations, at a Reynolds number equal to 100. This problem serves as a paradigm to investigate the impact of symmetry breaking on the phenomenon of vortex-induced vibrations (VIV), previously described in the non-rotating case. The cylinder exhibits free oscillations up to a rotation rate close to 4. Under forced rotation, the vibration amplitude reaches 1.9 diameters, i.e. three times the maximum amplitude in the non-rotating case. Contrary to galloping responses, the free vibrations of the rotating cylinder are found to involve a condition of wake-body synchronization similar to the lock-in condition driving non-rotating cylinder VIV. A variety of flow patterns including novel asymmetric wake topologies is identified; it is shown that free oscillations may develop in the absence of vortex shedding. The symmetry breaking substantially alters the fluid force spectra and phasing mechanisms. The flow three-dimensional transition is found to occur at high rotation rates; its influence on the fluid-structure system behavior is analyzed.
SO(5) symmetry in the quantum Hall effect in graphene
NASA Astrophysics Data System (ADS)
Wu, Fengcheng; Sodemann, Inti; Araki, Yasufumi; MacDonald, Allan H.; Jolicoeur, Thierry
2014-12-01
Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions, which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants gz and g⊥. In this paper, we demonstrate that when gz=-g⊥ , an exact SO(5) symmetry survives which unifies the Néel spin order parameter of the antiferromagnetic state and the X Y valley order parameter of the Kekulé distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at ν =0 to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor ν =0 quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.
Expediting model-based optoacoustic reconstructions with tomographic symmetries
Lutzweiler, Christian; Deán-Ben, Xosé Luís; Razansky, Daniel
2014-01-15
Purpose: Image quantification in optoacoustic tomography implies the use of accurate forward models of excitation, propagation, and detection of optoacoustic signals while inversions with high spatial resolution usually involve very large matrices, leading to unreasonably long computation times. The development of fast and memory efficient model-based approaches represents then an important challenge to advance on the quantitative and dynamic imaging capabilities of tomographic optoacoustic imaging. Methods: Herein, a method for simplification and acceleration of model-based inversions, relying on inherent symmetries present in common tomographic acquisition geometries, has been introduced. The method is showcased for the case of cylindrical symmetries by using polar image discretization of the time-domain optoacoustic forward model combined with efficient storage and inversion strategies. Results: The suggested methodology is shown to render fast and accurate model-based inversions in both numerical simulations andpost mortem small animal experiments. In case of a full-view detection scheme, the memory requirements are reduced by one order of magnitude while high-resolution reconstructions are achieved at video rate. Conclusions: By considering the rotational symmetry present in many tomographic optoacoustic imaging systems, the proposed methodology allows exploiting the advantages of model-based algorithms with feasible computational requirements and fast reconstruction times, so that its convenience and general applicability in optoacoustic imaging systems with tomographic symmetries is anticipated.
Symmetry breaking in molecular ferroelectrics.
Shi, Ping-Ping; Tang, Yuan-Yuan; Li, Peng-Fei; Liao, Wei-Qiang; Wang, Zhong-Xia; Ye, Qiong; Xiong, Ren-Gen
2016-07-11
Ferroelectrics are inseparable from symmetry breaking. Accompanying the paraelectric-to-ferroelectric phase transition, the paraelectric phase adopting one of the 32 crystallographic point groups is broken into subgroups belonging to one of the 10 ferroelectric point groups, i.e. C1, C2, C1h, C2v, C4, C4v, C3, C3v, C6 and C6v. The symmetry breaking is captured by the order parameter known as spontaneous polarization, whose switching under an external electric field results in a typical ferroelectric hysteresis loop. In addition, the responses of spontaneous polarization to other external excitations are related to a number of physical effects such as second-harmonic generation, piezoelectricity, pyroelectricity and dielectric properties. Based on these, this review summarizes recent developments in molecular ferroelectrics since 2011 and focuses on the relationship between symmetry breaking and ferroelectricity, offering ideas for exploring high-performance molecular ferroelectrics. PMID:27051889
CKM matrix and flavor symmetries
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Ishida, Hiroyuki; Ishimori, Hajime; Kobayashi, Tatsuo; Ogasahara, Atsushi
2013-11-01
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both θ13 and θ23 or only θ13 are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The Z7 symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the Δ(6N2) series are also briefly discussed.
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
Rotational propulsion enabled by inertia.
Nadal, François; Pak, On Shun; Zhu, LaiLai; Brandt, Luca; Lauga, Eric
2014-07-01
The fluid mechanics of small-scale locomotion has recently attracted considerable attention, due to its importance in cell motility and the design of artificial micro-swimmers for biomedical applications. Most studies on the topic consider the ideal limit of zero Reynolds number. In this paper, we investigate a simple propulsion mechanism --an up-down asymmetric dumbbell rotating about its axis of symmetry-- unable to propel in the absence of inertia in a Newtonian fluid. Inertial forces lead to continuous propulsion for all finite values of the Reynolds number. We study computationally its propulsive characteristics as well as analytically in the small-Reynolds-number limit. We also derive the optimal dumbbell geometry. The direction of propulsion enabled by inertia is opposite to that induced by viscoelasticity. PMID:25034393
Rotation and cooling of neutron stars
NASA Astrophysics Data System (ADS)
Negreiros, R.; Schramm, S.; Weber, F.
2014-09-01
Driven by the loss of energy, isolated rotating neutron stars (pulsars) are gradually slowing down to lower frequencies, which increases the tremendous compression of the matter inside of them. This increase in compression changes both the global properties of rotating neutron stars as well as their hadronic core compositions. Both effects may register themselves observationally in the thermal evolution of such stars, as demonstrated in this work. The rotation-driven particle process which we consider here is the direct Urca (DU) process, which is known to become operative in neutron stars if the number of protons in the stellar core exceeds a critical limit of around 11 % to 15 %. We find that neutron stars spinning down from moderately high rotation rates of a few hundred Hertz may be creating just the right conditions where the DU process becomes operative, leading to an observable effect (enhanced cooling) in the temperature evolution of such neutron stars. We will also study the thermal evolution of neutron stars whose spherical symmetry has been broken due to non-zero rotation. For this we will derive the energy balance and transport equations, taking into account the metric of a rotating fluid distribution and solve these equations numerically.
Rotational Doppler effect in nonlinear optics
NASA Astrophysics Data System (ADS)
Li, Guixin; Zentgraf, Thomas; Zhang, Shuang
2016-08-01
The translational Doppler effect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies, and for the Global Positioning System. The Doppler effect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms and has benefited cooling and trapping of atoms with laser light. Despite numerous successful applications of the translational Doppler effect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves--the so-called rotational Doppler effect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Three-flat test solutions based on simple mirror symmetry
Griesmann, Ulf
2006-08-10
In interferometric surface and wavefront metrology, three-flat tests are the archetypes of measurement procedures to separate errors in the interferometer reference wavefront from errors due to the test part surface, so-called absolute tests. What is believed to be a new class of solutions of the three-flat problem for circular flats is described in terms of functions that are symmetric or antisymmetric with respect to reflections at a single line passing through the center of the flat surfaces. The new solutions are simpler and easier to calculate than the known solutions based on twofold mirror symmetry or rotation symmetry.Strategies for effective azimuthal averaging and a method for determining the averaging error are also discussed.
Connections between the dynamical symmetries in the microscopic shell model
NASA Astrophysics Data System (ADS)
Georgieva, A. I.; Drumev, K. P.
2016-03-01
The dynamical symmetries of the microscopic shell model appear as the limiting cases of a symmetry adapted Pairing-Plus-Quadrupole Model /PQM/, with a Hamiltonian containing isoscalar and isovector pairing and quadrupole interactions. We establish a correspondence between each of the three types of pairing bases and Elliott's SU(3) basis, that describes collective rotation of nuclear systems with quadrupole deformation. It is derived from their complementarity to the same LS coupling chain of the shell model number conserving algebra. The probability distribution of the S U(3) basis states within the pairing eigenstates is also obtained through a numerical diagonalization of the PQM Hamiltonian in each limit. We introduce control parameters, which define the phase diagram of the model and determine the role of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
SO(5, 1) dynamical symmetry for electron Zitterbewegung
NASA Astrophysics Data System (ADS)
Bruce, S. A.; Minning, P. C.
1985-10-01
Electron rest-frame internal canonical coordinates are reobtained by the free-particle Foldy-Wouthuysen transformation: Schrödinger “microscopic momentum”, Barut-Bracken “microscopic coordinate”, and the rest Hamiltonian, which describe Zitterbewegung in this frame. SO(4, 1) Snyder space-time invariant quantization is considered in order to construct a dynamical group for Zitterbewegung. The electron's internal structure appears associated with its secondorder self-energy process and governed by the 15-parameter dynamical group SO(5, 1). This is a generalization of Barut-Bracken symmetry which describes Zitterbewegung as generated by an algebra of the rotation group SO(5). This noncompact symmetry SO(5, 1) permits a natural interpretation for the operators of its algebra and introduces a generalization to higher-dimensional fermionic representations.
Fourth Meeting on CPT and Lorentz Symmetry
NASA Astrophysics Data System (ADS)
Kostelecký, V. Alan
2008-03-01
Improved tests of Lorentz and CPT symmetry using noble-gas masers / A. Glenday, D. F. Phillips, and R. L. Walsworth -- A modern Michelson-Morley experiment using actively rotated optical resonators / S. Herrmann et al. -- Rotating experiments to test Lorentz invariance in the photon sector / M. E. Tobar et al. -- Lorentz violation, electrodynamics, and the cosmic microwave background / M. Mewes -- High energy astrophysical tests of Lorentz invariance / B. Altschul -- Fundamental physics experiments in space (within ESA) / T. J. Sumner -- The experimental foundations of the Dirac equation / C. Lämmerzahl -- Perspectives on Lorentz and CPT violation / V. A. Kostelecký -- Search for Lorentz and CPT violation effects in muon spin precession / B. L. Roberts -- Lorentz violation in a diffeomorphism-invariant theory / R. Jackiw -- Studies of CPT symmetry with ASACUSA / R. S. Hayano -- Neutrino oscillations and Lorentz violation with MiniBooNE / R. Tayloe and T. Katori -- Testing Lorentz and CPT invariance with MINOS near detector neutrinos / B. J. Rebel and S. L. Mufson -- Einstein-ther gravity: theory and observational constraints / T. Jacobson -- Tests of Lorentz-invariance violation in neutrino oscillations / K. Whisnant -- Search for CPT violation in neutral kaons at KLOE: status and perspectives / A. Di Domenico et al. -- Search for CPT violation in B[symbol]-B¯[symbol] oscillations with BABAR / D. P. Stoker -- Theoretical topics in spacetime-symmetry violations / R. Lehnert -- A second-generation co-magnetometer for testing fundamental symmetries / S. J. Smullin et al. -- Nambu-Goldstone and massive modes in gravitational theories with spontaneous Lorentz breaking / R. Bluhm -- The ALPHA antihydrogen experiment / N. Madsen et al. -- Atom interferometry tests the isotropy of post-Newtonian gravity / H. Müller et al. -- Probing Lorentz symmetry with gravitationally coupled matter / J. D. Tasson -- Torsion balance test of preferred-frame and weak coupling to
Symmetry-Based Tunnelings in High-Resolution Rovibrational Spectra of Octahedral Molecules
NASA Astrophysics Data System (ADS)
Mitchell, Justin; Harter, William
2010-06-01
High-resolution spectra of spherical-top molecules are known to demonstrate rotational level clustering. This clustering is well described as a rotational phase-space effect Multiple equivalent phase-space regions allow tunneling and thus splitting of the rotational clusters. So far this has been done with an ad hoc tunneling Hamiltonian. Similar splittings have been shown for low dimensional systems, also with an ad hoc parameterization. While ad hoc tunneling parameterization is simple to understand, it becomes extremely difficult to apply for higher symmetries and for locally low-symmetry clustering when many tunneling paths are possible. Symmetry-based parameterization mitigates this complication. This presentation will discuss how symmetry-based tunneling is applied for octahedral molecules and demonstrate how local-C1, C2, C3 or C4 clusters may be evaluated perturbatively. Connections to non-rotational systems, such as large amplitude motion, will be discussed as well. W.G. Harter and C.W. Patterson, Phys Rev Lett 38, 224 (1977) W.G. Harter and C.W. Patterson, J Chem Phys 66, 4872 (1977) J.T. Hougen J Mol Spect 123, 197 (1987)
Transport of Parallel Momentum Induced by Current-Symmetry Breaking in Toroidal Plasmas
Camenen, Y.; Peeters, A. G.; Casson, F. J.; Hornsby, W. A.; Snodin, A. P.; Angioni, C.; Strintzi, D.
2009-03-27
The symmetry of a physical system strongly impacts on its properties. In toroidal plasmas, the symmetry along a magnetic field line usually constrains the radial flux of parallel momentum to zero in the absence of background flows. By breaking the up-down symmetry of the toroidal currents, this constraint can be relaxed. The parallel asymmetry in the magnetic configuration then leads to an incomplete cancellation of the turbulent momentum flux across a flux surface. The magnitude of the subsequent toroidal rotation increases with the up-down asymmetry and its sign depends on the direction of the toroidal magnetic field and plasma current. Such a mechanism offers new insights in the interpretation and control of the intrinsic toroidal rotation in present day experiments.
Rotational excitation of CH4 by He atoms
NASA Astrophysics Data System (ADS)
Yanga, B. H.; Stancil, P. C.
2008-10-01
Quantum close-coupling and coupled-state approximation scattering calculations for rotational energy transfer of rotationally excited CH4 due to collisions with He are presented for collision energies between 10-7 and 3000 cm-1 using the MP4 potential of Calderoni et al. [J. Chem. Phys. 121, 8261 (2004)]. State-to-state cross sections and rate coefficients from selected initial rotational states of CH4 in symmetries A, E, and F are studied from the ultra-cold to the thermal regime. Comparison of the cross sections with available theoretical results and experimental data show good agreement. Applications to astrophysics and cold laboratory environments are briefly addressed.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Entanglement renormalization and gauge symmetry
Tagliacozzo, L.; Vidal, G.
2011-03-15
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
From symmetries to number theory
Tempesta, P.
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Quantitative Analysis of Face Symmetry.
Tamir, Abraham
2015-06-01
The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait. PMID:26080172
NASA Technical Reports Server (NTRS)
1976-01-01
The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.
Symmetry, Statistics and Structure in MHD Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.
Rotational preference in gymnastics.
Heinen, Thomas; Jeraj, Damian; Vinken, Pia M; Velentzas, Konstantinos
2012-06-01
In gymnastics, most skills incorporate rotations about one or more body axes. At present, the question remains open if factors such as lateral preference and/or vestibulo-spinal asymmetry are related to gymnast's rotational preference. Therefore, we sought to explore relationships in gymnast's rotation direction between different gymnastic skills. Furthermore, we sought to explore relationships between rotational preference, lateral preference, and vestibulo-spinal asymmetry. In the experiment n = 30 non-experts, n = 30 near-experts and n = 30 experts completed a rotational preference questionnaire, a lateral preference inventory, and the Unterberger-Fukuda Stepping Test. The results revealed, that near-experts and experts more often rotate rightward in the straight jump with a full turn when rotating leftward in the round-off and vice versa. The same relationship was found for experts when relating the rotation preference in the handstand with a full turn to the rotation preference in the straight jump with a full turn. Lateral preference was positively related to rotational preference in non-expert gymnasts, and vestibulo-spinal asymmetry was positively related to rotational preference in experts. We suggest, that gymnasts should explore their individual rotational preference by systematically practicing different skills with a different rotation direction, bearing in mind that a clearly developed structure in rotational preference between different skills may be appropriate to develop more complex skills in gymnastics. PMID:23486362
Rotational Preference in Gymnastics
Heinen, Thomas; Jeraj, Damian; Vinken, Pia M.; Velentzas, Konstantinos
2012-01-01
In gymnastics, most skills incorporate rotations about one or more body axes. At present, the question remains open if factors such as lateral preference and/or vestibulo-spinal asymmetry are related to gymnast’s rotational preference. Therefore, we sought to explore relationships in gymnast’s rotation direction between different gymnastic skills. Furthermore, we sought to explore relationships between rotational preference, lateral preference, and vestibulo-spinal asymmetry. In the experiment n = 30 non-experts, n = 30 near-experts and n = 30 experts completed a rotational preference questionnaire, a lateral preference inventory, and the Unterberger-Fukuda Stepping Test. The results revealed, that near-experts and experts more often rotate rightward in the straight jump with a full turn when rotating leftward in the round-off and vice versa. The same relationship was found for experts when relating the rotation preference in the handstand with a full turn to the rotation preference in the straight jump with a full turn. Lateral preference was positively related to rotational preference in non-expert gymnasts, and vestibulo-spinal asymmetry was positively related to rotational preference in experts. We suggest, that gymnasts should explore their individual rotational preference by systematically practicing different skills with a different rotation direction, bearing in mind that a clearly developed structure in rotational preference between different skills may be appropriate to develop more complex skills in gymnastics. PMID:23486362
Quantal rotation and its coupling to intrinsic motion in nuclei
NASA Astrophysics Data System (ADS)
Nakatsukasa, Takashi; Matsuyanagi, Kenichi; Matsuzaki, Masayuki; Shimizu, Yoshifumi R.
2016-07-01
Symmetry breaking is an important concept in nuclear physics and other fields of physics. Self-consistent coupling between the mean-field potential and the single-particle motion is a key ingredient in the unified model of Bohr and Mottelson, which could lead to a deformed nucleus as a consequence of spontaneous breaking of the rotational symmetry. Some remarks on the finite-size quantum effects are given. In finite nuclei, the deformation inevitably introduces the rotation as a symmetry-restoring collective motion (Anderson–Nambu–Goldstone mode), and the rotation affects the intrinsic motion. In order to investigate the interplay between the rotational and intrinsic motions in a variety of collective phenomena, we use the cranking prescription together with the quasiparticle random phase approximation (QRPA). At low spin, the coupling effect can be seen in the generalized intensity relation. A feasible quantization of the cranking model is presented, which provides a microscopic approach to the higher-order intensity relation. At high spin, the semiclassical cranking prescription works well. We discuss properties of collective vibrational motions under rapid rotation and/or large deformation. The superdeformed shell structure plays a key role in emergence of a new soft mode which could lead to instability toward the {K}π ={1}- octupole shape. A wobbling mode of excitation, which is a clear signature of the triaxiality, is discussed in terms of a microscopic point of view. A crucial role played by the quasiparticle alignment is presented.
Rotating magnetic quadrupole current drive for field-reversed configurations
Milroy, Richard D.; Guo, H.Y.
2005-07-15
In the translation, confinement, and sustainment experiment [A. L. Hoffman, H. Y. Guo, J. T. Slough, S. J. Tobin, L. S. Schrank, W. A. Reass, and G. A. Wurden, Fusion Sci. Technol. 41, 92 (2002)], field-reversed configurations (FRCs) are created and sustained using a rotating magnetic field (RMF). The RMF is usually in the form of a rotating dipole, which in vacuum penetrates uniformly to the axis of symmetry. However, plasma conditions in the FRC normally adjust so that the RMF only partially penetrates the plasma column. We have investigated the possibility of using a rotating quadrupole rather than a rotating dipole magnetic field. The vacuum field from a quadrupole is proportional to radius and cannot penetrate to the axis of symmetry; however, this is not a disadvantage if the current drive is confined to the outer region of the FRC. It was found that the quadrupole drive efficiency is comparable to that of a dipole, but the rotating dipole is more effective at stabilizing the n=2 rotational instability. A strong internal oscillation in B{sub {theta}} is often observed in FRCs sustained by a quadrupole field. The spectral content of the signals indicates that an internal n=1 magnetic structure forms and corotates with the electrons. Similar but much lower amplitude structures can form when a rotating dipole is employed (edge-driven mode)
Effective field theory of emergent symmetry breaking in deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2015-09-03
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. In this study, we extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. Lastly, in deformed nuclei these are vibrational modes each of which serves as band head of a rotational band.
Effective field theory of emergent symmetry breaking in deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2015-09-03
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. In this study, we extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. Lastly, in deformed nuclei these are vibrational modes each of whichmore » serves as band head of a rotational band.« less
Rotational order–disorder structure of fluorescent protein FP480
Pletnev, Sergei; Morozova, Kateryna S.; Verkhusha, Vladislav V.; Dauter, Zbigniew
2009-09-01
An analysis of the rotational order–disorder structure of fluorescent protein FP480 is presented. In the last decade, advances in instrumentation and software development have made crystallography a powerful tool in structural biology. Using this method, structural information can now be acquired from pathological crystals that would have been abandoned in earlier times. In this paper, the order–disorder (OD) structure of fluorescent protein FP480 is discussed. The structure is composed of tetramers with 222 symmetry incorporated into the lattice in two different ways, namely rotated 90° with respect to each other around the crystal c axis, with tetramer axes coincident with crystallographic twofold axes. The random distribution of alternatively oriented tetramers in the crystal creates a rotational OD structure with statistically averaged I422 symmetry, although the presence of very weak and diffuse additional reflections suggests that the randomness is only approximate.
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Black holes and Abelian symmetry breaking
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Niz, Gustavo; Tasinato, Gianmassimo
2016-09-01
Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector–tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector–tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.
Dynamical Symmetries Reflected in Realistic Interactions
Sviratcheva, K.D.; Draayer, J.P.; Vary, J.P.; /Iowa State U. /LLNL, Livermore /SLAC
2007-04-06
Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei. Based on spectral distribution methods, a comparison of these interactions to a most general Sp(4) dynamically symmetric interaction, which previously we found to reproduce well that part of the interaction that is responsible for shaping pairing-governed isobaric analog 0{sup +} states, can determine the extent to which this significantly simpler model Hamiltonian can be used to obtain an approximate, yet very good description of low-lying nuclear structure. And furthermore, one can apply this model in situations that would otherwise be prohibitive because of the size of the model space. In addition, we introduce a Sp(4) symmetry breaking term by including the quadrupole-quadrupole interaction in the analysis and examining the capacity of this extended model interaction to imitate realistic interactions. This provides a further step towards gaining a better understanding of the underlying foundation of realistic interactions and their ability to reproduce striking features of nuclei such as strong pairing correlations or collective rotational motion.
Time-resolved beam symmetry measurement for VMAT commissioning and quality assurance.
Barnes, Michael P; Greer, Peter B
2016-01-01
In volumetric-modulated arc therapy (VMAT) treatment delivery perfect beam symmetry is assumed by the planning system. This study aims to test this assump-tion and present a method of measuring time-resolved beam symmetry measure-ment during a VMAT delivery that includes extreme variations of dose rate and gantry speed. The Sun Nuclear IC Profiler in gantry mount was used to measure time-resolved in-plane and cross-plane profiles during plan delivery from which symmetry could be determined. Time-resolved symmetry measurements were performed throughout static field exposures at cardinal gantry angles, conformal arcs with constant dose rate and gantry speed, and during a VMAT test plan with gantry speed and dose rate modulation. Measurements were performed for both clockwise and counterclockwise gantry rotation and across four Varian 21iX lin-acs. The symmetry was found to be generally constant throughout the static field exposures to within 0.3% with an exception on one linac of up to 0.7%. Agreement in symmetry between cardinal angles was always within 1.0% and typically within 0.6%. During conformal arcs the results for clockwise and counterclockwise rotation were in agreement to within 0.3%. Both clockwise and counterclockwise tended to vary in similar manner by up to 0.5% during arc consistent with the cardinal gantry angle static field results. During the VMAT test plan the symmetry generally was in agreement with the conformal arc results. Greater variation in symmetry was observed in the low-dose-rate regions by up to 1.75%. All results were within clinically acceptable levels using the tolerances of NCS Report 24 (2015). PMID:27074485
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
Topological crystalline insulators and superconductors with order-two nonsymmorphic symmetry
NASA Astrophysics Data System (ADS)
Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori
Topological crystalline insulators (TCIs) and topological crystalline superconductors (TCSCs) are symmetry protected topological phases of free fermions with space group symmetry. Like conventional topological insulators and superconductors, TCIs and TCSCs support stable gapless boundary states associated with bulk topological nontriviality, when the additional symmetry is compatible with the boundary. Using the twisted equivariant K-theory, we complete the classification of TCIs and TCSCs in the presence of additional order-two nonsymmorphic space group (NSG) symmetry, which includes half lattice translation with Z2 spin flip, glide, two-fold screw rotation, and their magnetic symmetries. From isomorphisms connecting different space dimensions, the K-groups are evaluated by those in one-dimension. The resultant topological table shows several interesting features: (1) The NSGs allow various Z2 topological phases, even in the absence of time-reversal and/or particle-hole symmetries. Their boundary states are detached from the bulk spectrum in the direction of the non-primitive lattice translation. (2) Z4 phases are found to be realized. Especially, the TCI with the glide and the time-reversal symmetry in three-dimensions shows the Z4 phase.
An Analysis of Gravitational Redshift from Rotating Body
NASA Astrophysics Data System (ADS)
Dubey, Anuj Kumar; Sen, A. K.
2015-07-01
Gravitational redshift is generally calculated without considering the rotation of a body. Neglecting the rotation, the geometry of space time can be described by using the spherically symmetric Schwarzschild geometry. Rotation has great effect on general relativity, which gives new challenges on gravitational redshift. When rotation is taken into consideration spherical symmetry is lost and off diagonal terms appear in the metric. The geometry of space time can be then described by using the solutions of Kerr family. In the present paper we discuss the gravitational redshift for rotating body by using Kerr metric. The numerical calculations has been done under Newtonian approximation of angular momentum. It has been found that the value of gravitational redshift is influenced by the direction of spin of central body and also on the position (latitude) on the central body at which the photon is emitted. The variation of gravitational redshift from equatorial to non - equatorial region has been calculated and its implications are discussed in detail.
NASA Astrophysics Data System (ADS)
Kimura, Keiji; Takehiro, Shin-ichi; Yamada, Michio
2013-08-01
We investigate the stability and bifurcation of Boussinesq thermal convection in a moderately rotating spherical shell, with the inner sphere free to rotate as a solid body due to the viscous torque of the fluid. The ratio of the inner and outer radii of the spheres and the Prandtl number are fixed to 0.4 and 1, respectively. The Taylor number is varied from 522 to 5002 and the Rayleigh number from 1500 to 10 000. In this parameter range, the finite-amplitude traveling wave solutions, which have four-fold symmetry in the azimuthal direction, bifurcate supercritically at the critical points. The inner sphere rotates in the prograde direction due to the viscous torque of the fluid when the rotation rate is small while it rotates in the retrograde direction when the rotation rate is large. However, the stable region of these traveling wave solutions is quantitatively similar to that in the co-rotating system where the inner and outer spheres rotate with the same angular velocity. The structures of convective motions of these solutions such as the radial component of velocity are quantitatively similar to those in the co-rotating system, but the structure of mean zonal flows is effectively changed by the inner sphere rotation.
Rotationally resolved infrared spectroscopy of adamantane
NASA Astrophysics Data System (ADS)
Pirali, O.; Boudon, V.; Oomens, J.; Vervloet, M.
2012-01-01
We present the first rotationally resolved spectra of adamantane (C10H16) applying gas-phase Fourier transform infrared (IR) absorption spectroscopy. High-resolution IR spectra are recorded in the 33-4500 cm-1range using as source of IR radiation both synchrotron radiation (at the AILES beamline of the SOLEIL synchrotron) as well as a classical globar. Adamantane is a spherical top molecule with tetrahedral symmetry (Td point group) and has no permanent dipole moment in its vibronic ground state. Of the 72 fundamental vibrational modes in adamantane, only 11 are IR active. Here we present rotationally resolved spectra for seven of them: ν30, ν28, ν27, ν26, ν25, ν24, and ν23. The typical rotational structure of spherical tops is observed and analyzed using the STDS software developed in the Dijon group, which provides the first accurate energy levels and rotational constants for seven fundamental modes. Rotational levels with quantum numbers as high as J = 107 have been identified and included in the fit leading to a typical standard deviation of about 10-3 cm-1.
Symmetry Breaking for Black-Scholes Equations
NASA Astrophysics Data System (ADS)
Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng
2007-06-01
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
Applications of Symmetry to Problem Solving.
ERIC Educational Resources Information Center
Leikin, Roza; Berman, Abraham; Zaslavsky, Orit
2000-01-01
Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…
Power Harvesting from Rotation?
ERIC Educational Resources Information Center
Chicone, Carmen; Feng, Z. C.
2008-01-01
We show the impossibility of harvesting power from rotational motions by devices attached to the rotating object. The presentation is suitable for students who have studied Lagrangian mechanics. (Contains 2 figures.)
CP symmetry in optical systems
NASA Astrophysics Data System (ADS)
Dana, Brenda; Bahabad, Alon; Malomed, Boris A.
2015-04-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Symmetry and Stochastic Gene Regulation
NASA Astrophysics Data System (ADS)
Ramos, Alexandre F.; Hornos, José E. M.
2007-09-01
Lorentz-like noncompact Lie symmetry SO(2,1) is found in a spin-boson stochastic model for gene expression. The invariant of the algebra characterizes the switch decay to equilibrium. The azimuthal eigenvalue describes the affinity between the regulatory protein and the gene operator site. Raising and lowering operators are constructed and their actions increase or decrease the affinity parameter. The classification of the noise regime of the gene arises from the group theoretical numbers.
Scissors-Mode Vibrations and the Emergence of SU(3) Symmetry from the Projected Deformed Mean Field
Sun, Y.; Wu, C.; Bhatt, K.; Sun, Y.; Guidry, M.; Sun, Y.; Guidry, M.; Wu, C.; Bhatt, K.; Feng, D.H.
1998-01-01
Starting from a deformed potential we construct separate bases of collective neutron and proton rotational states by exact angular momentum projection. These rotational states are then coupled by diagonalizing a residual pairing plus quadrupole interaction. Many new bands emerge that are not found in the rotation of the usual BCS condensate, and may correspond to the geometrical scissors mode and its generalizations. These excitation modes can be understood as rotational bands built on spin-1{h_bar} phonon excitations; they exhibit a nearly perfect dynamical SU(3) fermion spectrum, even though there is no explicit dynamical symmetry in our model. {copyright} {ital 1998} {ital The American Physical Society}
Symmetry analysis of talus bone
Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.
2014-01-01
Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391
Dark matter and global symmetries
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.
2016-09-01
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system
NASA Astrophysics Data System (ADS)
Lian, Zeng-Ju; Chen, Li-Li; Lou, Sen-Yue
2005-08-01
The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.
Rotations with Rodrigues' Vector
ERIC Educational Resources Information Center
Pina, E.
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears…
Mechanism of rotational relaxation.
NASA Technical Reports Server (NTRS)
Polanyi, J. C.; Woodall, K. B.
1972-01-01
A model is presented which describes the characteristic pattern of relaxation of a nonthermal rotational distribution of hydrogen halide, peaked initially at high rotational quantum number J, to a thermal distribution without generating a peak at intermediate J. A method for correcting infrared chemiluminiscence data for modest rotational relaxation is also suggested.
Acoustic Faraday rotation in Weyl semimetals
NASA Astrophysics Data System (ADS)
Liu, Donghao; Shi, Junren
We investigate the phonon problems in Weyl semimetals, from which both the phonon Berry curvature and the phonon Damping could be obtained. We show that even without a magnetic field, the degenerate transverse acoustic modes could also be split due to the adiabatic curvature. In three dimensional case, acoustic Faraday rotation shows up. And furthermore, since the attenuation procedure could distinguish the polarized mode, single circularly polarized acoustic wave could be realized. We study the mechanism in the novel time reversal symmetry broken Weyl semimetal. New effects rise because of the linear dispersion, which give enlightenment in the measurement of this new kind of three-dimensional material.
TESTING CPT SYMMETRY WITH CURRENT AND FUTURE CMB MEASUREMENTS
Li, Si-Yu; Zhang, Xinmin; Xia, Jun-Qing; Li, Hong; Li, Mingzhe
2015-02-01
In this paper, we use the current and future cosmic microwave background (CMB) experiments to test the Charge-Parity-Time Reversal (CPT) symmetry. We consider a CPT-violating interaction in the photon sector L{sub cs}∼p{sub μ}A{sub ν} F-tilde {sup μν}, which gives rise to a rotation of the polarization vectors of the propagating CMB photons. By combining the 9 yr WMAP, BOOMERanG 2003, and BICEP1 observations, we obtain the current constraint on the isotropic rotation angle α-bar =−2.12±1.14 (1σ), indicating that the significance of the CPT violation is about 2σ. Here, we particularly take the systematic errors of CMB measurements into account. Then, we study the effects of the anisotropies of the rotation angle [Δα( n-hat )] on the CMB polarization power spectra in detail. Due to the small effects, the current CMB polarization data cannot constrain the related parameters very well. We obtain the 95% C.L. upper limit of the variance of the anisotropies of the rotation angle C {sup α}(0) < 0.035 from all of the CMB data sets. More interestingly, including the anisotropies of rotation angle could lower the best-fit value of r and relax the tension on the constraints of r between BICEP2 and Planck. Finally, we investigate the capabilities of future Planck polarization measurements on α-bar and Δα( n-hat ). Benefited from the high precision of Planck data, the constraints of the rotation angle can be significantly improved.
Testing CPT Symmetry with Current and Future CMB Measurements
NASA Astrophysics Data System (ADS)
Li, Si-Yu; Xia, Jun-Qing; Li, Mingzhe; Li, Hong; Zhang, Xinmin
2015-02-01
In this paper, we use the current and future cosmic microwave background (CMB) experiments to test the Charge-Parity-Time Reversal (CPT) symmetry. We consider a CPT-violating interaction in the photon sector {L}_cs˜ p_μ A_ν \\tilde{F}μ ν , which gives rise to a rotation of the polarization vectors of the propagating CMB photons. By combining the 9 yr WMAP, BOOMERanG 2003, and BICEP1 observations, we obtain the current constraint on the isotropic rotation angle \\bar{α } = -2.12 +/- 1.14 (1σ), indicating that the significance of the CPT violation is about 2σ. Here, we particularly take the systematic errors of CMB measurements into account. Then, we study the effects of the anisotropies of the rotation angle [Δ {α }({\\hat{n}})] on the CMB polarization power spectra in detail. Due to the small effects, the current CMB polarization data cannot constrain the related parameters very well. We obtain the 95% C.L. upper limit of the variance of the anisotropies of the rotation angle C α(0) < 0.035 from all of the CMB data sets. More interestingly, including the anisotropies of rotation angle could lower the best-fit value of r and relax the tension on the constraints of r between BICEP2 and Planck. Finally, we investigate the capabilities of future Planck polarization measurements on \\bar{α } and Δ {α }({\\hat{n}}). Benefited from the high precision of Planck data, the constraints of the rotation angle can be significantly improved.
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.
2014-06-01
In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.
Polyhedra with noncrystallographic symmetry as the orbits of crystallographic point symmetry groups
NASA Astrophysics Data System (ADS)
Ovsetsina, T. I.; Chuprunov, E. V.
2015-11-01
Polyhedra with noncrystallographic symmetry are analyzed as the orbits of crystallographic point symmetry groups on a set of smooth or structured ("hatched") planes. Polyhedra with symmetrically equivalent faces, obtained using crystallographic point groups but having noncrystallographic symmetry, and polyhedra, the symmetry group T of which is crystallographic but can be implemented only on the assumption of a noncrystallographic character of the internal structure of polyhedron, are studied. The results of the analysis for all 32 point symmetry groups are listed in table.
Geometry defects in bosonic symmetry-protected topological phases
NASA Astrophysics Data System (ADS)
You, Yizhi; You, Yi-Zhuang
2016-06-01
In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry-protected topological (SPT) phases. We start from eight copies of 3D time-reversal (T ) invariant topological superconductors (TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such a disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid crystal (TCL). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the T and translation invariant surface state is a double [e T m T ] state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in the 2D boson SPT state described by an O (4 ) nonlinear σ model (NL σ M ) with topological Θ term. By dressing the O (4 ) vector with spiral order and gauging the symmetry, the dislocation has mutual semion statistics with the gauge flux. Further reducing the O (4 )NL σ M to the Ising limit, we arrive at the Levin-Gu model with stripy modulation whose dislocation has nontrivial braiding statistics.
Algorithms for computer detection of symmetry elements in molecular systems.
Beruski, Otávio; Vidal, Luciano N
2014-02-01
Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry. PMID:24403016
Evidence for triangular D3h symmetry in 12C.
Marín-Lámbarri, D J; Bijker, R; Freer, M; Gai, M; Kokalova, Tz; Parker, D J; Wheldon, C
2014-07-01
We report a measurement of a new high spin Jπ=5- state at 22.4(2) MeV in 12C which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a D3h symmetry characterized by the sequence 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D3h symmetry was observed in triatomic molecules, and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in 12C such as the (0+) Hoyle band and the (1-) bending mode band and suggest measurements in search of the predicted ("missing") states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or nonobservation) of the predicted ("missing") states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in 12C. PMID:25032922
Coexistence of chiral symmetry restoration and random orientation of galaxies
NASA Astrophysics Data System (ADS)
Aryal, B.; Paudel, S.; Saurer, W.
2008-02-01
We studied the chiral symmetry restoration and the spatial orientation of 2288 spiral and spiral barred galaxies that have radial velocities (RV) less than 5000 km s-1. A random direction of the rotation of galaxies is assumed in order to classify the structural modes. The distribution of spin vector and spin vector projections of leading and trailing arm galaxies in the total sample and subsamples are studied. We use chi-square, auto-correlation and Fourier tests in order to discriminate the preferred alignments from the random alignments. A good correlation between the random alignment and the chiral symmetry is noticed in the Local Supercluster (RV < 3000 km s-1) and in galaxies nearby the Local Supercluster (3000 < RV (km s-1) ≤ 5000). Spiral galaxies show a similar result. The barred spirals show an opposite trend to that observed for the spirals. Nearby the Local Supercluster, we noticed a preferred spatial alignment and non-chiral property in the leading and trailing arm spiral barred galaxies. Our result predicts that the progressive loss of chirality might have some connection with the rotationally supported (spirals, barred spirals) and randomized (lenticulars, ellipticals) systems. Thus, we suspect that the dynamical processes in the cluster evolution give rise to a dynamical loss of chirality.
True and false symmetries in the classification of optical scatterers
NASA Astrophysics Data System (ADS)
Crosta, Giovanni F.; Videen, Gorden
2014-05-01
A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential, q0 induce transformations of the scattered wave. The latter can be represented by means of Born sequences, where q0 appears under the integral sign: non-local formulas are thus derived, the properties of which are discussed. Next, the symmetries induced by the 1st BORN approximation are addressed. Invariance of the squared modulus of the scattering amplitude holds for translation and reflection. The transformation Tɛ := 13 +Σ3ℓ=1ɛℓAℓ, with {ɛℓ;} real and {Aℓ} the generators of rotations in IR3, is investigated. Conditions on the {ɛ ℓ} are derived, by which the scattering amplitude coming from the first BORN approximation is invariant to Tɛ. As an application, these "false symmetries" are compared to those induced by limited angular resolution of a detector in light scattering experiments. Namely, scattering patterns are made available by the TAOS (Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting single airborne aerosol particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. The optics and the detector properties determine the resolution at which a pattern is saved. The implications on the performance of TAOS pattern analysis are briefly discussed.
Curl force dynamics: symmetries, chaos and constants of motion
NASA Astrophysics Data System (ADS)
Berry, M. V.; Shukla, Pragya
2016-06-01
This is a theoretical study of Newtonian trajectories governed by curl forces, i.e. position-dependent but not derivable from a potential, investigating in particular the possible existence of conserved quantities. Although nonconservative and nonhamiltonian, curl forces are not dissipative because volume in the position–velocity state space is preserved. A physical example is the effective forces exerted on small particles by light. When the force has rotational symmetry, for example when generated by an isolated optical vortex, particles spiral outwards and escape, even with an attractive gradient force, however strong. Without rotational symmetry, and for dynamics in the plane, the state space is four-dimensional, and to search for possible constants of motion we introduce the Volume of section: a numerical procedure, in which orbits are plotted as dots in a three-dimensional subspace. For some curl forces, e.g. optical fields with two opposite-strength vortices, the dots lie on a surface, indicating a hidden constant of motion. For other curl forces, e.g. those from four vortices, the dots explore clouds, in an unfamiliar kind of chaos, suggesting that no constant of motion exists. The curl force dynamics generated by optical vortices could be studied experimentally.
Coffman, R.T.
1957-12-10
A seal is described for a rotatable shaft that must highly effective when the shaft is not rotating but may be less effective while the shaft is rotating. Weights distributed about a sealing disk secured to the shaft press the sealing disk against a tubular section into which the shiilt extends, and whem the shaft rotates, the centrifugal forces on the weights relieve the pressurc of the sealing disk against the tubular section. This action has the very desirible result of minimizing the wear of the rotating disk due to contact with the tubular section, while affording maximum sealing action when it is needed.
Optimal fold symmetry of LH2 rings on a photosynthetic membrane
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
Enhanced Facial Symmetry Assessment in Orthodontists
Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342
Symmetries in nuclei: New methods and applications
NASA Astrophysics Data System (ADS)
Caprio, Mark A.
2011-04-01
When a symmetry is a ``good'' symmetry of the nuclear system, as in the dynamical symmetries of the shell model and interacting boson model, this symmetry can directly give the spectroscopic properties of the nucleus, without the need for involved calculations. However, even if a symmetry is strongly broken, it nonetheless provides a calculational tool, classifying the basis states used in a full computational treatment of the many-body problem and greatly simplifying the underlying computational machinery. The symmetry then serves as the foundation for a physically meaningful truncation scheme for the calculation. This talk will provide an introduction to new applications of symmetry approaches to the nuclear problem, including the required mathematical developments. Supported by the US DOE under grant DE-FG02-95ER-40934 and by the Research Corporation for Science Advancement under a Cottrell Scholar Award.
Symmetry Breaking in the Hidden-Order Phase of URu2Si2
NASA Astrophysics Data System (ADS)
Shibauchi, Takasada
2013-03-01
In the heavy fermion compound URu2Si2, the hidden-order transition occurs at 17.5 K, whose nature has posed a long-standing mystery. A second-order phase transition is characterized by spontaneous symmetry breaking, and thus the nature of the hidden order cannot be determined without understanding which symmetry is being broken. Our magnetic torque measurements in small pure crystals reveal the emergence of an in-plane anisotropy of the magnetic susceptibility below the transition temperature, indicating the spontaneous breaking of four-fold rotational symmetry of the tetragonal URu2Si2. In addition, our recent observation of cyclotron resonance allows the full determination of the electron-mass structure of the main Fermi-surface sheets, which implies an anomalous in-plane mass anisotropy consistent with the rotational symmetry breaking. These results impose strong constraints on the symmetry of the hidden order parameter. This work has been done in collaboration with R. Okazaki, S. Tonegawa, K. Hashimoto, K. Ikada, Y. H. Lin, H. Shishido, H. J. Shi, Y. Haga, T. D. Matsuda, E. Yamamoto, Y. Onuki, H. Ikeda, and Y. Matsuda.
Effective field theory for one-dimensional valence-bond-solid phases and their symmetry protection
NASA Astrophysics Data System (ADS)
Fuji, Yohei
2016-03-01
We investigate valence-bond-solid (VBS) phases in one-dimensional spin systems by an effective field theory developed by Schulz [Phys. Rev. B 34, 6372 (1986), 10.1103/PhysRevB.34.6372]. While the distinction among the VBS phases is often understood in terms of different entanglement structures protected by certain symmetries, we adopt a different but more fundamental point of view, that is, different VBS phases are separated by a gap closing under certain symmetries. In this way, the effective field theory reproduces the known three symmetries: time reversal, bond-centered inversion, and dihedral group of π spin rotations. It also predicts that there exists another symmetry: site-centered inversion combined with a spin rotation by π . We demonstrate that the last symmetry gives distinct trivial phases, which cannot be characterized by their entanglement structure, in terms of a simple perturbative analysis in a spin chain. We also discuss several applications of the effective field theory to the phase transitions among VBS phases in microscopic models and an extension of the Lieb-Schultz-Mattis theorem to non-translational-invariant systems.
Macek, M. Leviatan, A.
2014-12-15
We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon–Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.
Spontaneous rotation in a driven mechanical system
NASA Astrophysics Data System (ADS)
Alexander, T. J.
2016-06-01
We show that a mass free to circulate around a shaken pivot point exhibits resonance-like effects and large amplitude dynamics even though there is no natural frequency in the system, simply through driving under geometrical constraint. We find that synchronization between force and mass occurs over a wide range of forcing amplitudes and frequencies, even when the forcing axis is dynamically, and randomly, changed. Above a critical driving amplitude the mass will spontaneously rotate, with a fractal boundary dividing clockwise and anti-clockwise rotations. We show that this has significant implications for energy harvesting, with large output power over a wide frequency range. We examine also the effect of driving symmetry on the resultant dynamics, and show that if the shaking is circular the motion becomes constrained, whereas for anharmonic rectilinear shaking the dynamics may become chaotic, with the system mimicking that of the kicked rotor.
Killing symmetries as Hamiltonian constraints
NASA Astrophysics Data System (ADS)
Lusanna, Luca
2016-02-01
The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.
Hidden symmetries in jammed systems
NASA Astrophysics Data System (ADS)
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
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.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
Global Rotation of Non-Rotating Origin
NASA Astrophysics Data System (ADS)
Fukushima, T.
2001-11-01
At its 24th General Assembly held at Manchester last year, the IAU has adopted the Celestial Ephemeris Origin (CEO) as a new longitude origin of the celestial coordinate system (Capitaine et al. 2000, IAU 2001). The CEO is the application of Guinot's non-rotating origin (NRO) to the Earth's equator (Guinot 1979, Capitaine et al. 1986, Capitaine 1990). By using the current IAU precession/nutation theory, we integrated the global orbit of CEO. It is a slightly curved zigzag pattern of the amplitude of around 23o moving secularly along the ecliptic. Among its kinematical features, we note that CEO has a large secular component of rotation with respect to the inertial reference frame. The current speed of this global rotation is as large as around -4.15 ''/yr. The negative sign shows that CEO rotates clockwise with respect to the inertial frame when viewed from the north celestial pole. Unfortunately this is a general property of NROs. On the other hand, such secular rotation does not exist for some geometrically-defined longitude origins like K, H, and Σ already discussed in Kovalevsky and McCarthy (1998). We think that the existence of a global secular rotaion means that the CEO, and NROs in general, is not appropriate to be specified as the x-axis of celestial coordinate systems.
Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity
NASA Astrophysics Data System (ADS)
Al-Hashimi, M. H.; Shalaby, A. M.; Wiese, U.-J.
2015-11-01
The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson-Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R =(l + 1) (l + 2) a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ = ∞ or γ =2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards
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.
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Duality symmetries in string theory
Nunez, Carmen A.
1999-10-25
The search for a unified theory of quantum gravity and gauge interactions leads naturally to string theory. This field of research has received a revival of interest after the discovery of duality symmetries in recent years. We present a self contained account of some non-perturbative aspects of string theory which have been recently understood. The spectrum and interactions of the five consistent superstring theories in ten dimensions are recollected and the fundamental principles underlying this initial stage in the construction of the theory are briefly reviewed. We next discuss some evidences that these apparently different superstrings are just different aspects of one unique theory. The key to this development is given by the non-perturbative duality symmetries which have modified and improved our understanding of string dynamics in many ways. In particular, by relating the fundamental objects of one theory to solitons of another theory, they have unraveled the presence of extended objects in the theory which stand on an equal footing with strings. We introduce these higher dimensional objects, named D-branes, and discuss applications of D-brane physics.
Introduction to Electroweak Symmetry Breaking
Dawson,S.
2008-10-02
The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: Gν=Zn with n ≥3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry Gℓ=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries Gℓ, an agreement with the data can be achieved if ˜10 % corrections related to breaking of Gℓ and Gν are included.
Emergence of symmetry breaking in fucoid zygotes.
Homblé, Fabrice; Léonetti, Marc
2007-06-01
Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents. PMID:17499009
Rasmusson, A; Hahn, U; Larsen, J O; Gundersen, H J G; Jensen, E B Vedel; Nyengaard, J R
2013-05-01
This paper presents a new local volume estimator, the spatial rotator, which is based on measurements on a virtual 3D probe, using computer assisted microscopy. The basic design of the probe builds upon the rotator principle which requires only a few manual intersection markings, thus making the spatial rotator fast to use. Since a 3D probe is involved, it is expected that the spatial rotator will be more efficient than the the nucleator and the planar rotator, which are based on measurements in a single plane. An extensive simulation study shows that the spatial rotator may be more efficient than the traditional local volume estimators. Furthermore, the spatial rotator can be seen as a further development of the Cavalieri estimator, which does not require randomization of sectioning or viewing direction. The tissue may thus be sectioned in any arbitrary direction, making it easy to identify the specific tissue region under study. In order to use the spatial rotator in practice, however, it is necessary to be able to identify intersection points between cell boundaries and test rays in a series of parallel focal planes, also at the peripheral parts of the cell boundaries. In cases where over- and underprojection phenomena are not negligible, they should therefore be corrected for if the spatial rotator is to be applied. If such a correction is not possible, it is needed to avoid these phenomena by using microscopy with increased resolution in the focal plane. PMID:23488880
On the analysis of rotational symmetric microstructured surfaces
NASA Astrophysics Data System (ADS)
Benítez, Pablo; Miñano, Juan C.; Santamaría, Asunción; Hernández, Maikel
2007-03-01
A previous paper [2] presented an analysis of a class of microstructured optical surfaces in two dimensions, in which a classification of the microstructures was obtained (regular and anomalous) and a concept of 2D ideal microstructures was introduced. In this paper the study of those microstructured optical surfaces is extended to three dimensions with rotational symmetry. As a starting point, non-microstructured rotational optical systems in the First Order Approximation are also classified as point-spot type and ring-spot type, with remarkable perfect particular cases. This classification is also extended to the case in which ideal microstructured rotational surfaces are used, for both regular and anomalous type. The case of perfect ring-spot type system with an odd number of rotational, anomalous, ideal microstructures enables the definition of an anomalous aplanatic system that has direct application for mixing spatially and angularly the light emitted by several sources.
Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas
Artun, M.; Tang, W.M.
1994-03-01
The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. PMID:25354765
Scars of symmetries in quantum chaos
Delande, D.; Gay, J.C.
1987-10-19
The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
ERIC Educational Resources Information Center
Graham, John P.
2014-01-01
Symmetry properties of molecules are generally introduced in second-year or third-year-level inorganic or physical chemistry courses. Students generally adapt readily to understanding and applying the operations of rotation (C[subscript n]), reflection (s), and inversion (i). However, the two-step operation of improper rotation-reflection…
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
A K3 sigma model with : symmetry
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto; Wendland, Katrin
2014-02-01
The K3 sigma model based on the -orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra . By combining these different viewpoints we show that the = (4 , 4) preserving symmetries of this theory are described by the discrete symmetry group : . This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Issues in standard model symmetry breaking
Golden, M.
1988-04-01
This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
Hopf Bifurcation from Rotating Waves and Patterns in Physical Space
NASA Astrophysics Data System (ADS)
Golubitsky, M.; LeBlanc, V. G.; Melbourne, I.
2000-02-01
Hopf bifurcations from time periodic rotating waves to two frequency tori have been studied for a number of years by a variety of authors including Rand and Renardy. Rotating waves are solutions to partial differential equations where time evolution is the same as spatial rotation. Thus rotating waves can exist mathematically only in problems that have at least SO (2) symmetry. In this paper we study the effect on this Hopf bifurcation when the problem has more than SO (2) symmetry. These effects manifest themselves in physical space and not in phase space. We use as motivating examples the experiments of Gorman et al . on porous plug burner flames, of Swinney et al . on the Taylor-Couette system, and of a variety of people on meandering spiral waves in the Belousov-Zhabotinsky reaction. In our analysis we recover and complete Rand's classification of modulated wavy vortices in the Taylor-Couette system. It is both curious and intriguing that the spatial manifestations of the two frequency motions in each of these experiments is different, and it is these differences that we seek to explain. In particular, we give a mathematical explanation of the differences between the nonuniform rotation of cellular flames in Gorman's experiments and the meandering of spiral waves in the Belousov-Zhabotinsky reaction. Our approach is based on the center bundle construction of Krupa with compact group actions and its extension to noncompact group actions by Sandstede, Scheel, and Wulff.
Scott, Hayley S; Bajpai, Alankriti; Chen, Kai-Jie; Pham, Tony; Space, Brian; Perry, John J; Zaworotko, Michael J
2015-10-14
A primitive cubic (pcu) network of formula [Ni(1,2-bis(4-pyridyl)acetylene)2(Cr2O7)]n, , has been synthesised and found to exhibit a novel type of inclined 2-fold interpenetration and an isosteric heat of adsorption (Q(st)) of 30.5 kJ mol(-1) towards CO2 at zero loading. Q(st) is relatively high in the broad context but less than that observed in related hybrid ultramicroporous materials, a feature that can be understood after studying pore structure and molecular simulations of CO2 adsorption. PMID:26307270
Vibrational spectrum and internal rotation in 2,6-dimethylpyrazine
NASA Astrophysics Data System (ADS)
Arenas, J. F.; Lopez-Navarrete, J. T.; Marcos, J. I.; Otero, J. C.
1989-06-01
The infrared and Raman spectra of 2,6-dimethylpyrazine have been recorded and assigned on the basis of a C2v molecular geometry previously determined by MINDO/3. The potential energy function corresponding to the internal rotation of both methyl groups has been used to solve the Schrödinger equation, and to obtain the energy levels of that motion on the basis of a molecular symmetry G36. The rotation of each methyl group is found to be independent of the other.
Vibrational spectrum and internal rotation in 2,5-dimethylpyrazine
NASA Astrophysics Data System (ADS)
Arenas, J. F.; López-Navarrete, J. T.; Marcos, J. I.; Otero, J. C.
1987-11-01
The infrared and Raman spectra of 2,5-dimethylpyrazine have been recorded and assigned on the basis of a C2h molecular geometry previously determined by MINDO/3. The potential energy function corresponding to the internal rotation of both methyl groups has been used to solve the Schrödinger equation, and to obtain the energy levels of that motion on the basis of a molecular symmetry G36. The rotation of each substituent is found to be almost independent of the other.
Neoclassical electron and ion transport in toroidally rotating plasmas
Sugama, H.; Horton, W.
1997-06-01
Neoclassical transport processes of electrons and ions are investigated in detail for toroidally rotating axisymmetric plasmas with large flow velocities on the order of the ion thermal speed. The Onsager relations for the flow-dependent neoclassical transport coefficients are derived from the symmetry properties of the drift kinetic equation with the self-adjoint collision operator. The complete neoclassical transport matrix with the Onsager symmetry is obtained for the rotating plasma consisting of electrons and single-species ions in the Pfirsch{endash}Schl{umlt u}ter and banana regimes. It is found that the inward banana fluxes of particles and toroidal momentum are driven by the parallel electric field, which are phenomena coupled through the Onsager symmetric off-diagonal coefficients to the parallel currents caused by the radial thermodynamic forces conjugate to the inward fluxes, respectively. {copyright} {ital 1997 American Institute of Physics.}
Optical rotation in excess of 100 rad generated by Rb vapor in a multipass cell
Li, S.; Vachaspati, P.; Sheng, D.; Dural, N.; Romalis, M. V.
2011-12-15
Paramagnetic Faraday rotation is a powerful technique for atom sensing widely used in quantum nondemolition measurements, fundamental symmetry tests, and other precision measurements. We demonstrate the use of a multipass optical cell for Faraday rotation spectroscopy and observe polarization rotation in excess of 100 rad from spin-polarized Rb vapor. Unlike optical cavities, multipass cells have a deterministic number of light passes and can be used to measure large optical rotations. We also observe a tenfold suppression of transverse spin relaxation when Rb atoms are placed in a coherent superposition state immune to spin-exchange collisions.
Optical rotation in excess of 100 rad generated by Rb vapor in a multipass cell
NASA Astrophysics Data System (ADS)
Li, S.; Vachaspati, P.; Sheng, D.; Dural, N.; Romalis, M. V.
2011-12-01
Paramagnetic Faraday rotation is a powerful technique for atom sensing widely used in quantum nondemolition measurements, fundamental symmetry tests, and other precision measurements. We demonstrate the use of a multipass optical cell for Faraday rotation spectroscopy and observe polarization rotation in excess of 100 rad from spin-polarized Rb vapor. Unlike optical cavities, multipass cells have a deterministic number of light passes and can be used to measure large optical rotations. We also observe a tenfold suppression of transverse spin relaxation when Rb atoms are placed in a coherent superposition state immune to spin-exchange collisions.
Stationary axisymmetric and slowly rotating spacetimes in Hořava-Lifshitz gravity.
Wang, Anzhong
2013-03-01
Stationary, axisymmetric, and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and it is shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary, and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution. This is in contrast to the claim of Barausse and Sotiriou [Phys. Rev. Lett. 109, 181101 (2012)], in which slowly rotating black holes were reported (incorrectly) not to exist in the infrared limit of the nonprojectable HL theory. PMID:23496699
Voit, E O
1992-04-01
An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems. PMID:1591448
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
Modeling rapidly rotating stars
NASA Astrophysics Data System (ADS)
Rieutord, M.
2006-06-01
We review the quest of modeling rapidly rotating stars during the past 40 years and detail the challenges to be taken up by models facing new data from interferometry, seismology, spectroscopy... We then present the progress of the ESTER project aimed at giving a physically self-consistent model for the structure and evolution of rapidly rotating stars.
Rotatable shear plate interferometer
Duffus, Richard C.
1988-01-01
A rotatable shear plate interferometer comprises a transparent shear plate mounted obliquely in a tubular supporting member at 45.degree. with respect to its horizontal center axis. This tubular supporting member is supported rotatably around its center axis and a collimated laser beam is made incident on the shear plate along this center axis such that defocus in different directions can be easily measured.
CONTROL ROD ROTATING MECHANISM
Baumgarten, A.; Karalis, A.J.
1961-11-28
A threaded rotatable shaft is provided which rotates in response to linear movement of a nut, the shaft being surrounded by a pair of bellows members connected to either side of the nut to effectively seal the reactor from leakage and also to store up energy to shut down the reactor in the event of a power failure. (AEC)
Technology Transfer Automated Retrieval System (TEKTRAN)
The Old Rotation (circa 1896) is the oldest, continuous cotton experiment in the world. Its 13 plots on 1 acre of land on the campus of Auburn University continue to document the long-term effects of crop rotations with and without winter legumes (crimson clover) as a source of nitrogen for cotton,...
Neutrino properties and fundamental symmetries
Bowles, T.J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V{sub ub}/V{sub cb} = {radical}m{sub u}/m{sub c} and V{sub td}/V{sub ts} = {radical}m{sub d}/m{sub s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay {beta} {yields} s{gamma} constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan{Beta}, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Rare Isotopes and Fundamental Symmetries
NASA Astrophysics Data System (ADS)
Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy
2009-01-01
Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
NASA Astrophysics Data System (ADS)
Jin, Yan; Jia, Man; Lou, Sen-Yue
2012-12-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Arthroscopic rotator cuff repair.
Burkhart, Stephen S; Lo, Ian K Y
2006-06-01
Arthroscopic rotator cuff repair is being performed by an increasing number of orthopaedic surgeons. The principles, techniques, and instrumentation have evolved to the extent that all patterns and sizes of rotator cuff tear, including massive tears, can now be repaired arthroscopically. Achieving a biomechanically stable construct is critical to biologic healing. The ideal repair construct must optimize suture-to-bone fixation, suture-to-tendon fixation, abrasion resistance of suture, suture strength, knot security, loop security, and restoration of the anatomic rotator cuff footprint (the surface area of bone to which the cuff tendons attach). By achieving optimized repair constructs, experienced arthroscopic surgeons are reporting results equal to those of open rotator cuff repair. As surgeons' arthroscopic skill levels increase through attendance at surgical skills courses and greater experience gained in the operating room, there will be an increasing trend toward arthroscopic repair of most rotator cuff pathology. PMID:16757673
Interferometry for rotating sources
NASA Astrophysics Data System (ADS)
Velle, S.; Mehrabi Pari, S.; Csernai, L. P.
2016-06-01
The two particle interferometry method to determine the size of the emitting source after a heavy ion collision is extended. Following the extension of the method to spherical expansion dynamics, here we extend the method to rotating systems. It is shown that rotation of a cylindrically symmetric system leads to modifications, which can be perceived as spatial asymmetry by the "azimuthal HBT" method. We study an exact rotating and expanding solution of the fluid dynamical model of heavy ion reactions. We consider a source that is azimuthally symmetric in space around the axis of rotation, and discuss the features of the resulting two particle correlation function. This shows the azimuthal asymmetry arising from the rotation. We show that this asymmetry leads to results similar to those given by spatially asymmetric sources.
Sevec, John B.
1978-01-01
A protective device to provide a warning if a piece of rotating machinery slows or stops comprises a pair of hinged weights disposed to rotate on a rotating shaft of the equipment. When the equipment is rotating, the weights remain in a plane essentially perpendicular to the shaft and constitute part of an electrical circuit that is open. When the shaft slows or stops, the weights are attracted to a pair of concentric electrically conducting disks disposed in a plane perpendicular to the shaft and parallel to the plane of the weights when rotating. A disk magnet attracts the weights to the electrically conducting plates and maintains the electrical contact at the plates to complete an electrical circuit that can then provide an alarm signal.
NASA Astrophysics Data System (ADS)
Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi
2013-08-01
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
On the existence of periodic solutions to nonlinear elasto-dynamic systems with symmetry
NASA Astrophysics Data System (ADS)
Whalen, Timothy Michael
The nonlinear dynamics of periodic motion for elastic structures are investigated. By exploiting the underlying symmetry of the structure, the linearized dynamics problem is solved efficiently. Using these solutions as approximations, the existence of solution branches for the nonlinear dynamics is proved using bifurcation theorems and group theoretic ideas. The technique is illustrated for two discretized, rotating systems: a three bar truss with D(3) symmetry and a dish antenna with D(6) symmetry. Linear solutions are obtained by employing coordinate transformations motivated by the symmetry that block-diagonalise the governing equations. Although these equations are only C(n) symmetric (due to the gyroscopic effects), a theorem is proved that allows the use of D(n) group-theoretic information in the computation of the transformation. Using Liapunov-Schmidt reduction, conditions are checked that guarantee bifurcation of certain solutions. These conditions hold only when the natural frequencies are nonresonant. This is shown to occur generically for stiffening constitutive laws. The antenna problem is analyzed numerically, and the computational savings obtained by exploiting symmetry are shown. Problems involving vibration of elastic loops are examined. For a rotating loop, the symmetry group S0(2) is used to find families of linear solutions. One family is found to possess resonant natural frequencies, invalidating our method. Bifurcation is proved formally for the other families. For a pressurized loop, bifurcating travelling wave solutions are sought, and the existence of such motions is formally exhibited. The applicability of certain analysis results in our calculations is discussed. Resonance is investigated by studying the vibration of a pinned string. The linearization is shown to have resonance problems for all natural frequencies because of scale invariance.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Symmetry Properties of Potentiometric Titration Curves.
ERIC Educational Resources Information Center
Macca, Carlo; Bombi, G. Giorgio
1983-01-01
Demonstrates how the symmetry properties of titration curves can be efficiently and rigorously treated by means of a simple method, assisted by the use of logarithmic diagrams. Discusses the symmetry properties of several typical titration curves, comparing the graphical approach and an explicit mathematical treatment. (Author/JM)
Hidden flavor symmetries of SO(10) GUT
NASA Astrophysics Data System (ADS)
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Topological phases protected by point group symmetry
NASA Astrophysics Data System (ADS)
Huang, Sheng-Jie; Song, Hao; Hermele, Michael
There has been remarkable progress in the theoretical understanding of symmetry protected topological (SPT) phases. However, most theories focus on internal, or on-site, symmetries, even though spatial symmetries are important in solids. In this talk, we classify bosonic SPT phases protected by crystalline point group symmetry, which we dub point group SPT (pgSPT) phases. Our approach is based on a procedure to reduce a d-dimensional pgSPT phase to lower-dimensional SPT phases protected by internal symmetry. For three-dimensional pgSPT phases, this approach allows us to gain insight into non-trivial properties at symmetry preserving surfaces. In particular, we obtain toy models for the surfaces of certain pgSPT phases at which there is a symmetry preserving Z2 topological order with anomalous symmetry fractionalization. We also discuss connections between bosonic pgSPT phases and electronic topological crystalline insulators. This research is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
Copper Keplerates: High-Symmetry Magnetic Molecules.
Palacios, Maria A; Moreno Pineda, Eufemio; Sanz, Sergio; Inglis, Ross; Pitak, Mateusz B; Coles, Simon J; Evangelisti, Marco; Nojiri, Hiroyuki; Heesing, Christian; Brechin, Euan K; Schnack, Jürgen; Winpenny, Richard E P
2016-01-01
Keplerates are molecules that contain metal polyhedra that describe both Platonic and Archimedean solids; new copper keplerates are reported, with physical studies indicating that even where very high molecular symmetry is found, the low-temperature physics does not necessarily reflect this symmetry. PMID:26530901
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Extracting hidden symmetry from the energy spectrum
NASA Astrophysics Data System (ADS)
Yuzbashyan, Emil A.; Happer, William; Altshuler, Boris L.; Shastry, Sriram B.
2003-03-01
In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapours. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the hydrogen atom.
On Gauging Symmetry of Modular Categories
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-05-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4} -obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Tests of gravitational symmetries with radio pulsars
NASA Astrophysics Data System (ADS)
Shao, LiJing; Wex, Norbert
2016-09-01
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.
Symmetries in geology and geophysics
Turcotte, Donald L.; Newman, William I.
1996-01-01
Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters. PMID:11607719
Chiral symmetries associated with angular momentum
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Kleinert, M.
2014-03-01
In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this paper, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.
Symmetric rotating-wave approximation for the generalized single-mode spin-boson system
Albert, Victor V.; Scholes, Gregory D.; Brumer, Paul
2011-10-15
The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra- and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime. Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.
Bianchini, P.; Varri, A. L.; Bertin, G.; Zocchi, A.
2013-07-20
Internal rotation is thought to play a major role in the dynamics of some globular clusters. However, in only a few cases has internal rotation been studied by the quantitative application of realistic and physically justified global models. Here, we present a dynamical analysis of the photometry and three-dimensional kinematics of {omega} Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is interpreted very well by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster {omega} Cen, the selected model reproduces the complex three-dimensional kinematics; in particular, the observed anisotropy profile, characterized by a transition from isotropy to weakly radial anisotropy and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2⊂SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
Stability of unsteady flow in a rotating torus
NASA Astrophysics Data System (ADS)
Hewitt, Richard; Hazel, Andrew; Clarke, Richard; Denier, James
2011-11-01
We consider the temporal evolution of a viscous incompressible fluid in a torus of finite curvature; a problem first investigated experimentally by Madden and Mullin (1994), herein referred to as MM. The system is initially in a state of rigid-body rotation (about the axis of rotational symmetry) and the container's rotation rate is then changed impulsively. We describe the transient flow that is induced at small values of the Ekman number, over a time scale that is comparable to one complete rotation of the container. We show that (rotationally symmetric) eruptive singularities (of the boundary layer) occur at the inner or outer bend of the pipe for a decrease or an increase in rotation rate respectively. Moreover, there is a ratio of initial-to-final rotation frequencies for which eruptive singularities can occur at both the inner and outer bend simultaneously. We also demonstrate that the flow is susceptible to non-axisymmetric inflectional instabilities. The inflectional instability arises as a consequence of the developing eruption and is shown to be in qualitative agreement with the experimental observations of MM. Detailed quantitative comparisons are made between asymptotic predictions and finite (but small) Ekman number Navier-Stokes computations using a finite-element method.
NASA Technical Reports Server (NTRS)
Roberts, Glyn O.
1991-01-01
Undesired gravitational effects such as convection or sedimentation in a fluid can sometimes be avoided or decreased by the use of a closed chamber uniformly rotated about a horizontal axis. In a previous study, the spiral orbits of a heavy or buoyant particle in a uniformly rotating fluid were determined. The particles move in circles, and spiral in or out under the combined effects of the centrifugal force and centrifugal buoyancy. A optimization problem for the rotation rate of a cylindrical reactor rotated about its axis and containing distributed particles was formulated and solved. Related studies in several areas are addressed. A computer program based on the analysis was upgraded by correcting some minor errors, adding a sophisticated screen-and-printer graphics capability and other output options, and by improving the automation. The design, performance, and analysis of a series of experiments with monodisperse polystyrene latex microspheres in water were supported to test the theory and its limitations. The theory was amply confirmed at high rotation rates. However, at low rotation rates (1 rpm or less) the assumption of uniform solid-body rotation of the fluid became invalid, and there were increasingly strong secondary motions driven by variations in the mean fluid density due to variations in the particle concentration. In these tests the increase in the mean fluid density due to the particles was of order 0.015 percent. To a first approximation, these flows are driven by the buoyancy in a thin crescent-shaped depleted layer on the descending side of the rotating reactor. This buoyancy distribution is balanced by viscosity near the walls, and by the Coriolis force in the interior. A full analysis is beyond the scope of this study. Secondary flows are likely to be stronger for buoyant particles, which spiral in towards the neutral point near the rotation axis under the influence of their centrifugal buoyancy. This is because the depleted layer is
Rotatable seal assembly. [Patent application; rotating targets
Logan, C.M.; Garibaldi, J.L.
1980-11-12
An assembly is provided for rotatably supporting a rotor on a stator so that vacuum chambers in the rotor and stator remain in communication while the chambers are sealed from ambient air, which enables the use of a ball bearing or the like to support most of the weight of the rotor. The apparatus includes a seal device mounted on the rotor to rotate therewith, but shiftable in position on the rotor while being sealed to the rotor as by an O-ring. The seal device has a flat face that is biased towards a flat face on the stator, and pressurized air is pumped between the faces to prevent contact between them while spacing them a small distance apart to avoid the inflow of large amounts of air between the faces and into the vacuum chambers.
Classical and Quantum Symmetries of de Sitter Space
NASA Astrophysics Data System (ADS)
Anninos, Dionysios Theodoros
2011-10-01
De Sitter space is the maximally symmetric cosmology satisfying Einstein's equations with a positive cosmological constant. It has played a crucial role in the theory of inflationary cosmology. Recent astronomical observations indicate our universe is entering a new asymptotically de Sitter phase, with a mysteriously small value for the cosmological constant. We study several aspects of de Sitter and de Sitter-esque geometries in three and four spacetime dimensions. Particularly, we discuss the asymptotic symmetry group (ASG) of four-dimensional de Sitter space at future infinity, I+ , in Einstein gravity with positive cosmological constant. We find, very much unlike its anti-de Sitter cousin, an infinite dimensional group consisting of the three-dimensional diffeomorphisms acting on I+ . We then move on to rotating black holes in de Sitter space and focus on a limit where the black hole and cosmological horizons coincide. We compute the ASG of the near (cosmological) horizon geometry, the rotating Nariai geometry, which has its own future boundary I+RN and find a Virasoro algebra. This is suggestive of a holographically dual interpretation in terms of a two-dimensional CFT. Scalar waves in the rotating Nariai geometry are studied to provide further evidence for the proposal. Finally, we find toy models of the rotating Nariai geometry in three-dimensional theories of gravity with a gravitational Chern-Simons term and further explore the possibility of a holographic duality. Interestingly, we find a de Sitter like vacuum, warped dS3, whose smooth quotients contain both a cosmological as well as an internal event horizon. In contrast, quotients of Lorentzian dS3 always contain conical singularities.
NASA Astrophysics Data System (ADS)
Penotti, Fabio E.; Cooper, David L.
2015-07-01
We examine the symmetry properties of spin-coupled (or full generalised valence bond) wavefunctions for C2H2 and N2. The symmetry-separated (σ,π) and bent-bond (ω) solutions are totally symmetric only in the D4h and D3h subgroups of D∞h, respectively. Two fairly different strategies are explored for imposing full cylindrical symmetry, with one of them (small nonorthogonal configuration interaction calculations involving rotated versions of the wavefunction) turning out to be somewhat preferable on energetic grounds to the other one (application of additional spin constraints to a single spatial configuration). It is also shown that mixing together the cylindrically symmetric symmetry-separated and bent-bond spin-coupled models leads to relatively small energy improvements unless the valence orbitals in each type of configuration are reoptimised.
Symmetry in chemistry from the hydrogen atom to proteins
Kellman, Michael E.
1996-01-01
The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules. PMID:8962040
Jumps, somersaults, and symmetry breaking in Leidenfrost drops.
Chen, Simeng; Bertola, Volfango
2016-08-01
When a droplet of water impacts a heated surface, the drop may be observed to bounce. Recently is has been found that small quantities (∼100 ppm) of polymer additives such as polyethylene oxide can significantly increase the maximum bouncing height of drops. This effect has been explained in terms of the reduction of energy dissipation caused by polymer additives during the drop retraction and rebound, resulting in higher mechanical energy available for bouncing. Here we demonstrate, by comparing three types of fluids (Newtonian, shear-thinning, and viscoelastic), that the total kinetic energy carried by low-viscosity Newtonian drops during retraction is partly transformed into rotational kinetic energy rather than dissipated when compared with high-viscosity or non-Newtonian drops. We also show that non-Newtonian effects play little role in the energy distribution during drop impact, while the main effect is due to the symmetry break observed during the retraction of low-viscosity drops. PMID:27627234
Quasi-periodic continuation along a continuous symmetry
NASA Astrophysics Data System (ADS)
Salomone, Matthew David
Given a system of differential equations which admits a continuous group of symmetries and possesses a periodic solution, we show that under certain nondegeneracy assumptions there always exists a continuous family containing infinitely many periodic and quasi-periodic trajectories. This generalizes the continuation method of Poincaré to orbits which are not necessarily periodic. We apply these results in the setting of the Lagrangian N -body problem of homogeneous potential to characterize an infinite family of rotating nonplanar "hip-hop" orbits in the four-body problem of equal masses, and show how some other trajectories in the N -body theory may be extended to infinite families of periodic and quasi-periodic trajectories.
Fainter and closer: finding planets by symmetry breaking.
Ribak, Erez N; Gladysz, Szymon
2008-09-29
Imaging of planets is very difficult, due to the glare from their nearby, much brighter suns. Static and slowly-evolving aberrations are the limiting factors, even after application of adaptive optics. The residual speckle pattern is highly symmetrical due to diffraction from the telescope's aperture. We suggest to break this symmetry and thus to locate planets hidden beneath it. An eccentric pupil mask is rotated to modulate the residual light pattern not removed by other means. This modulation is then exploited to reveal the planet's constant signal. In well-corrected ground-based observations we can reach planets six stellar magnitudes fainter than their sun, and only 2-3 times the diffraction limit from it. At ten times the diffraction limit, we detect planets 16 magnitudes fainter. The stellar background drops by five magnitudes. PMID:18825194
NASA Technical Reports Server (NTRS)
Binzel, R. P.; Green, J. R.; Opal, C. B.
1986-01-01
Thomas et al. (1984) analyzed 14 Voyager 2 images of Saturn's satellite Hyperion and interpreted them to be consistent with a coherent (nonchaotic) rotation period of 13.1 days. This interpretation was criticized by Peale and Wisdom (1984), who argued that the low sampling frequency of Voyager data does not allow chaotic or nonchaotic rotation to be distinguished. New observations obtained with a higher sampling frequency are reported here which conclusively show that the 13.1 day period found by Thomas et al. was not due to coherent rotation.
NASA Technical Reports Server (NTRS)
Elleman, D. D.; Croonquist, A. P.; Wang, T. G. (Inventor)
1983-01-01
A system is described for acoustically controlled rotation of a levitated object, which avoids deformation of a levitated liquid object. Acoustic waves of the same wavelength are directed along perpendicular directions across the object, and with the relative phases of the acoustic waves repeatedly switched so that one wave alternately leads and lags the other by 90 deg. The amount of torque for rotating the object, and the direction of rotation, are controlled by controlling the proportion of time one wave leads the other and selecting which wave leads the other most of the time.
Symmetry Breaking in a Model for Nodal Cilia
NASA Astrophysics Data System (ADS)
Brokaw, Charles J.
2005-03-01
Nodal cilia are very short cilia found in the embryonic node on the ventral surface of early mammalian embryos. They create a right to left fluid flow that is responsible for determining the normal asymmetry of the internal organs of the mammalian body. To do this, the distal end of the cilium must circle in a counterclockwise sense. Computer simulations with 3-dimensional models of flagella allow examination of 3-dimensional movements such as those of nodal cilia. 3-dimensional circling motions of short cilia can be achieved with velocity controlled models, in which dynein activity is regulated by sliding velocity. If dyneins on one outer doublet are controlled by the sliding velocity experienced by that doublet, the system is symmetric, and the 3-dimensional models can show either clockwise or counterclockwise circling. My computer simulations have examined two possible symmetry breaking mechanisms: 1) dyneins on doublet N are regulated by a mixture of the sliding velocities experienced by doublets N and N+1 (numbered in a clockwise direction, looking from the base). or 2) symmetry is broken by an off-axis force that produces a right-handed twist of the axoneme, consistent with observations that some dyneins can rotate their substrate microtubules in a clockwise direction.
Hidden and generalized conformal symmetry of Kerr-Sen spacetimes
NASA Astrophysics Data System (ADS)
Ghezelbash, A. M.; Siahaan, H. M.
2013-07-01
It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory (CFT) in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum J and electric charge Q of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by SL(2, {Z}) modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in the background of Kerr-Sen black hole and show that in the ‘near region’, the wave equation can be reproduced by the Casimir operator of a local SL(2, {R})_L \\times SL(2, {R})_R hidden conformal symmetry. We find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of SL(2, {R})_L \\times SL(2, {R})_R hidden conformal symmetry, parameterized by one parameter. For some special values of the parameter, we find a copy of SL(2, {R}) hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
Natural quasicrystal with decagonal symmetry.
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S; Andronicos, Christopher L; Distler, Vadim V; Eddy, Michael P; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J; Steinhardt, William M; Yudovskaya, Marina; Steinhardt, Paul J
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Stability of skyrmion lattices and symmetries of Dzyaloshinskii-Moriya magnets
NASA Astrophysics Data System (ADS)
Güngördü, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
Recently, there has been substantial interest in realizations of skyrmions, in particular in 2D systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultra-dense magnetic memories. Here, we use the most general form of the 2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with four-fold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental rea lizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyro-dynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. DOE Early Career Award DE-SC0014189, NSF Grants Nos. Phy-1415600, PHY11-25915, DMR-1420645, and DMR-1308751; Grants-in-Aid from MEXT and SpinNet (Nos. 25800184, 25247056, and 15H01009).
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
Gungordu, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
2016-02-24
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices withmore » fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. As a result, we find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.« less
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
NASA Astrophysics Data System (ADS)
Güngördü, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
2016-02-01
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. We find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.
Nahum, Adam; Serna, P; Chalker, J T; Ortuño, M; Somoza, A M
2015-12-31
We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories. PMID:26765019
... cuff are common. They include tendinitis, bursitis, and injuries such as tears. Rotator cuff tendons can become ... cuff depends on age, health, how severe the injury is, and how long you've had the ...
ERIC Educational Resources Information Center
Greenslade, Thomas B., Jr.
1981-01-01
Discusses theory of the rotating mirror, its use in measuring the velocity of the electrical signal in wires, and the velocity of light. Concludes with a description of the manometric flame apparatus developed for analyzing sound waves. (SK)
NASA Technical Reports Server (NTRS)
Gregory, T. J.
1977-01-01
Apparatus holds remotely piloted arm that accelerates until launching speed is reached. Then vehicle and counterweight at other end of arm are released simultaneously to avoid structural damage from unbalanced rotating forces.
... tear occurs when one of the tendons is torn from the bone from overuse or injury. Causes ... surgery with a larger incision) to repair the torn tendon. Outlook (Prognosis) With rotator cuff tendinitis, rest, ...
... already torn from chronic rotator cuff problems. A partial tear may not require surgery. Instead, rest and ... Follow any discharge and self-care instructions you are given. You will be wearing a sling when you leave the hospital. ...
FAST TRACK COMMUNICATION Single-charge rotating black holes in four-dimensional gauged supergravity
NASA Astrophysics Data System (ADS)
Chow, David D. K.
2011-02-01
We consider four-dimensional U(1)4 gauged supergravity, and obtain asymptotically AdS4, non-extremal, charged, rotating black holes with one non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a generalization that includes a NUT parameter. The general solution has a discrete symmetry involving inversion of the rotation parameter, and has a string frame metric that admits a rank-2 Killing-Stäckel tensor.
Molecular collisions. 11: Semiclassical approximation to atom-symmetric top rotational excitation
NASA Technical Reports Server (NTRS)
Russell, D.; Curtiss, C. F.
1973-01-01
In a paper of this series a distorted wave approximation to the T matrix for atom-symmetric top scattering was developed which is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.
Molecular collisions 21: Semiclassical approximation to atom-symmetric top rotational excitation
NASA Technical Reports Server (NTRS)
Russell, D.; Curtiss, C. F.
1973-01-01
A distorted wave approximation to the T matrix for atom-symmetric top scattering was developed. The approximation is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Electromagnetic rotational actuation.
Hogan, Alexander Lee
2010-08-01
There are many applications that need a meso-scale rotational actuator. These applications have been left by the wayside because of the lack of actuation at this scale. Sandia National Laboratories has many unique fabrication technologies that could be used to create an electromagnetic actuator at this scale. There are also many designs to be explored. In this internship exploration of the designs and fabrications technologies to find an inexpensive design that can be used for prototyping the electromagnetic rotational actuator.
Hunter, Steven L.
2002-01-01
A rate sensor for angular/rotational acceleration includes a housing defining a fluid cavity essentially completely filled with an electrolyte fluid. Within the housing, such as a toroid, ions in the fluid are swept during movement from an excitation electrode toward one of two output electrodes to provide a signal for directional rotation. One or more ground electrodes within the housing serve to neutralize ions, thus preventing any effect at the other output electrode.
NASA Technical Reports Server (NTRS)
Wilcox, Brian H.; Tso, Kam S.; Litwin, Todd E.; Hayati, Samad A.; Bon, Bruce B.
1991-01-01
Experimental robotic system semiautomatically grasps rotating object, stops rotation, and pulls object to rest in fixture. Based on combination of advanced techniques for sensing and control, constructed to test concepts for robotic recapture of spinning artificial satellites. Potential terrestrial applications for technology developed with help of system includes tracking and grasping of industrial parts on conveyor belts, tracking of vehicles and animals, and soft grasping of moving objects in general.
Instability in Rotating Machinery
NASA Technical Reports Server (NTRS)
1985-01-01
The proceedings contain 45 papers on a wide range of subjects including flow generated instabilities in fluid flow machines, cracked shaft detection, case histories of instability phenomena in compressors, turbines, and pumps, vibration control in turbomachinery (including antiswirl techniques), and the simulation and estimation of destabilizing forces in rotating machines. The symposium was held to serve as an update on the understanding and control of rotating machinery instability problems.
Whealton, John H.; Tsai, Chin-Chi
2003-05-27
A spark plug device includes a structure for modification of an arc, the modification including arc rotation. The spark plug can be used in a combustion engine to reduce emissions and/or improve fuel economy. A method for operating a spark plug and a combustion engine having the spark plug device includes the step of modifying an arc, the modifying including rotating the arc.
Symmetries and "simple" solutions of the classical n-body problem
NASA Astrophysics Data System (ADS)
Chenciner, Alain
2006-03-01
The Lagrangian of the classical n-body problem has well known symmetries: isometries of the ambient Euclidean space (translations, rotations, reflexions) and changes of scale coming from the homogeneity of the potential. To these symmetries are associated "simple" solutions of the problem, the so-called homographic motions, which play a basic role in the global understanding of the dynamics. The classical subproblems (planar, isosceles) are also consequences of the existence of symmetries: invariance under reflexion through a plane in the first case, invariance under exchange of two equal masses in the second. In these two cases, the symmetry acts at the level of the "shape space" (the oriented one in the first case) whose existence is the main difference between the 2-body problem and the (n ≥ 3)-body problem. These symmetries of the Lagrangian imply symmetries of the action functional, which is defined on the space of regular enough loops of a given period in the configuration space of the problem. Minimization of the action under well-chosen symmetry constraints leads to remarkable solutions of the n-body problem which may also be called simple and could play after the homographic ones the role of organizing centers in the global dynamics. In [13] and [16], I have given a survey of the new classes of solutions which had been obtained in this way, mainly choreographies of n equal masses in a plane or in space and generalized Hip-Hops of at least 4 arbitrary masses in space. I give here an updated overview of the results and a quick glance at the methods of proofs.
Symmetries of supergravity black holes
NASA Astrophysics Data System (ADS)
Chow, David D. K.
2010-10-01
We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stäckel tensors. These are induced by rank-2 Killing-Stäckel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the 'physical' metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity but also consider some other solutions.
Mobile-bearing knees reduce rotational asymmetric wear.
Ho, Fang-Yuan; Ma, Hon-Ming; Liau, Jiann-Jong; Yeh, Chuan-Ren; Huang, Chun-Hsiung
2007-09-01
Polyethylene wear of bearing components is the most common long-term complication in total knee arthroplasty. One would anticipate differing kinematics would generate different wear patterns (including wear type, degree, and symmetry) on the articulating surface of mobile-bearing and fixed-bearing inserts. Because mobile-bearing designs facilitate movement of the insert relative to the tray when the knee rotates, we hypothesized mobile-bearing designs would reduce the incidence of rotational asymmetric wear. We examined 51 worn tibial inserts, including 15 from mobile-bearing rotating-platform posterior-cruciate-sacrificing dished prostheses and 36 from fixed-bearing posterior-cruciate-retaining flat prostheses, which were retrieved at revision surgery with an average implantation time of 115 months. We divided wear types into low-grade wear (burnishing, abrasion, and cold flow) and high-grade wear (scratching, pitting, metal embedding, and delamination) to assess wear degree of polyethylene. To assess symmetry of wear, the insert surface was divided into medial and lateral sides and each side was further divided into three equal zones along the anteroposterior direction. Low-grade wear was more common in mobile-bearing knees, whereas high-grade wear was more common in fixed-bearing knees. We identified no internal/external rotational asymmetric wear or anteroposterior asymmetric wear in mobile-bearing knees. PMID:17483732
NASTRAN forced vibration analysis of rotating cyclic structures
NASA Technical Reports Server (NTRS)
Elchuri, V.; Smith, G. C. C.; Gallo, A. M.
1983-01-01
Theoretical aspects of a new capability developed and implemented in NASTRAN level 17.7 to analyze forced vibration of a cyclic structure rotating about its axis of symmetry are presented. Fans, propellers, and bladed shrouded discs of turbomachines are some examples of such structures. The capability includes the effects of Coriolis and centripetal accelerations on the rotating structure which can be loaded with: (1) directly applied loads moving with the structure and (2) inertial loas due to the translational acceleration of the axis of rotation (''base' acceleration). Steady-state sinusoidal or general periodic loads are specified to represent: (1) the physical loads on various segments of the complete structure, or (2) the circumferential harmonic components of the loads in (1). The cyclic symmetry feature of the rotating structure is used in deriving and solving the equations of forced motion. Consequently, only one of the cyclic sectors is modelled and analyzed using finite elements, yielding substantial savings in the analysis cost. Results, however, are obtained for the entire structure. A tuned twelve bladed disc example is used to demonstrate the various features of the capability.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Electromagnetic Radiation under Explicit Symmetry Breaking
NASA Astrophysics Data System (ADS)
Sinha, Dhiraj; Amaratunga, Gehan A. J.
2015-04-01
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
\\cal{PT} -symmetry in Rydberg atoms
NASA Astrophysics Data System (ADS)
Ziauddin; Chuang, You-Lin; Lee, Ray-Kuang
2016-07-01
We propose a scheme to realize parity-time ( {PT} )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87Rb atoms in a four-level inverted Y-type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from {PT} -symmetry to non-PT -symmetry via different external parameters, i.e., coupling field detuning, probe field intensity and control field intensity.
Polytopes vibrations within Coxeter group symmetries
NASA Astrophysics Data System (ADS)
Chadzitaskos, Goce; Patera, Jiıř´; Szajewska, Marzena
2016-05-01
We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean space R3. By changing one simple element of the polytope (position of one vertex or length of an edge), one can retain the exact symmetry of the polytope by simultaneously changing other corresponding elements of the polytope. A simple method of using the symmetry of polytopes in order to determine several resonant frequencies is presented. Knowledge of these frequencies, or at least their ratios can be used for control of some principal changes of the polytopes.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Critical Symmetry and Supersymmetry in Nuclei
Iachello, Francesco
2006-04-26
The role of dynamic symmetries and supersymmetries in nuclei is reviewed. The concept of critical symmetry, appropriate to describe bosonic systems (even-even nuclei) at the critical point of a phase transition, is introduced, and the symmetry, E(5), at the critical point of spherical to {gamma}-unstable shape phase transition, is discussed. The recently introduced concept of critical supersymmetry, appropriate to describe mixed systems of bosons and fermions (odd-even nuclei) at the critical point of a phase transition is presented. The case of a j=3/2 particle at the critical point of spherical to {gamma}-unstable transition, called E(5/4), is discussed.
Mirror Symmetry for Quasi-Homogeneous Singularities
NASA Astrophysics Data System (ADS)
Rathnakumara, Himal; Jarvis, Tyler
2008-10-01
I will present an introduction to mirror symmetry in the context of string theory. Then I will describe an instance of mirror symmetry for singularties defined by quasi-homogeneous polynomials in weighted projective spaces. Milnor rings and the FJRW (Fan-Jarvis-Ruan-Witten) rings associated with these singularities and their relation to the Landua-Ginzburg A model and the Landua-Ginzburg B model will be explained. Results of the calculations for certain singularities for which the mirror symmetry conjecture has been verified will be presented.
Rotating superconductor magnet for producing rotating lobed magnetic field lines
Hilal, Sadek K.; Sampson, William B.; Leonard, Edward F.
1978-01-01
This invention provides a rotating superconductor magnet for producing a rotating lobed magnetic field, comprising a cryostat; a superconducting magnet in the cryostat having a collar for producing a lobed magnetic field having oppositely directed adjacent field lines; rotatable support means for selectively rotating the superconductor magnet; and means for energizing the superconductor magnet.
NASA Astrophysics Data System (ADS)
García-Senz, D.; Cabezón, R. M.; Domínguez, I.; Thielemann, F. K.
2016-03-01
Currently the number of models aimed at explaining the phenomena of type Ia supernovae is high and distinguishing between them is a must. In this work we explore the influence of rotation on the evolution of the nuclear flame that drives the explosion in the so-called gravitational confined detonation models. Assuming that the flame starts in a pointlike region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very dependent on the angle between the rotational axis and the line connecting the initial bubble of burned material with the center of the WD at the moment of ignition. The impact of rotation is larger for angles close to 90° because the Coriolis force on a floating element of fluid is maximum and its principal effect is to break the symmetry of the deflagration. Such symmetry breaking weakens the convergence of the nuclear flame at the antipodes of the initial ignition volume, changing the environmental conditions around the convergence region with respect to non-rotating models. These changes seem to disfavor the emergence of a detonation in the compressed volume at the antipodes and may compromise the viability of the so-called gravitational confined detonation mechanism.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Vortex formation in a fast rotating Bose-Einstein condensate
Ghosh, Tarun Kanti
2004-04-01
We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a noninteracting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.
Pletnev, Sergei; Subach, Fedor V.; Verkhusha, Vladislav V.; Dauter, Zbigniew
2014-01-01
An analysis of the rotational order–disorder structure of the reversibly photoswitchable red fluorescent protein rsTagRFP is presented. The rotational order–disorder (OD) structure of the reversibly photoswitchable fluorescent protein rsTagRFP is discussed in detail. The structure is composed of tetramers of 222 symmetry incorporated into the lattice in two different orientations rotated 90° with respect to each other around the crystal c axis and with tetramer axes coinciding with the crystallographic twofold axes. The random distribution of alternatively oriented tetramers in the crystal creates the rotational OD structure with statistically averaged I422 symmetry. Despite order–disorder pathology, the structure of rsTagRFP has electron-density maps of good quality for both non-overlapping and overlapping parts of the model. The crystal contacts, crystal internal architecture and a possible mechanism of rotational OD crystal formation are discussed.
Symmetry energy of warm nuclear systems
NASA Astrophysics Data System (ADS)
Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.
2014-02-01
The temperature dependence of the symmetry energy and symmetry free energy coefficients of infinite nuclear matter and of finite nuclei is investigated. For infinite matter, both these coefficients are found to have a weaker dependence on temperature at densities close to saturation; at low but homogeneous densities, the temperature dependence becomes stronger. For finite systems, different definitions of symmetry energy coefficients are encountered in the literature yielding different values. A resolution to this problem is suggested from a global liquid-drop-inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nucleus is modeled in a subtracted finite-temperature Thomas-Fermi framework, with dynamical surface phonon coupling to nucleonic motion plugged in. Contrary to infinite nuclear matter, a substantial change in the symmetry energy coefficients is observed for finite nuclei with temperature.
RNA quaternary structure and global symmetry.
Jones, Christopher P; Ferré-D'Amaré, Adrian R
2015-04-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, by contrast, virtually all RNAs with complex 3D structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA) and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic di-AMP (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spatial Symmetries of the Local Densities
Rohozinski, S.; Dobaczewski, J.; Nazarewicz, Witold
2010-01-01
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Matrix Models, Emergent Spacetime and Symmetry Breaking
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2009-12-15
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
RNA quaternary structure and global symmetry
Jones, Christopher P.; Ferré-D'Amaré, Adrian R.
2015-01-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, in contrast, virtually all RNAs with complex three-dimensional structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here, we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA), and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic diadenosine monophosphate (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spontaneous chiral symmetry breaking in metamaterials
NASA Astrophysics Data System (ADS)
Liu, Mingkai; Powell, David A.; Shadrivov, Ilya V.; Lapine, Mikhail; Kivshar, Yuri S.
2014-07-01
Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains.
Modelling Symmetry Classes 233 and 432.
ERIC Educational Resources Information Center
Dutch, Steven I.
1986-01-01
Offers instructions and geometrical data for constructing solids of the enantiomorphous symmetry classes 233 and 432. Provides background information for each class and highlights symmetrical relationships and construction patterns. (ML)
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Matrix Models, Emergent Spacetime and Symmetry Breaking
NASA Astrophysics Data System (ADS)
Grosse, Harald; Lizzi, Fedele; Steinacker, Harold
2009-12-01
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
Shift symmetry and inflation in supergravity
Brax, Philippe; Martin, Jerome
2005-07-15
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one modulus and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the modulus, but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the {eta} problem is alleviated. Combining the KKLT mechanism for modulus stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we find models reminiscent of 'mutated hybrid inflation' where the inflationary trajectory is curved in the modulus-inflaton plane. We analyze the phenomenology of these models and stress their differences with both chaotic and hybrid inflation.
Compact stars and the symmetry energy
NASA Astrophysics Data System (ADS)
Providência, Constana; Cavagnoli, Rafael; Menezes, Debora P.; Panda, Prafulla K.; Rabhi, Aziz
2013-02-01
The effect of the symmetry energy on some properties of compact stars which contain strange degrees of freedom is discussed. Both the onset of hyperons or kaon condensation will be considered. The hyperon-meson couplings are chosen according to experimental values of the hyperon nuclear matter potentials and possible uncertainties are considered. It is shown that a softer symmetry energy affects the onset of strangeness, namely neutral (negatively charged) strange particles set on at larger (smaller) densities, and gives rise to a smaller strangeness fraction as a function of density. A softer symmetry energy will possibily give rise to maximum mass configurations with larger masses. Hyperon-meson couplings have a strong effect on the mass of the star. It is shown that, for stars with masses above 1 Msolar, the radius of the star varies linearly with the symmetry energy slope L.
Symmetry and the Cosmic Microwave Background
NASA Technical Reports Server (NTRS)
Wollock, Edward J.
2012-01-01
A brief historical introduction to the development of observational astronomy and cosmology will be presented. The close relationship between the properties of light, symmetry, and our understanding the contents of our universe will be explored.
Composite fermions and broken symmetries in graphene.
Amet, F; Bestwick, A J; Williams, J R; Balicas, L; Watanabe, K; Taniguchi, T; Goldhaber-Gordon, D
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields. PMID:25562690
Composite fermions and broken symmetries in graphene
NASA Astrophysics Data System (ADS)
Amet, F.; Bestwick, A. J.; Williams, J. R.; Balicas, L.; Watanabe, K.; Taniguchi, T.; Goldhaber-Gordon, D.
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.
NASA Astrophysics Data System (ADS)
Barker, J. A. T.; Singh, D.; Thamizhavel, A.; Hillier, A. D.; Lees, M. R.; Balakrishnan, G.; Paul, D. McK.; Singh, R. P.
2015-12-01
The superconductivity of the noncentrosymmetric compound La7 Ir3 is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature Tc=2.25 K —a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La7 Ir3 may be unconventional and paves the way for further studies of this family of materials.
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-André; Oberli, D. Y.; Karlsson, K. F.; Dalessi, S.; Gallinet, B.; Svendsen, G.
2014-03-31
We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.