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.