1985-08-01
spanner wrench and the teaspoon, the pointed jaws of the wrench, and the main axes of the gourd , the pear, the squash, and the bowl of the teaspoon...regions such as the handle of the spanner wrench and the main axes of the gourd , squash, and teaspoon, and also pointed regions such as the end of the...Local Symmetry representation does not provide in- tuitively acceptable analyses for round regions, such as the lemon and the round ends of the gourd
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.
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.
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.
Rotation roots and neoclassical viscosity in quasi-symmetry
NASA Astrophysics Data System (ADS)
Cole, A. J.; Hegna, C. C.; Callen, J. D.
2009-11-01
In a quasi-symmetric device, there exists a symmetry angle αh= θ-Nζ/M, such that |B| = B0(1 - ɛhM αh ) along a field-line, with several much smaller helical `sidebands.' Provided the departure from symmetry is small, i.e. δBeff/B0ɛh where δBeff/B0 is the effective helical sideband strength, flow damping and thus flow evolution along and `cross' the direction of symmetry in a flux surface decouple [1,2], and can be determined successively. In the context of a fluid-moment approach [3], the momentum equation in the symmetry direction is equivalent to the ambipolarity condition. Steady state rotation solutions of this equation are equivalent to ambipolar radial electric field `roots' in conventional stellarator theory and will be presented for various banana-drift neoclassical flow damping regimes [2].[4pt] [1] J. D. Callen, A. J. Cole, and C. C. Hegna, Tech. Rep. UW-CPTC 08-7, Univ. of Wisconsin, http://www.cptc.wisc.edu (2009).[0pt] [2] A. J. Cole, C. C. Hegna, and J. D. Callen, Tech. Rep. UW-CPTC 08-8, Univ. of Wisconsin, http://www.cptc.wisc.edu (2009).[0pt] [3] K. C. Shaing and J. D. Callen, Phys. Fluids 26, 3315 (1983).
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.
SVD for imaging systems with discrete rotational symmetry.
Clarkson, Eric; Palit, Robin; Kupinski, Matthew A
2010-11-22
The singular value decomposition (SVD) of an imaging system is a computationally intensive calculation for tomographic imaging systems due to the large dimensionality of the system matrix. The computation often involves memory and storage requirements beyond those available to most end users. We have developed a method that reduces the dimension of the SVD problem towards the goal of making the calculation tractable for a standard desktop computer. In the presence of discrete rotational symmetry we show that the dimension of the SVD computation can be reduced by a factor equal to the number of collection angles for the tomographic system. In this paper we present the mathematical theory for our method, validate that our method produces the same results as standard SVD analysis, and finally apply our technique to the sensitivity matrix for a clinical CT system. The ability to compute the full singular value spectra and singular vectors will augment future work in system characterization, image-quality assessment and reconstruction techniques for tomographic imaging systems.
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.
NASA Astrophysics Data System (ADS)
Lee, Joong-Wook; Yang, Jin-Kyu; Sohn, Ik-Bu; Choi, Hun-Kook; Kang, Chul; Kee, Chul-Sik
2012-11-01
We investigate the terahertz (THz) transmission characteristics of complex slot arrays with various order of rotation symmetry. Our experimental results reveal that an asterisk-shaped aperture with sixfold rotational symmetry is the most appropriate shape for realizing polarization-independent, highly efficient, and frequency-selective transmission of THz radiation. A systematic understanding of the THz transmission characteristics is useful for achieving versatile platforms and custom-designed metallic devices with specific electromagnetic responses.
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.
Nonlinear modes and symmetry breaking in rotating double-well potentials
NASA Astrophysics Data System (ADS)
Li, Yongyao; Pang, Wei; Malomed, Boris A.
2012-08-01
We study modes trapped in a rotating ring carrying the self-focusing (SF) or self-defocusing (SDF) cubic nonlinearity and double-well potential cos2θ, where θ is the angular coordinate. The model, based on the nonlinear Schrödinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC) trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes and the transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground states are identified in both the SF and SDF systems.
Polynomial shape of an inclined ellipsoid with rotational symmetry about its major axis.
Castañeda-Escobar, Lizbeth A; Malacara-Hernández, Daniel
2006-08-01
We present the approximate polynomial expression for an ellipsoid with rotational symmetry about its major axis, which is on the y-z plane and at angle theta with respect to the z axis. These expressions have many possible useful applications in optics as shown. The main optical properties of these types of inclined ellipsoidal surface will be reviewed.
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
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.
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.
NASA Astrophysics Data System (ADS)
Busuladžić, M.; Gazibegović-Busuladžić, A.; Milošević, D. B.
2017-03-01
We investigate above-threshold ionization (ATI) of homonuclear diatomic molecules by the so-called bicircular field using the improved molecular strong-field approximation. Bicircular field is a two-color laser field having coplanar circularly polarized counter-rotating components of frequencies r ω and s ω , with r and s integers. Our analysis includes the high-energy part of the corresponding spectra, i.e., high-order ATI (HATI). The obtained molecular (H)ATI spectra are more complicated than the corresponding atomic spectra. We have identified four symmetries which are satisfied in (H)ATI of homonuclear diatomic molecules. Two of these symmetries are general rotational symmetries valid both for direct and rescattered HATI electrons. The remaining two symmetries are reflection symmetries valid only for the direct ATI electrons. Analytical proof of these symmetries is also given. These symmetries are illustrated using numerical examples of HATI spectra of the N2 molecule for various molecular orientations.
Rotational Symmetry Breaking in a Trigonal Superconductor Nb-doped Bi2 Se3
NASA Astrophysics Data System (ADS)
Asaba, Tomoya; Lawson, B. J.; Tinsman, Colin; Chen, Lu; Corbae, Paul; Li, Gang; Qiu, Y.; Hor, Y. S.; Fu, Liang; Li, Lu
2017-01-01
The search for unconventional superconductivity has been focused on materials with strong spin-orbit coupling and unique crystal lattices. Doped bismuth selenide (Bi2 Se3 ) is a strong candidate, given the topological insulator nature of the parent compound and its triangular lattice. The coupling between the physical properties in the superconducting state and its underlying crystal symmetry is a crucial test for unconventional superconductivity. In this paper, we report direct evidence that the superconducting magnetic response couples strongly to the underlying trigonal crystal symmetry in the recently discovered superconductor with trigonal crystal structure, niobium (Nb)-doped Bi2 Se3 . As a result, the in-plane magnetic torque signal vanishes every 60°. More importantly, the superconducting hysteresis loop amplitude is enhanced along one preferred direction, spontaneously breaking the rotational symmetry. This observation indicates the presence of nematic order in the superconducting ground state of Nb-doped Bi2 Se3 .
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.
Lu, Xiancong; Wu, Ziwen; Zhang, Wuhong; Chen, Lixiang
2014-05-02
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.
Nász, I; Adám, Eva
2006-06-01
The icosahedral adenovirus capsid has three rotational symmetry axes of different types. The six five-fold, ten three-fold and the fifteen two-fold axes have two superficial points each, altogether 62. The axes determine the number and location of the identical rotational facet groups and that during the different rotational phases which other regular facets and with what multiplicity shall be covered by them. The number of rotational facets of the five-, three- and two-fold rotational symmetry axes is 4, 6.66 and 10, respectively. In all the three cases, there are two kinds of possible arrangements of the facets. During the rotation--when the facets of the facet group placed on one by one to the neighbouring identical facet groups--at the five-fold axes, the facets of the rotational facet group get into cover position 12 times with all the 20 regular capsid facets, 20 times at the three-fold axes, and 30 times at the two-fold axes in a way that a different facet combination (facet hit) falls to every facet, and the original symmetry is not disturbed. After all, this means 240, 400 and 600 facet combinations, i.e. multiplicity in case of five-, three- and two-fold symmetry axes respectively, and these numbers correspond with that of the theoretically possible variations. The same results can be calculated by multiplying the number of real rotations of the capsid bringing the body into itself, i.e. the number 60 with the number of facets contributing to the five-, three- and two-fold rotational phases. The other way of the determination of multiplicity takes into account that all the facet groups of the capsid rotate simultaneously during all the rotational phases, and this multiplies the number of multiplicity with the number of the rotational types five-, three- and two-fold which result in one and the same multiplicity number in the case of five-, three- and two-fold symmetry, alike 1200. Perpendicular to the five-fold symmetry axes with the line of intersection
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).
Nász, István; Adám, Eva
2006-01-08
The icosahedral adenovirus capsid has three rotational axes of different types. The six five-fold, ten three-fold and the fifteen two-fold axes have two superficial points each, altogether 62. The axes determine the number and location of the identical rotational facet groups and that during the different rotational phases which other regular facets and with what multiplicity shall be covered by them. The number of rotational facets of the five-, three- and two-fold rotational symmetry axes is 4, 6.66 and 10, respectively. In all the three cases, there are two kinds of possible arrangements of the facets. During the rotation - when the facets of the facet group placed on one by one to the neighbouring identical facet groups - at the five-fold axes, the facets of the rotational facet group get into cover position 12 times with all the 20 regular capsid facets, 20 times at the three-fold axes, and 30 times at the two-fold axes in a way that a different facet combination (facet hit) falls to every facet, and the original symmetry is not disturbed. After all, this means 240, 400 and 600 facet combinations, i.e. multiplicity in case of five-, three- and two-fold symmetry axes respectively, and these numbers correspond with that of the theoretically possible variations. The same results can be calculated by multiplying the number of real rotations of the capsid bringing the body into itself i.e. the number 60 with the number of facets contributing to the five-, three- and two-fold rotational phases. The other way of the determination of multiplicity takes into account that all the facet groups of the capsid rotate simultaneously during all the rotational phases, and this multiplies the number of multiplicity with the number of the rotational types five-, three- and two-fold which result in one and the same multiplicity number in the case of five-, three- and two-fold symmetry, alike 1200. Perpendicular to the five-fold symmetry axes with the line of intersection drawn
On the vacuum Einstein equations along curves with a discrete local rotation and reflection symmetry
Korzyński, Mikołaj; Bentivegna, Eloisa E-mail: ian.hinder@aei.mpg.de
2015-08-01
We discuss the possibility of a dimensional reduction of the Einstein equations in S{sup 3} black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotation and reflection symmetry (LDRRS) can be carried out via a system of ODEs along these curves. However, 3+1 Numerical Relativity computations demonstrate that this is not the case, and we show analytically that this is due to the presence of a tensorial quantity which is not suppressed by the symmetry. We calculate the term analytically, and verify numerically for an 8-black-hole lattice that it fully accounts for the anomalous results, and thus quantify its magnitude in this specific case. The presence of this term prevents the exact evolution of these spaces via previously-reported methods which do not involve a full 3+1 integration of Einstein's equation.
Interacting fermions in rotation: chiral symmetry restoration, moment of inertia and thermodynamics
NASA Astrophysics Data System (ADS)
Chernodub, M. N.; Gongyo, Shinya
2017-01-01
We study rotating fermionic matter at finite temperature in the framework of the Nambu-Jona-Lasinio model. In order to respect causality the rigidly rotating system must be bound by a cylindrical boundary with appropriate boundary conditions that confine the fermions inside the cylinder. We show the finite geometry with the MIT boundary conditions affects strongly the phase structure of the model leading to three distinct regions characterized by explicitly broken (gapped), partially restored (nearly gapless) and spontaneously broken (gapped) phases at, respectively, small, moderate and large radius of the cylinder. The presence of the boundary leads to specific steplike irregularities of the chiral condensate as functions of coupling constant, temperature and angular frequency. These steplike features have the same nature as the Shubnikov-de Haas oscillations with the crucial difference that they occur in the absence of both external magnetic field and Fermi surface. At finite temperature the rotation leads to restoration of spontaneously broken chiral symmetry while the vacuum at zero temperature is insensitive to rotation ("cold vacuum cannot rotate"). As the temperature increases the critical angular frequency decreases and the transition becomes softer. A phase diagram in angular frequency-temperature plane is presented. We also show that at fixed temperature the fermion matter in the chirally restored (gapless) phase has a higher moment of inertia compared to the one in the chirally broken (gapped) phase.
Symmetries and security of a quantum-public-key encryption based on single-qubit rotations
NASA Astrophysics Data System (ADS)
Seyfarth, U.; Nikolopoulos, G. M.; Alber, G.
2012-02-01
Exploring the symmetries underlying a previously proposed encryption scheme that relies on single-qubit rotations, we derive an improved upper bound on the maximum information that an eavesdropper might extract from all the available copies of the public key. Subsequently, the robustness of the scheme is investigated in the context of attacks that address each public-key qubit independently. The attacks under consideration make use of projective measurements on single qubits and their efficiency is compared to attacks that address many qubits collectively and require complicated quantum operations.
Rotational and Fine Structure of Pseudo-Jahn Molecules with C_1 Symmetry
NASA Astrophysics Data System (ADS)
Liu, Jinjun
2016-06-01
It has been found in our previous works that rotational and fine-structure analysis of spectra involving nearly degenerate electronic states may aid in interpretation and analysis of the vibronic structure, specifically in the case of pseudo-Jahn-Teller (pJT) molecules with C_s symmetry. The spectral analysis of pJT derivatives (isopropoxy and cyclohexoxy of a prototypical JT molecule (the methoxy radical) allowed for quantitative determination of various contributions to the energy separation between the nearly degenerate electronic states, including the relativistic spin-orbit (SO) effect, the electrostatic interaction, and their zero-point energy difference. These states are coupled by SO and Coriolis interactions, which can also be determined accurately in rotational and fine structure analysis. Most recently, the spectroscopic model for rotational analysis of pJT molecules has been extended for analysis of molecules with C_1 symmetry, i.e., no symmetry. This model includes the six independently determinable components of the spin-rotation (SR) tensor and the three components of the SO and Coriolis interactions. It has been employed to simulate and fit high-resolution laser-induced fluorescence (LIF) spectra of jet-cooled alkoxy radicals with C_1 symmetry, including the 2-hexoxy and the 2-pentoxy radicals, as well as previously recorded LIF spectrum of the trans-conformer (defined by its OCCC dihedral angle) of the 2-butoxy radical. Although the LIF spectra can be reproduced by using either the SR constants or SO and Coriolis constants, the latter simulation offers results that are physically more meaningful whereas the SR constants have to be regarded as effective constants. Furthermore, we will review the SO and Coriolis constants of alkoxy radicals that have been investigated, starting from the well-studied methoxy radical (CH_3O). J. Liu, D. Melnik, and T. A. Miller, J. Chem. Phys. 139, 094308 (2013) J. Liu and T. A. Miller, J. Phys. Chem. A 118, 11871
Breaking of symmetries for stabilization of rotating continua in frictional contact
NASA Astrophysics Data System (ADS)
Spelsberg-Korspeter, Gottfried
2009-05-01
Rotating structures subject to frictional contact are susceptible to self-excited vibrations that are responsible for noise problems. In previous work the underlying mechanism has been explained through mathematical-mechanical models. From practical experience it is known that breaking the symmetry of a rotor can have a stabilizing effect. The present paper is devoted to a mathematical justification of this phenomenon. At the same time a method for a quantitative investigation of the influence of asymmetries on the stability behavior is outlined. As an example a rotating annular Kirchhoff plate in contact with friction pads is studied serving as a minimal model for brake squeal. A possible application of the results is the support of the design process for squeal free brake rotors where currently only experimental methods yield information about the tendency of an asymmetric brake rotor to squeal.
Hidden conformal symmetry of a rotating black hole with four charges
Shao Kainan; Zhang Zhibai
2011-05-15
Kerr/CFT correspondence exhibits many remarkable connections between the near-horizon Kerr black hole and a conformal field theory (CFT). Recently, Castro, Maloney, and Strominger showed that a hidden conformal symmetry exists in the solution space of a Kerr black hole. In this paper we investigate a rotating black hole with four independent U(1) charges derived from string theory which is known as the four-dimensional Cvetic-Youm solution, and we prove that the same hidden conformal symmetry also holds. We obtain the exact black hole entropy using the temperatures derived. The entropy and absorption cross section agree with the previous results [M. Cvetic and F. Larsen, Nucl. Phys. B506, 107 (1997).] and [M. Cvetic and F. Larsen, J. High Energy Phys. 09 (2009) 088.]. In addition, we clarify a previous explanation on the temperatures of the Cvetic-Youm solution's dual CFT. This work provides more robust derivation of the hidden conformal symmetry of Kerr-like black holes and as well as Kerr/CFT correspondence.
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke; Sugiyama, Naonori S.; Okumura, Teppei
2017-03-01
We propose an efficient way to test rotational invariance in the cosmological perturbations by use of galaxy correlation functions. In symmetry-breaking cases, the galaxy power spectrum can have extra angular dependence in addition to the usual one due to the redshift-space distortion, k ^ .n ^ . We confirm that, via the decomposition into not the usual Legendre basis Lℓ(k ^.n ^) but the bipolar spherical harmonic one {Yℓ(k ^)⊗Yℓ'(n ^)}LM, the symmetry-breaking signal can be completely distinguished from the usual isotropic one since the former yields nonvanishing L ≥1 modes but the latter is confined to the L =0 one. As a demonstration, we analyze the signatures due to primordial-origin symmetry breakings such as the well-known quadrupolar-type and dipolar-type power asymmetries and find nonzero L =2 and 1 modes, respectively. Fisher matrix forecasts of their constraints indicate that the Planck-level sensitivity could be achieved by the SDSS or BOSS-CMASS data, and an order-of-magnitude improvement is expected in a near future survey as PFS or Euclid by virtue of an increase in accessible Fourier mode. Our methodology is model-independent and hence applicable to the searches for various types of statistically anisotropic fluctuations.
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.
NASA Astrophysics Data System (ADS)
Schmiedt, Hanno; Jensen, Per; Schlemmer, Stephan
2016-08-01
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.
Broken rotational and translational symmetries in the pseudogap phase of cuprates
NASA Astrophysics Data System (ADS)
Taillefer, Louis
2011-03-01
A large in-plane anisotropy of the Nernst coefficient in YBCO is found to set in precisely at the pseudogap temperature T* throughout the doping phase diagram. This implies that the pseudogap phase is an electronic state that breaks the four-fold rotational symmetry of the copper-oxide planes. At a somewhat lower temperature, of order T* /2, the positive Hall and Seebeck coefficients of YBCO start dropping, and they reach large negative values at T = 0 , in the normal state accessed by applying high magnetic fields [2,3]. We interpret this in terms of an electron pocket forming in the Fermi surface of YBCO as a result of a Fermi-surface reconstruction caused by some order which breaks the translational symmetry of the lattice. Because very similar transport anomalies are observed in Eu-LSCO, where they coincide with the onset of stripe order, we infer that some form of stripe order is also at play in YBCO, and argue that the pseudogap phase is a precursor region of stripe (or spin-density-wave) fluctuations. In collaboration with F. Laliberte, N. Doiron-Leyraud, J. Chang, R. Daou, O. Cyr-Choiniere, D. LeBoeuf, B. Vignolle, C. Proust, I. Sheikin, L. Malone, K. Behnia, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy, S. Pyon, T. Takayama, Y. Tanaka, H. Takagi.
NASA Astrophysics Data System (ADS)
Leverrier, A.; Karpov, E.; Grangier, P.; Cerf, N. J.
2009-11-01
Proving the unconditional security of quantum key distribution (QKD) is a highly challenging task as one needs to determine the most efficient attack compatible with experimental data. This task is even more demanding for continuous-variable QKD as the Hilbert space where the protocol is described is infinite dimensional. A possible strategy to address this problem is to make an extensive use of the symmetries of the protocol. In this paper, we investigate a rotation symmetry in phase space that is particularly relevant to continuous-variable QKD, and explore the way towards a new quantum de Finetti theorem that would exploit this symmetry and provide a powerful tool to assess the security of continuous-variable protocols. As a first step, a single-party asymptotic version of this quantum de Finetti theorem in phase space is derived.
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)
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
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
2016-06-28
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.
NASA Astrophysics Data System (ADS)
Dawber, Matthew
2013-03-01
In this talk I will present results on two superlattice systems which contain ultra fine layers of PbTiO3 and another perovskite material. In recent years, much work has been done on the PbTiO3/SrTiO3 system, with a focus on improper ferroelectricity and the arrangement of ferroelectric domains. Here, we consider two different partner materials for PbTiO3, each of which introduces markedly different behavior in the resulting superlattice. PbTiO3/SrRuO3 superlattices with ultra-thin SrRuO3 layers were studied both experimentally and using density functional theory. Due to the superlattice geometry, the samples show a large anisotropy in their electrical resistivity, which can be controlled by changing the thickness of the PbTiO3 layers. Therefore, along the ferroelectric direction, SrRuO3 layers can act as dielectric, rather than metallic, elements. We show that, by reducing the thickness of the PbTiO3 layers, an increasingly important effect of polarization asymmetry due to compositional inversion symmetry breaking occurs. The compositional inversion symmetry breaking is seen in this bi-color superlattice due to the combined variation of A and B site ions within the superlattice. We have also achieved an experimental enhancement of the piezoelectric response and dielectric tunability in artificially layered epitaxial PbTiO3/CaTiO3 superlattices through an engineered rotation of the polarization direction. As the relative layer thicknesses within the superlattice were changed from sample to sample we found evidence for polarization rotation in multiple x-ray diffraction measurements. Associated changes in functional properties were seen in electrical measurements and piezoforce microscopy. These results demonstrate a new approach to inducing polarization rotation under ambient conditions in an artificially layered thin film. Work supported by NSF DMR1055413
Asymptotically flat radiative space-times with boost-rotation symmetry: The general structure
Biicak, J.; Schmidt, B. )
1989-09-15
This paper deals for the first time with boost-rotation-symmetric space-times from a unified point of view. Boost-rotation-symmetric space-times are the only explicitly known exact solutions of the Einstein vacuum field equations which describe moving singularities or black holes, are radiative and asymptotically flat in the sense that they admit global, though not complete, smooth null infinity, as well as spacelike and timelike infinities. They very likely represent the exterior fields of uniformly accelerated sources in general relativity and may serve as tests of various approximation methods, as nontrivial illustrations of the theory of the asymptotic structure of radiative space-times, and as test beds in numerical relativity. Examples are the {ital C}-metric or the solutions of Bonnor and Swaminarayan. The space-times are defined in a geometrical manner and their global properties are studied in detail, in particular their asymptotic structure. It is demonstrated how one can construct any asymptotically flat boost-rotation-symmetric space-time starting from the boost-rotation-symmetric solution of the flat-space wave equation. The problem of uniformly accelerated sources in special relativity is also discussed. The radiative properties and specific examples of the boost-rotation-symmetric space-times will be analyzed in a following paper.
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.
Symmetry Breaking Bifurcations and the Growth of Chaos in a Rotating Fluid
1989-08-01
34Instabilities and chaos in rotating fluids," in Nonlinear Evolution and Chaotic Phenomena, ed. by G. Gallavotti and P. W. Zweifel (Plenum Publishing...Chaotic Phenomena, ed. by G. Gallavotti and P. W. Zweifel (Plenum Publisling Co., 1988), pp. 319-326. This brief report, contained in a NATO Advanced
Ruf, Armin; Tetaz, Tim; Schott, Brigitte; Joseph, Catherine; Rudolph, Markus G
2016-11-01
Fructose-1,6-bisphosphatase (FBPase) is a key regulator of gluconeogenesis and a potential drug target for type 2 diabetes. FBPase is a homotetramer of 222 symmetry with a major and a minor dimer interface. The dimers connected via the minor interface can rotate with respect to each other, leading to the inactive T-state and active R-state conformations of FBPase. Here, the first crystal structure of human liver FBPase in the R-state conformation is presented, determined at a resolution of 2.2 Å in a tetragonal setting that exhibits an unusual arrangement of noncrystallographic symmetry (NCS) elements. Self-Patterson function analysis and various intensity statistics revealed the presence of pseudo-translation and the absence of twinning. The space group is P41212, but structure determination was also possible in space groups P43212, P4122 and P4322. All solutions have the same arrangement of three C2-symmetric dimers spaced by 1/3 along an NCS axis parallel to the c axis located at (1/4, 1/4, z), which is therefore invisible in a self-rotation function analysis. The solutions in the four space groups are related to one another and emulate a body-centred lattice. If all NCS elements were crystallographic, the space group would be I4122 with a c axis three times shorter and a single FBPase subunit in the asymmetric unit. I4122 is a minimal, non-isomorphic supergroup of the four primitive tetragonal space groups, explaining the space-group ambiguity for this crystal.
Ruf, Armin; Tetaz, Tim; Schott, Brigitte; Joseph, Catherine; Rudolph, Markus G.
2016-01-01
Fructose-1,6-bisphosphatase (FBPase) is a key regulator of gluconeogenesis and a potential drug target for type 2 diabetes. FBPase is a homotetramer of 222 symmetry with a major and a minor dimer interface. The dimers connected via the minor interface can rotate with respect to each other, leading to the inactive T-state and active R-state conformations of FBPase. Here, the first crystal structure of human liver FBPase in the R-state conformation is presented, determined at a resolution of 2.2 Å in a tetragonal setting that exhibits an unusual arrangement of noncrystallographic symmetry (NCS) elements. Self-Patterson function analysis and various intensity statistics revealed the presence of pseudo-translation and the absence of twinning. The space group is P41212, but structure determination was also possible in space groups P43212, P4122 and P4322. All solutions have the same arrangement of three C 2-symmetric dimers spaced by 1/3 along an NCS axis parallel to the c axis located at (1/4, 1/4, z), which is therefore invisible in a self-rotation function analysis. The solutions in the four space groups are related to one another and emulate a body-centred lattice. If all NCS elements were crystallographic, the space group would be I4122 with a c axis three times shorter and a single FBPase subunit in the asymmetric unit. I4122 is a minimal, non-isomorphic supergroup of the four primitive tetragonal space groups, explaining the space-group ambiguity for this crystal. PMID:27841754
Wen, Zichao; Yan, Zhenya
2017-03-01
We report new matter-wave solutions of the one-dimensional spin-1 Bose-Einstein condensate system by combining global spin-rotation states and similarity transformation. Dynamical behaviors of non-stationary global spin-rotation states derived from the SU(2) spin-rotation symmetry are discussed, which exhibit temporal periodicity. We derive generalized bright-dark mixed solitons and new rogue wave solutions and reveal the relations between Euler angles in spin-rotation symmetry and parameters in ferromagnetic and polar solitons. In the modulated spin-1 Bose-Einstein condensate system, new solutions are derived and graphically illustrated for different types of modulations. Moreover, numerical simulations are performed to investigate the stability of some obtained solutions for chosen parameters.
High-efficiency free-form nonimaging condenser overcoming rotational symmetry limitations
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Benítez, Pablo; Blen, José; Santamaría, Asunción
2008-09-01
The importance of condenser optics is the fact that it is the bottleneck limiting efficiency in commercially available projection systems. Conventional condensers use rotational symmetric devices, most of them being elliptic or parabolic mirrors. They perform very far from the theoretical limits for sources such as arc lamps or halogen bulbs. Typical small displays in the 5-15 mm2 etendue range have geometrical efficiencies about 40-50% for the best condensers; although theory allows about 100% (no reflection nor absorption losses are considered). The problem is in the coma aberration of the reflectors and the rotational symmetric image of the source making the source projected image to unfit with the target. Thus, the only way to improve this performance is to generate a free form design that is able to control the shape and rotation of the source projected images. As yet, this can only be done with the SMS3D design method. We present here one of such designs achieving a collection efficiency 1.8 times that of an elliptical condenser for a 4:1 target aspect ratio and for the range of target etendue with practical interest and 1.5 for 16:9 target. These designs use only 1 additional reflection, i.e., use a total of 2 reflections from the source to the target. A prototype of one type of free form condenser has already been built.
Evolution of the X(5) critical-point symmetry in rotating {\\mathbf {^{176}Os}}
NASA Astrophysics Data System (ADS)
Hao, X.; Zhu, L. H.; Wu, X. G.; He, C. Y.; Pan, B.; Zheng, Y.; Wang, L. L.; Wang, L.; Li, X. Q.; Liu, Y.; Ding, H. B.; Li, Z. Y.; Zhang, J. F.; Sun, H. B.; Li, G. S.
2011-02-01
Lifetimes of excited states above 10+ in the yrast band in 176Os have been measured using the Doppler shift attenuation method, via the fusion evaporation reaction {^{152}Sm(^{28}Si, 4{{\\it n}})^{176}Os}. Lifetimes of states over 12+ were measured for the first time. The deduced transitional quadruple moments (Qt), together with the previous data using a recoil distance method, are compared with theoretical calculations based on the X(5) model and the interaction boson model. For the states below spin 10+, the data of previous work support an X(5)-like structure, but for the states above 10+, the value of Qt remains almost constant, being the characteristic of a symmetric rotor. The present result suggests that the shape of the nucleus 176Os changes from X(5) critical-point symmetry to an axially deformed rotor with increasing spin.
Design of a novel free-form condenser overcoming rotational symmetry limitations
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Benítez, Pablo; Blen, José; Santamaría, Asunción
2008-08-01
The importance of condenser optics is the fact that it is the bottleneck limiting efficiency in commercially available projection systems. Efficiency is a key parameter of projector performance, since it augments screen luminance, enabling the system to perform well under increasing levels of ambient light. Conventional condensers use rotational symmetric devices, most of them being elliptic or parabolic mirrors. They perform very far from the theoretical limits for sources such as arc lamps or halogen bulbs. Typical small displays in the 5-15 mm2 etendue range have geometrical efficiencies about 40-50% for the best condensers; although theory allows about 100% (no reflection nor absorption losses are considered). Two basic facts are underlying this effect: The coma aberration of the reflectors and the rotational symmetric image of the source making the source projected image to unfit with the target. Thus, the only way to improve this performance is to generate a free form design that is able to control the shape and rotation of the source projected images. As yet, this can only be done with the SMS3D design method. We present here one of such designs achieving a geometrical efficiency that is 1.8 times that of an elliptical condenser for a 4:1 target aspect ratio and for the range of target etendue with practical interest and 1.5 for 16:9 target. This design uses only 1 additional reflection, i.e., uses a total of 2 reflections from the source to the target. A prototype of this free form condenser has already been built.
High-efficiency free-form nonimaging condenser overcoming rotational symmetry limitations
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Benítez, Pablo; Blen, José; Santamaría, Asunción
2008-08-01
The importance of condenser optics is the fact that it is the bottleneck limiting efficiency in commercially available projection systems. Efficiency is a key parameter of projector performance, since it augments screen luminance, enabling the system to perform well under increasing levels of ambient light. Conventional condensers use rotational symmetric devices, most of them being elliptic or parabolic mirrors. They perform very far from the theoretical limits for sources such as arc lamps or halogen bulbs. Typical small displays in the 5-15 mm2 etendue range have geometrical efficiencies about 40-50% for the best condensers; although theory allows about 100% (no reflection nor absorption losses are considered). The problem is in the coma aberration of the reflectors and the rotational symmetric image of the source making the source projected image to unfit with the target. Thus, the only way to improve this performance is to generate a free form design that is able to control the shape and rotation of the source projected images. As yet, this can only be done with the SMS3D design method. We present here two of such designs types; one of them achieving a geometrical efficiency that is 1.8 times that of an elliptical condenser for a 4:1 target aspect ratio and for the range of target etendue with practical interest and 1.5 for 16:9 target. The other design type is more adequate for circular targets and gets a geometrical efficiency up to 1.4 that of an elliptical condenser. These designs use only 1 additional reflection, i.e., use a total of 2 reflections from the source to the target. A prototype of one type of free form condenser has already been built.
Design of a novel free-form condenser overcoming rotational symmetry limitations
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Benítez, Pablo; Blen, José; Santamaría, Asunción
2008-09-01
The importance of condenser optics is the fact that it is the bottleneck limiting efficiency in commercially available projection systems. Efficiency is a key parameter of projector performance, since it augments screen luminance, enabling the system to perform well under increasing levels of ambient light. Conventional condensers use rotational symmetric devices, most of them being elliptic or parabolic mirrors. They perform very far from the theoretical limits for sources such as arc lamps or halogen bulbs. Typical small displays in the 5-15 mm2 etendue range have geometrical efficiencies about 40-50% for the best condensers; although theory allows about 100% (no reflection nor absorption losses are considered). Two basic facts are underlying this effect: The coma aberration of the reflectors and the rotational symmetric image of the source making the source projected image to unfit with the target. Thus, the only way to improve this performance is to generate a free form design that is able to control the shape and rotation of the source projected images. As yet, this can only be done with the SMS3D design method. We present here one of such designs achieving a geometrical efficiency that is 1.8 times that of an elliptical condenser for a 4:1 target aspect ratio and for the range of target etendue with practical interest and 1.5 for 16:9 target. This design uses only 1 additional reflection, i.e., uses a total of 2 reflections from the source to the target. A prototype of this free form condenser has already been built.
SU(3) gauge symmetry for collective rotational states in deformed nuclei
NASA Astrophysics Data System (ADS)
Rosensteel, George; Sparks, Nick
2016-09-01
How do deformed nuclei rotate? The qualitative answer is that a velocity-dependent interaction causes a strong coupling between the angular momentum and the vortex momentum (or Kelvin circulation). To achieve a quantitative explanation, we propose a significant extension of the Bohr-Mottelson legacy model in which collective wave functions are vector-valued in an irreducible representation of SU(3). This SU(3) is not the usual Elliott choice, but rather describes internal vorticity in the rotating frame. The circulation values C of an SU(3) irreducible representation, say the (8,0) for 20Ne, are C = 0, 2, 4, 6, 8, which is the same as the angular momentum spectrum in the Elliott model; the reason is a reciprocity theorem in the symplectic model. The differential geometry of Yang-Mills theory provides a natural mathematical framework to solve the angular-vortex coupling riddle. The requisite strong coupling is a ``magnetic-like'' interaction arising from the covariant derivative and the bundle connection. The model builds on prior work about the Yang-Mills SO(3) gauge group model.
Yoo, Won-Gyu
2014-05-01
[Purpose] This study compared the symmetry of right and left lateral cervical flexion and rotation, and the cervical flexion-relaxation ratio (FRR) in young computer workers in Korea. [Subjects and Methods] Twenty computer workers (14 males and 6 females) participated in this study. We measured their right and left lateral cervical flexion, rotation, and FRR. [Results] Right and left lateral flexion and right and left rotation showed no significant differences between the sides. The left cervical FRR was significantly lower than the right cervical FRR. [Conclusion] The cervical FRR, expressed as a numerical value, is a more sensitive marker for measuring neuromuscular changes associated with mild asymmetry than CROM.
Anisotropic non-gaussianity from rotational symmetry breaking excited initial states
Ashoorioon, Amjad; Koivisto, Tomi
2016-12-01
If the initial quantum state of the primordial perturbations broke rotational invariance, that would be seen as a statistical anisotropy in the angular correlations of the cosmic microwave background radiation (CMBR) temperature fluctuations. This can be described by a general parameterisation of the initial conditions that takes into account the possible direction-dependence of both the amplitude and the phase of particle creation during inflation. The leading effect in the CMBR two-point function is typically a quadrupole modulation, whose coefficient is analytically constrained here to be |B|≲0.06. The CMBR three-point function then acquires enhanced non-gaussianity, especially for the local configurations. In the large occupation number limit, a distinctive prediction is a modulation of the non-gaussianity around a mean value depending on the angle that short and long wavelength modes make with the preferred direction. The maximal variations with respect to the mean value occur for the configurations which are coplanar with the preferred direction and the amplitude of the non-gaussianity increases (decreases) for the short wavelength modes aligned with (perpendicular to) the preferred direction. For a high scale model of inflation with maximally pumped up isotropic occupation and ϵ≃0.01 the difference between these two configurations is about 0.27, which could be detectable in the future. For purely anisotropic particle creation, the non-Gaussianity can be larger and its anisotropic feature very sharp. The non-gaussianity can then reach f{sub NL}∼30 in the preferred direction while disappearing from the correlations in the orthogonal plane.
Anisotropic non-gaussianity from rotational symmetry breaking excited initial states
NASA Astrophysics Data System (ADS)
Ashoorioon, Amjad; Casadio, Roberto; Koivisto, Tomi
2016-12-01
If the initial quantum state of the primordial perturbations broke rotational invariance, that would be seen as a statistical anisotropy in the angular correlations of the cosmic microwave background radiation (CMBR) temperature fluctuations. This can be described by a general parameterisation of the initial conditions that takes into account the possible direction-dependence of both the amplitude and the phase of particle creation during inflation. The leading effect in the CMBR two-point function is typically a quadrupole modulation, whose coefficient is analytically constrained here to be |B| lesssim 0.06. The CMBR three-point function then acquires enhanced non-gaussianity, especially for the local configurations. In the large occupation number limit, a distinctive prediction is a modulation of the non-gaussianity around a mean value depending on the angle that short and long wavelength modes make with the preferred direction. The maximal variations with respect to the mean value occur for the configurations which are coplanar with the preferred direction and the amplitude of the non-gaussianity increases (decreases) for the short wavelength modes aligned with (perpendicular to) the preferred direction. For a high scale model of inflation with maximally pumped up isotropic occupation and epsilonsimeq 0.01 the difference between these two configurations is about 0.27, which could be detectable in the future. For purely anisotropic particle creation, the non-Gaussianity can be larger and its anisotropic feature very sharp. The non-gaussianity can then reach 0fNL ~ 3 in the preferred direction while disappearing from the correlations in the orthogonal plane.
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…
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.; ...
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
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.
NASA Astrophysics Data System (ADS)
Fukumoto, Yasuhide; Mie, Youichi
2015-02-01
We develop a general framework of using the Lagrangian variables for calculating the energy of waves on a steady Euler flow and the mean flow induced by their nonlinear interaction. With the mean flow at hand we can determine, without ambiguity, all the coefficients of the amplitude equations to third order in amplitude for a rotating flow subject to a steady perturbation breaking the circular symmetry of the streamlines. Moreover, a resonant triad of waves is identified which brings in the secondary instability of the Moore-Saffman-Tsai-Widnall instability, and with the aid of the energetic viewpoint, resonant amplification of the waves without bound is numerically confirmed.
Aagren, O.; Savenko, N.
2005-04-15
One of the main issues of the open ended plasma confining devices is to provide a magnetohydrodynamic stable plasma equilibrium. A nonaxisymmetric, marginally stable confining magnetic field for a conventional, single mirror device has been studied for a long thin flux tube. The marginally stable minimum B magnetic field is proven to have quadrupolar symmetry under the assumptions of a straight paraxial central flux line and zero plasma {beta}. The quadrupolar symmetry geometrically means that the flux lines are not twisted. The perpendicular drift of the gyro centers is zero. A possible external current distribution which can generate the magnetic field is determined. The most convenient set of flux coordinates for this magnetic field are (x{sub 0},y{sub 0},s), where x{sub 0} and y{sub 0} are Cartesian-like Clebsch coordinates and s is the arclength of the magnetic field line. Analytical expressions for the magnetic flux coordinates are derived for this magnetic field.
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
Pinsky, Mark; Casanova, David; Alemany, Pere; Alvarez, Santiago; Avnir, David; Dryzun, Chaim; Kizner, Ziv; Sterkin, Alexander
2008-01-30
We introduce a new mathematical tool for quantifying the symmetry contents of molecular structures: the Symmetry Operation Measures. In this approach, we measure the minimal distance between a given structure and the structure which is obtained after applying a selected symmetry operation on it. If the given operation is a true symmetry operation for the structure, this distance is zero; otherwise it gives an indication of how different the transformed structure is from the original one. Specifically, we provide analytical solutions for measures of all the improper rotations, S n p, including mirror symmetry and inversion, as well as for all pure rotations, C n p. These measures provide information complementary to the Continuous Symmetry Measures (CSM) that evaluate the distance between a given structure and the nearest structure which belongs to a selected symmetry point-group.
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…
A universal symmetry detection algorithm.
Maurer, Peter M
2015-01-01
Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.
NASA Astrophysics Data System (ADS)
Roussou, A.; Smyrnakis, J.; Magiropoulos, M.; Efremidis, Nikolaos K.; Kavoulakis, G. M.
2017-03-01
Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular and/or toroidal traps, we study the effect of the finiteness of the atom number N on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean-field approximation. This many-body state breaks the symmetry of the Hamiltonian; it has the same energy to leading order in N as the mean-field state and the corresponding eigenstate of the Hamiltonian, however, it has a lower energy to subleading order in N and thus it is energetically favorable.
Bodo, G.; Rossi, P.; Cattaneo, F.; Ferrari, A.; Mignone, A.
2011-10-01
We consider the problem of convergence in homogeneous shearing-box simulations of magneto-rotationally driven turbulence. When there is no mean magnetic flux, if the equations are non-dimensionalized with respect to the diffusive scale, the only free parameter in the problem is the size of the computational domain. The problem of convergence then relates to the asymptotic form of the solutions as the computational box size becomes large. By using a numerical code with a high order of accuracy we show that the solutions become asymptotically independent of domain size. We also show that cases with weak magnetic flux join smoothly to the zero-flux cases as the flux vanishes. These results are consistent with the operation of a subcritical small-scale dynamo driving the turbulence. We conclude that for this type of turbulence the angular momentum transport is proportional to the diffusive flux and therefore has limited relevance in astrophysical situations.
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.
Lemouchi, Cyprien; Iliopoulos, Konstantinos; Zorina, Leokadiya; Simonov, Sergey; Wzietek, Pawel; Cauchy, Thomas; Rodríguez-Fortea, Antonio; Canadell, Enric; Kaleta, Jiří; Michl, Josef; Gindre, Denis; Chrysos, Michael; Batail, Patrick
2013-06-26
The rod-like molecule bis((4-(4-pyridyl)ethynyl)bicyclo[2.2.2]oct-1-yl)buta-1,3-diyne, 1, contains two 1,4-bis(ethynyl)bicyclo[2.2.2]octane (BCO) chiral rotators linked by a diyne fragment and self-assembles in a one-dimensional, monoclinic C2/c centrosymmetric structure where two equilibrium positions with large occupancy imbalance (88% versus 12%) are identified on a single rotor site. Combining variable-temperature (70-300 K) proton spin-lattice relaxation, (1)H T1(-1), at two different (1)H Larmor frequencies (55 and 210 MHz) and DFT calculations of rotational barriers, we were able to assign two types of Brownian rotators with different activation energies, 1.85 and 6.1 kcal mol(-1), to the two (1)H spin-lattice relaxation processes on the single rotor site. On the basis of DFT calculations, the low-energy process has been assigned to adjacent rotors in a well-correlated synchronous motion, whereas the high-energy process is the manifestation of an abrupt change in their kinematics once two blades of adjacent rotors are seen to rub together. Although crystals of 1 should be second harmonic inactive, a large second-order optical response is recorded when the electric field oscillates in a direction parallel to the unique rotor axle director. We conclude that conformational mutations by torsional interconversion of the three blades of the BCO units break space-inversion symmetry in sequences of mutamers in dynamic equilibrium in the crystal in domains at a mesoscopic scale comparable with the wavelength of light used. A control experiment was performed with a crystalline film of a similar tetrayne molecule, 1,4-bis(3-((trimethylsilyl)ethynyl)bicyclo[1.1.1]pent-1-yl)buta-1,3-diyne, whose bicyclopentane units can rotate but are achiral and produce no second-order optical response.
NASA Astrophysics Data System (ADS)
Moszynski, Robert; Jeziorski, Bogumil; van der Avoird, Ad; Wormer, Paul E. S.
1994-08-01
Starting from an ab initio symmetry-adapted perturbation theory potential energy surface we have performed converged variational and close-coupling calculations of the bound rovibrational states and of the positions and widths of rotationally predissociating resonances of HeHF and HeDF van der Waals complexes. The energy levels were used to compute transition frequencies in the near-infrared spectra of these complexes corresponding to the simultaneous excitation of vibration and internal rotation in the HF(DF) subunit in the complex. The computed transition energies and other model independent characteristics of the near-infrared spectra are in excellent agreement with the results of high-resolution measurements of Lovejoy and Nesbitt [C. M. Lovejoy and D. J. Nesbitt, J. Chem. Phys. 93, 5387 (1990)]. In particular, the ab initio potential predicts dissociation energies of 7.38 and 7.50 cm-1 for HeHF and HeDF, respectively, in very good agreement with the Lovejoy and Nesbitt results of 7.35 and 7.52 cm-1. The agreement of the observed and calculated linewidths is less satisfactory. We have found, however, that the linewidths are very sensitive to the accuracy of the short-range contribution to the V1(r,R) term in the anisotropic expansion of the potential. By simple scaling of the latter component we have obtained linewidths in very good agreement with the experimental results. We have also found that this scaling introduces a very small (2%) change in the total potential around the van der Waals minimum.
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).
Rotational dynamics of confined C60 from near-infrared Raman studies under high pressure.
Zou, Yonggang; Liu, Bingbing; Wang, Liancheng; Liu, Dedi; Yu, Shidan; Wang, Peng; Wang, Tianyi; Yao, Mingguang; Li, Quanjun; Zou, Bo; Cui, Tian; Zou, Guangtian; Wågberg, Thomas; Sundqvist, Bertil; Mao, Ho-Kwang
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.
Symmetry impedes symmetry discrimination.
Tjan, Bosco S; Liu, Zili
2005-12-16
Objects in the world, natural and artificial alike, are often bilaterally symmetric. The visual system is likely to take advantage of this regularity to encode shapes for efficient object recognition. The nature of encoding a symmetric shape, and of encoding any departure from it, is therefore an important matter in visual perception. We addressed this issue of shape encoding empirically, noting that a particular encoding scheme necessarily leads to a specific profile of sensitivity in perceptual discriminations. We studied symmetry discrimination using human faces and random dots. Each face stimulus was a frontal view of a three-dimensional (3-D) face model. The 3-D face model was a linearly weighted average (a morph) between the model of an original face and that of the corresponding mirror face. Using this morphing technique to vary the degree of asymmetry, we found that, for faces and analogously generated random-dot patterns alike, symmetry discrimination was worst when the stimuli were nearly symmetric, in apparent opposition to almost all studies in the literature. We analyzed the previous work and reconciled the old and new results using a generic model with a simple nonlinearity. By defining asymmetry as the minimal difference between the left and right halves of an object, we found that the visual system was disproportionately more sensitive to larger departures from symmetry than to smaller ones. We further demonstrated that our empirical and modeling results were consistent with Weber-Fechner's and Stevens's laws.
None
2016-07-12
- 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 ârenormalizableâ. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged âvectorâ 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
2011-02-24
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of
Kim, Min-hee; Yoo, Won-gyu; Choi, Bo-ram
2013-04-01
The present study was performed to examine lumbopelvic rotation and to identify asymmetry of the erector spinae and hamstring muscles in people with and without low back pain (LBP). The control group included 16 healthy subjects, the lumbar-flexion-rotation syndrome LBP group included 17 subjects, and the lumbar-extension-rotation syndrome LBP group included 14 subjects. Kinematic parameters were recorded using a 3D motion-capture system, and electromyography parameters were measured using a Noraxon TeleMyo 2400T. The two LBP subgroups showed significantly more lumbopelvic rotation during trunk flexion in standing than did the control group. The muscle activity and flexion-relaxation ratio asymmetries of the erector spinae muscles in the lumbar-flexion-rotation syndrome LBP group were significantly greater than those in the control group, and the muscle activity and flexion-relaxation ratio asymmetry of the hamstring muscles in the lumbar-extension-rotation syndrome LBP group were significantly greater than those in the control group. Imbalance or asymmetry of passive tissue could lead to asymmetry of muscular activation. Muscle imbalance can cause asymmetrical alignment or movements such as unexpected rotation. The results showed a greater increase in lumbopelvic rotation during trunk flexion in standing among the lumbar-flexion-rotation syndrome and lumbar-extension-rotation syndrome LBP groups compared with the control group. The differences between the two LBP subgroups may be a result of imbalance and asymmetry in erector spinae and hamstring muscle properties.
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…
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2016-09-01
We review some of our recent work devoted to the problem of quantization with preservation of Noether symmetries, finding hidden linearity in superintegrable systems, and showing that nonlocal symmetries are in fact local. In particular, we derive the Schrödinger equation for the isochronous Calogero goldfish model using its relation to Darwin equation. We prove the linearity of a classical superintegrable system on a plane of nonconstant curvature. We find the Lie point symmetries that correspond to the nonlocal symmetries (also reinterpreted as λ-symmetries) of the Riccati chain.
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
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.
Park, G. Barratt; Jiang, Jun; Saladrigas, Catherine A.; Field, Robert W.
2016-04-14
Here, the C ^{1}B_{2} state of SO_{2} 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 (b_{2} 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 b_{2} 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 a_{1} and b_{2} vibrational symmetry, and to determine accurately the vibrational dependence of the rotational constants in the distorted C electronic state.
NASA Astrophysics Data System (ADS)
Lowell, David; George, David; Lutkenhaus, Jeffery; Philipose, Usha; Zhang, Hualiang; Lin, Yuankun
2016-03-01
A method of fabricating large-volume three-dimensional (3D) photonic crystal and quasicrystal templates using holographic lithography is presented. Fabrication is accomplished using a single-beam and single exposure by a reflective optical element (ROE). The ROE is 3D printed support structure which holds reflecting surfaces composed of silicon or gallium arsenide. Large-volume 3D photonic crystal and quasicrystal templates with 4-fold, 5-fold, and 6-fold symmetry were fabricated and found to be in good agreement with simulation. Although the reflective surfaces were setup away from the Brewster's angle, the interference among the reflected s and p-polarizations still generated bicontinuous structures, demonstrating the flexibility of the ROE. The ROE, being a compact and inexpensive alternative to diffractive optical elements and top-cut prisms, facilitates the large-scale integration of holographically fabricated photonic structures into on-chip applications.
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
NASA Astrophysics Data System (ADS)
Melandri, Sonia; Velino, Biagio; Favero, Paolo G.; Dell'Erba, Adele; Caminati, Walther
2000-04-01
The van der Waals complex between Ar and 1,2-difluoroethane has been investigated by free-jet absorption millimeter-wave spectroscopy in the frequency range 60-78 GHz. The analysis of the spectroscopic constants derived from the rotational spectrum allowed the determination of the dimer's structure. 1,2-Difluoroethane is in the gauche conformation and the Ar atom is in a position stabilized by the interaction with one fluorine and the two carbon atoms. The distance between Ar and the center of mass (CM) of the monomer is 3.968 Å, the angle between the Ar-CM line and the C-C bond is 65° and the dihedral angle Ar-CM-C-C is 99°. From centrifugal distortion effects the dissociation energy of the complex has been estimated to be 2.1 kJ/mol.
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)
Inotani, Daisuke; Hanai, Ryo; Ohashi, Yoji
2016-10-01
We extend our recent work [Y. Endo et al., Phys. Rev. A 92, 023610 (2015)], 10.1103/PhysRevA.92.023610 for a parity-mixing effect in a model of two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at T =0 , we point out that an odd-parity p -wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) s -wave superfluid Fermi gas with spin imbalance. This indicates that when one suddenly changes the s -wave pairing interaction to an appropriate p -wave one by using a Feshbach technique in this case, a nonvanishing p -wave superfluid order parameter is immediately obtained, which is given by the product of the p -wave interaction and the p -wave pair amplitude that has already been induced in the spin-imbalanced s -wave superfluid Fermi gas. Thus, by definition, the system is in the p -wave superfluid state, at least just after this manipulation. Since the achievement of a p -wave superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond the LDA.
Asymptotic symmetries on Killing horizons
NASA Astrophysics Data System (ADS)
Koga, Jun-Ichirou
2001-12-01
We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.
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…
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…
Symmetry fractionalization of visons in Z2 spin liquids
NASA Astrophysics Data System (ADS)
Qi, Yang; Cheng, Meng; Fang, Chen
In this work we study symmetry fractionalization of vison excitations in topological Z2 spin liquids. We show that in the presence of the full SO (3) spin-rotational symmetry and if there is an odd number of spin-1/2 per unit cell, the symmetry fractionalization of visons is completely fixed. On the other hand, visons can have different classes of symmetry fractionalization if the spin-rotational symmetry is reduced. As a concrete example, we show that visons in the Balents-Fisher-Girvin Z2 spin liquid have crystal symmetry fractionalization classes which are not allowed in SO (3) symmetric spin liquids, due to the reduced spin-rotational symmetry.
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.
Continuous symmetry measures for complex symmetry group.
Dryzun, Chaim
2014-04-05
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.
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.
Newton–Hooke-type symmetry of anisotropic oscillators
Zhang, P.M.; Horvathy, P.A.; Andrzejewski, K.; Gonera, J.; Kosiński, P.
2013-06-15
Rotation-less Newton–Hooke-type symmetry, found recently in the Hill problem, and instrumental for explaining the center-of-mass decomposition, is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton–Hooke symmetry is recovered in the isotropic case. Star escape from a galaxy is studied as an application. -- Highlights: ► Rotation-less Newton–Hooke (NH) symmetry is generalized to an arbitrary anisotropic oscillator. ► The orbit method is used to find the most general case for rotation-less NH symmetry. ► The NH symmetry is decomposed into Heisenberg algebras based on chiral decomposition.
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.
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…
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.
1993-08-01
desirability of a rotation as a function of the set of planar angles. Criteria for the symmetry of the design (such as the same set of factor levels for...P is -1. Hence there is no theoretical problem in obtaining rotations of a design; there are only the practical questions Why rotate a design? And...star points, which can be represented in a shorthand notation by the permutations of (±1,0, "’" , 0), and (c) factorial points, which are a two- level
NASA Astrophysics Data System (ADS)
Cheng, Meng; Zaletel, Michael; Barkeshli, Maissam; Vishwanath, Ashvin; Bonderson, Parsa
2016-10-01
The Lieb-Schultz-Mattis theorem and its higher-dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases with on-site unitary symmetries, enables us to develop a framework for understanding the structure of symmetry-enriched topological phases with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling," which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing degeneracies protected by on-site symmetry.
Bose-Einstein condensates in rotating lattices.
Bhat, Rajiv; Holland, M J; Carr, L D
2006-02-17
Strongly interacting bosons in a two-dimensional rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries.
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.
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
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
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
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.
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
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.
Nász, István; Adám, Eva
2005-10-09
Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino acids--are in symmetrical location. Every kind of polypeptide forms also a separately symmetrical network in the capsid distributed according to their functions in the inner and outer side and inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four hexons according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each group of four hexons orient towards the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the group of four hexons: the hexons surround either a polypeptide IX or a polypeptide IIIa. The two versions of group of four hexons on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of the hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the anti-symmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an anti-symmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest
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)
Sheared and unsheared rotation of driven dust clusters
Schablinski, Jan; Block, Dietmar; Carstensen, Jan; Greiner, Franko; Piel, Alexander
2014-07-15
Finite size plasma crystals confined in an anisotropic potential well were studied under a rotating and radially unsheared drive in experiment and simulation at moderate rotational frequencies. A radially sheared rotation of these strongly coupled systems is observed for most cluster configurations with a low symmetry. The results show that a differential rotation can be effected by a non-sheared driving force.
Nász, I; Adám, Eva
2006-03-01
Each of the more than 1500 polypeptide molecules of 7 different types building up the adenovirus capsid--probably even those of their amino-acids--are in symmetrical location. Every kind of polypeptide forms a separately also symmetrical network in the capsid distributed according to their functions in the inner and outer side and the inside of the facets and edges, but always in compliance with the icosahedral symmetry. Therefore, each different polypeptide also means a general symmetry motif in the capsid in its own symmetry network. Hexons can be considered as general symmetry motifs in some special association that is because of their environmental position four kinds of hexon types can be found, which are on every facet, next to one another, like three identical groups of four (GOF) according to the three-fold rotational symmetry. Two polypeptides of a peripentonal hexon of each GOF orient toward the penton and the third toward the other penton located further on the same edge. There are two versions of the arrangement of the GOFs: the hexons surround either a polypeptide IX or a polypeptide IlIa. The two versions of GOFs on 20 facets symmetrically recurring 60 times as general hexon symmetry motifs form the capsid in combination with the network of other polypeptides. Ideally, the surface of the hexon trimer shows three-fold rotational and three-fold reflexional symmetries. In the arrangement of hexons in the facets the translational, rotational, horizontal and vertical reflexional symmetry and the combination of these, as well as the glide reflexion and the antisymmetry can be found. Each hexon has six nearest neighbours and every hexon takes part in the construction of three hexon rows. Every facet and every vertex made up of five facets has an antisymmetrical pair located on the opposite side of the capsid. Every triangular facet participates in forming three vertices and every facet has three nearest neighbouring facets. In the facets, the polypeptide
Symmetry, Point Groups, and Character Tables, Part 3, Character Tables and Their Significance
ERIC Educational Resources Information Center
Orchin, Milton; Jaffe, H. H.
1970-01-01
Presents the third of a series of articles on symmetry. Describes the symmetry properties of molecules in translatiional and rotational motion. Presents these dynamic symmetry properties in character tables for five point groups. Supplements the article with more rigorous material involving spectroscopic states, degenerate point groups and…
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
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.
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…
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.
From physical symmetries to emergent gauge symmetries
NASA Astrophysics Data System (ADS)
Barceló, Carlos; Carballo-Rubio, Raúl; Di Filippo, Francesco; Garay, Luis J.
2016-10-01
Gauge symmetries indicate redundancies in the description of the relevant degrees of freedom of a given field theory and restrict the nature of observable quantities. One of the problems faced by emergent theories of relativistic fields is to understand how gauge symmetries can show up in systems that contain no trace of these symmetries at a more fundamental level. In this paper we start a systematic study aimed to establish a satisfactory mathematical and physical picture of this issue, dealing first with abelian field theories. We discuss how the trivialization, due to the decoupling and lack of excitation of some degrees of freedom, of the Noether currents associated with physical symmetries leads to emergent gauge symmetries in specific situations. An example of a relativistic field theory of a vector field is worked out in detail in order to make explicit how this mechanism works and to clarify the physics behind it. The interplay of these ideas with well-known results of importance to the emergent gravity program, such as the Weinberg-Witten theorem, are discussed.
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
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…
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.
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 analysis of transport properties in helical superconductor junctions
NASA Astrophysics Data System (ADS)
Cheng, Qiang; Zhang, Yinhan; Zhang, Kunhua; Jin, Biao; Zhang, Changlian
2017-03-01
We study the discrete symmetries satisfied by helical p-wave superconductors with the d-vectors {{k}x}\\hat{x}+/- {{k}y}\\hat{y} or {{k}y}\\hat{x}+/- {{k}x}\\hat{y} and the transformations brought by symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with the transport properties in heterojunctions, including helical superconductors. In particular, the partial symmetries of the Hamiltonian under spin-rotation and gauge-rotation operations are responsible for the novel invariances of the conductance in tunnel junctions and the new selection rules for the lowest current and peculiar phase diagrams in Josephson junctions, which were reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed, and are consistent with the results from the Hamiltonian.
Symmetry analysis of transport properties in helical superconductor junctions.
Cheng, Qiang; Zhang, Yinhan; Zhang, Kunhua; Jin, Biao; Zhang, Changlian
2017-03-01
We study the discrete symmetries satisfied by helical p-wave superconductors with the d-vectors [Formula: see text] or [Formula: see text] and the transformations brought by symmetry operations to ferromagnet and spin-singlet superconductors, which show intimate associations with the transport properties in heterojunctions, including helical superconductors. In particular, the partial symmetries of the Hamiltonian under spin-rotation and gauge-rotation operations are responsible for the novel invariances of the conductance in tunnel junctions and the new selection rules for the lowest current and peculiar phase diagrams in Josephson junctions, which were reported recently. The symmetries of constructed free energies for Josephson junctions are also analyzed, and are consistent with the results from the Hamiltonian.
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.
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.
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.
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.
Gauge symmetry from decoupling
NASA Astrophysics Data System (ADS)
Wetterich, C.
2017-02-01
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.
Sekhar Chivukula
2016-07-12
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 presentÂ at the classical level. Â Quantum Chromodynamics (QCD),Â the modern theoryÂ of the strong interactions, exemplify each ofÂ these possibilities.Â The interplayÂ of these effects determine theÂ spectrum of particles that we observeÂ and, ultimately, account forÂ 99% of the mass of ordinary matter.Â
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)
Hamhalter, Jan; Turilova, Ekaterina
2017-02-01
Quantum symmetries of spectral lattices are studied. Basic properties of spectral order on A W ∗-algebras are summarized. Connection between projection and spectral automorphisms is clarified by showing that, under mild conditions, any spectral automorphism is a composition of function calculus and Jordan ∗-automorphism. Complete description of quantum spectral symmetries on Type I and Type II A W ∗-factors are completely described.
NASA Astrophysics Data System (ADS)
Baldo, M.; Burgio, G. F.
2016-11-01
The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years.
Furman, J M
2016-01-01
The natural stimulus for the semicircular canals is rotation of the head, which also might stimulate the otolith organs. Vestibular stimulation usually induces eye movements via the vestibulo-ocular reflex (VOR). The orientation of the subject with respect to the axis of rotation and the orientation of the axis of rotation with respect to gravity together determine which labyrinthine receptors are stimulated for particular motion trajectories. Rotational testing usually includes the measurement of eye movements via a video system but might use a subject's perception of motion. The most common types of rotational testing are whole-body computer-controlled sinusoidal or trapezoidal stimuli during earth-vertical axis rotation (EVAR), which stimulates primarily the horizontal semicircular canals bilaterally. Recently, manual impulsive rotations, known as head impulse testing (HIT), have been developed to assess individual horizontal semicircular canals. Most types of rotational stimuli are not used routinely in the clinical setting but may be used in selected research environments. This chapter will discuss clinically relevant rotational stimuli and several types of rotational testing that are used primarily in research settings.
Laminar Flow past a Rotating Sphere
NASA Astrophysics Data System (ADS)
Kim, Dongjoo; Choi, Haecheon
2000-11-01
In this study, laminar flow past a rotating sphere is numerically investigated to understand the effect of the streamwise rotation on the flow characteristics behind a sphere. The present numerical method is based on a newly developed immersed boundary method in a cylindrical coordinate. Numerical simulations are performed at Re =100, 250 and 300 in the range of 0 <= ω^* <= 1.0, where ω^* is the maximum circumferential speed at the sphere surface normalized by the free-stream velocity. At ω^*=0 (without rotation), the flow past a sphere experiences steady axisymmetry, steady plane-symmetry, and unsteady plane-symmetry, respectively, at Re =100, 250 and 300. When the rotational speed increases, the drag increases for all the Reynolds numbers investigated, whereas the lift shows a non-monotonic behavior depending on the Reynolds number. At Re =100, the flow past a sphere shows steady axisymmetry for all the rotational speeds considered and thus the lift is zero. On the other hand, at Re =250 and 300, the flow becomes unsteady with rotation. With increasing rotational speed, the lift first decreases and then increases, showing a local minimum of lift at a specific rotational speed. The three-dimensional vortical structures behind a sphere are significantly modified by the streamwise rotation. For example, the vortical structures at Re =300 are completely changed and phase locked with rotation at ω^*=0.6.
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.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment.
Symmetry in context: salience of mirror symmetry in natural patterns.
Cohen, Elias H; Zaidi, Qasim
2013-05-31
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.
Symmetry in context: Salience of mirror symmetry in natural patterns
Cohen, Elias H.; Zaidi, Qasim
2013-01-01
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773
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).
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…
Unidirectional Heat Transport Driven by Rotating Cholesteric Droplets
NASA Astrophysics Data System (ADS)
Sato, Sayumi; Bono, Shinji; Tabe, Yuka
2017-02-01
When a cholesteric liquid crystal (LC) is submitted to a thermal gradient, it exhibits continuous director rotation. The phenomenon is called the Lehmann effect and is understood as a thermomechanical coupling in chiral LCs without mirror symmetry. Since the Lehmann effect is considered to possess time-reversal symmetry, one can expect the inverse process, i.e., rotating chiral LCs to pump heat along the rotational axis. We report the first observation of heat transport driven by rotating cholesteric droplets. This result suggests a new function of the cholesterics as a micro heat pump.
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)
Liu, Keh-Fei
The relevance of chiral symmetry in baryons is highlighted in three examples in the nucleon spectroscopy and structure. The first one is the importance of chiral dynamics in understanding the Roper resonance. The second one is the role of chiral symmetry in the lattice calculation of πNσ term and strangeness. The third one is the role of chiral U(1) anomaly in the anomalous Ward identity in evaluating the quark spin and the quark orbital angular momentum. Finally, the chiral effective theory for baryons is discussed.
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.
Symmetry constraint for foreground extraction.
Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai
2014-05-01
Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.
Symmetry Lasts Longer Than Random, but Only for Brief Presentations
Makin, Alexis D. J.; Palumbo, Letizia; Bertamini, Marco
2016-01-01
Previous research has shown that explicit emotional content or physical image properties (e.g., luminance, size, and numerosity) alter subjective duration. Palumbo recently demonstrated that the presence or absence of abstract reflectional symmetry also influenced subjective duration. Here, we explored this phenomenon further by varying the type of symmetry (reflection or rotation) and the objective duration of stimulus presentation (less or more than 1 second). Experiment 1 used a verbal estimation task in which participants estimated the presentation duration of reflection, rotation symmetry, or random square-field patterns. Longer estimates were given for reflectional symmetry images than rotation or random, but only when the image was presented for less than 1 second. There was no difference between rotation and random. These findings were confirmed by a second experiment using a paired-comparison task. This temporal distortion could be because reflection has positive valence or because it is processed efficiently be the visual system. The mechanism remains to be determined. We are relatively sure, however, that reflectional patterns can increase subjective duration in the absence of explicit semantic content, and in the absence of changes in the size, luminance, or numerosity in the images. PMID:27895887
Symmetry Lasts Longer Than Random, but Only for Brief Presentations.
Ogden, Ruth; Makin, Alexis D J; Palumbo, Letizia; Bertamini, Marco
2016-01-01
Previous research has shown that explicit emotional content or physical image properties (e.g., luminance, size, and numerosity) alter subjective duration. Palumbo recently demonstrated that the presence or absence of abstract reflectional symmetry also influenced subjective duration. Here, we explored this phenomenon further by varying the type of symmetry (reflection or rotation) and the objective duration of stimulus presentation (less or more than 1 second). Experiment 1 used a verbal estimation task in which participants estimated the presentation duration of reflection, rotation symmetry, or random square-field patterns. Longer estimates were given for reflectional symmetry images than rotation or random, but only when the image was presented for less than 1 second. There was no difference between rotation and random. These findings were confirmed by a second experiment using a paired-comparison task. This temporal distortion could be because reflection has positive valence or because it is processed efficiently be the visual system. The mechanism remains to be determined. We are relatively sure, however, that reflectional patterns can increase subjective duration in the absence of explicit semantic content, and in the absence of changes in the size, luminance, or numerosity in the images.
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.
ERIC Educational Resources Information Center
Seidel, Judith Day
1998-01-01
Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change…
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)
ERIC Educational Resources Information Center
Lockett, Keith
1988-01-01
Demonstrates several objects rolling down a slope to explain the energy transition among potential energy, translational kinetic energy, and rotational kinetic energy. Contains a problem from Galileo's rolling ball experiment. (YP)
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.
Realization of Translational Symmetry in Trapped Cold Ion Rings
NASA Astrophysics Data System (ADS)
Li, Hao-Kun; Urban, Erik; Noel, Crystal; Chuang, Alexander; Xia, Yang; Ransford, Anthony; Hemmerling, Boerge; Wang, Yuan; Li, Tongcang; Häffner, Hartmut; Zhang, Xiang
2017-02-01
We crystallize up to 15 40Ca+ ions in a ring with a microfabricated silicon surface Paul trap. Delocalization of the Doppler laser-cooled ions shows that the translational symmetry of the ion ring is preserved at millikelvin temperatures. By characterizing the collective motion of the ion crystals, we identify homogeneous electric fields as the dominant symmetry-breaking mechanism at this energy scale. With increasing ion numbers, such detrimental effects are reduced. We predict that, with only a ten-ion ring, uncompensated homogeneous fields will not break the translational symmetry of the rotational ground state. This experiment opens a door towards studying quantum many-body physics with translational symmetry at the single-particle level.
Gain-Sparsity and Symmetry-Forced Rigidity in the Plane.
Jordán, Tibor; Kaszanitzky, Viktória E; Tanigawa, Shin-Ichi
We consider planar bar-and-joint frameworks with discrete point group symmetry in which the joint positions are as generic as possible subject to the symmetry constraint. We provide combinatorial characterizations for symmetry-forced rigidity of such structures with rotation symmetry or dihedral symmetry of order 2k with odd k, unifying and extending previous work on this subject. We also explore the matroidal background of our results and show that the matroids induced by the row independence of the orbit matrices of the symmetric frameworks are isomorphic to gain sparsity matroids defined on the quotient graph of the framework, whose edges are labeled by elements of the corresponding symmetry group. The proofs are based on new Henneberg type inductive constructions of the gain graphs that correspond to the bases of the matroids in question, which can also be seen as symmetry preserving graph operations in the original graph.
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.
Symmetry in the Generalized Rotor Model for Extremely Floppy Molecules
NASA Astrophysics Data System (ADS)
Schmiedt, Hanno; Jensen, Per; Schlemmer, Stephan
2016-06-01
Protonated methane CH_5^+ is unique: It is an extremely fluxional molecule. All attempts to assign quantum numbers to the high-resolution transitions obtained over the last 20 years have failed because molecular rotation and vibration cannot be separated in the conventional way. The first step towards a theoretical description is to include internal rotational degrees of freedom into the overall ones, which can be used to formulate a fundamentally new zero order approximation for the (now) generalized rotational states and energies. Predictions from this simple five-dimensional rotor model compare very favorably with the combination differences of protonated methane found in recent low temperature experiments. This talk will focus on symmetry aspects and implications of permutation symmetry for the generalized rotational states. Furthermore, refinements of the theory will be discussed, ranging from the generalization to even higher-dimensional rotors to explicit symmetry breaking and corresponding energy splittings. The latter includes the link to well-known theories of internal rotation dynamics and will show the general validity of the presented theory. Schmiedt, H., et al.; J. Chem. Phys. 143 (15), 154302 (2015) Wodraszka, R. et al.; J. Phys. Chem. Lett. 6, 4229-4232 (2015) Asvany, O. et al.; Science, 347, (6228), 1346-1349 (2015)
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…
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.
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.
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.
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.
Symmetry and Condensed Matter Physics
NASA Astrophysics Data System (ADS)
El-Batanouny, M.; Wooten, F.
2008-03-01
Preface; 1. Symmetry and physics; 2. Symmetry and group theory; 3. Group representations: concepts; 4. Group representations: formalism and methodology; 5. Dixon's method for computing group characters; 6. Group action and symmetry projection operators; 7. Construction of the irreducible representations; 8. Product groups and product representations; 9. Induced representations; 10. Crystallographic symmetry and space-groups; 11. Space groups: Irreps; 12. Time-reversal symmetry: color groups and the Onsager relations; 13. Tensors and tensor fields; 14. Electronic properties of solids; 15. Dynamical properties of molecules, solids and surfaces; 16. Experimental measurements and selection rules; 17. Landau's theory of phase transitions; 18. Incommensurate systems and quasi-crystals; References; Bibliography; Index.
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.
Invariants of broken discrete symmetries.
Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Invariants of Broken Discrete Symmetries
NASA Astrophysics Data System (ADS)
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
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.
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.
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.
The double cover of the icosahedral symmetry group and quark mass textures
NASA Astrophysics Data System (ADS)
Everett, Lisa L.; Stuart, Alexander J.
2011-04-01
We investigate the idea that the double cover of the rotational icosahedral symmetry group is the family symmetry group in the quark sector. The icosahedral (A5) group was previously proposed as a viable family symmetry group for the leptons. To incorporate the quarks, it is highly advantageous to extend the group to its double cover, as in the case of tetrahedral (A4) symmetry. We provide the basic group theoretical tools for flavor model-building based on the binary icosahedral group I‧ and construct a model of the quark masses and mixings that yields many of the successful predictions of the well-known U (2) quark texture models.
Wigner rotations and Iwasawa decompositions in polarization optics.
Han, D; Kim, Y S; Noz, M E
1999-07-01
Wigner rotations and Iwasawa decompositions are manifestations of the internal space-time symmetries of massive and massless particles, respectively. It is shown to be possible to produce combinations of optical filters which exhibit transformations corresponding to Wigner rotations and Iwasawa decompositions. This is possible because the combined effects of rotation, phase-shift, and attenuation filters lead to transformation matrices of the six-parameter Lorentz group applicable to Jones vectors and Stokes parameters for polarized light waves. The symmetry transformations in special relativity lead to a set of experiments which can be performed in optics laboratories.
Nonlinear Zel'dovich Effect: Parametric Amplification from Medium Rotation
NASA Astrophysics Data System (ADS)
Faccio, Daniele; Wright, Ewan M.
2017-03-01
The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel'dovich more than forty years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbital angular momentum drives parametric interaction in a rotating medium. The crystal rotation is shown to take the phase-mismatched parametric interaction with negligible energy exchange at zero rotation to amplification for sufficiently large rotation rates. The amplification is shown to result from breaking of anti-P T symmetry induced by the medium rotation.
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.
Experimental confirmation of the transversal symmetry breaking in laser profiles
NASA Astrophysics Data System (ADS)
Carvalho, Silvânia A.; De Leo, Stefano; Oliveira-Huguenin, José A.; da Silva, Ladário
2017-02-01
The Snell phase effects on the propagation of optical beams through dielectric blocks have been matter of recent theoretical studies. The effects of this phase on the laser profiles have been tested in our experiment. The data show an excellent agreement with the theoretical predictions confirming the axial spreading modification and the transversal symmetry breaking. The possibility to set, by rotating the dielectric blocks, different configurations allows to recover the transversal symmetry. Based on this experimental evidence, dielectric blocks can be used as alternative optical tools to control the beam profile.
Whirling orbits around twirling black holes from conformal symmetry
NASA Astrophysics Data System (ADS)
Hadar, Shahar; Porfyriadis, Achilleas P.
2017-03-01
Dynamics in the throat of rapidly rotating Kerr black holes is governed by an emergent near-horizon conformal symmetry. The throat contains unstable circular orbits at radii extending from the ISCO down to the light ring. We show that they are related by conformal transformations to physical plunges and osculating trajectories. These orbits have angular momentum arbitrarily higher than that of ISCO. Using the conformal symmetry we compute analytically the radiation produced by the physical orbits. We also present a simple formula for the full self-force on such trajectories in terms of the self-force on circular orbits.
The fundamental role of symmetry in nuclear models
Rowe, D. J.
2013-06-10
The purpose of these lectures is to illustrate how symmetry and pattern recognition play essential roles in the progression from experimental observation to an understanding of nuclear phenomena in terms of interacting neutrons and protons. We do not discuss weak interactions nor relativistic and sub-nucleon degrees of freedom. The explicit use of symmetry and the power of algebraic methods, in combination with analytical and geometrical methods are illustrated by their use in deriving a shell-model description of nuclear rotational dynamics and the structure of deformed nuclei.
ERIC Educational Resources Information Center
Roscoe, Matt B.; Zephyrs, Joe
2016-01-01
Geometric transformations have long been topics of middle school mathematics. Generations of middle school students have learned to reflect, rotate, and translate geometric objects. Historically, though, the mathematics of "movement" might have been considered a departure from other more central middle-grades geometric content areas,…
NASA Astrophysics Data System (ADS)
Lee, Allen; Lee, Ha Youn; Kardar, Mehran
2005-09-01
Locomotion of bacteria by actin polymerization and in vitro motion of spherical beads coated with a protein catalyzing polymerization are examples of active motility. Starting from a simple model of forces locally normal to the surface of a bead, we construct a phenomenological equation for its motion. The singularities at a continuous transition between moving and stationary beads are shown to be related to the symmetries of its shape. Universal features of the phase behavior are calculated analytically and confirmed by simulations. Fluctuations in velocity are shown to be generically non-Maxwellian and correlated to the shape of the bead.
Symmetry and structure of SrTiO3 nanotubes
NASA Astrophysics Data System (ADS)
Evarestov, Robert
2011-06-01
The full study of perovskite type nanotubes with square morphology is given for the first time. The line symmetry group L = ZP (a product of one axial point group P and one infinite cyclic group Z of generalized translations) of single-walled (SW) and double-walled (DW) SrTiO3 nanotubes (NT) is considered. The nanotube is defined by the square lattice translation vector L = l1a + l2b and chiral vector R = n1a + n2b, (l1, l2, n1 and n2 are integers). The nanotube of the chirality (n1,n2) is obtained by folding the (001) slabs of two- layers (with the layer group P4mm) and of three layers (with the layer group P4/mmm) in a way that the chiral vector R becomes circumference of the nanotube. Due to the orthogonality relation (RL) = 0, l1/l2 = -n2/n1 i.e. SW nanotubes with square morphology are commensurate for any rolling vector R(n1,n2). For SW (n,0) NTs the line symmetry groups belong to family 11 (T^Dnh) and are n/mmm or for even and odd n, respectively. For SW (n,n) NTs the line symmetry groups (2n)n/mcm belong to family 13 (T2n1 Dnh). The line symmetry group of a double-wall nanotube is found as intersection L2 = Z2P2 = (L ∩ L') of the symmetry groups L and L' of its single-wall constituents as earlier considered for DW CNTs. The symmetry group of DWNT (n,0)@M(n,0) belongs to the same family 11 (T^Dnh) as its SW constituents. The symmetry group of DWNT (n,n)@M(n,n) depends on the parity of M. For DW NTs with odd M, the line symmetry groups are the same as for their SW constituents and belong to family 13 (T2n1 Dnh). For even M, the rotations about screw axis of order 2n are changed by rotations around pure rotation axis of order n so that DW NT line symmetry groups belong to family 11 (T^Dnh). Commensurate STO DWNTs (n1,0)@(n2,0) and (n1, n1)@(n2, n2) belong to family 11 (T^Dnh) with n equal to the greatest common divisor of n1 and n2.
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.
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.
Observability and Controllability of Nonlinear Networks: The Role of Symmetry
NASA Astrophysics Data System (ADS)
Whalen, Andrew J.; Brennan, Sean N.; Sauer, Timothy D.; Schiff, Steven J.
2015-01-01
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 have subspaces that influence model behavior, but cannot be controlled by an input. Such subspaces can be difficult to determine in complex nonlinear networks. Since almost all 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 nonlinear measures of observability and controllability. We numerically observe and theoretically predict that not all symmetries have the same effect on network observation and control. Our analysis shows 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.
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-02-13
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures-and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body-bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body-bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains.
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-01-01
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures—and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body–bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body–bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains. PMID:24379431
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.
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.
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.
[Symmetries and homologies of Geomerida].
Zarenkov, N A
2005-01-01
The symmetry of Earths life cover (Geomerida) was described generally by L.A. Zenkevich (1948). It coincides with the symmetry of geographic cover. Its symmetry elements are equatorial plane and three meridonal planes corresponded to oceans and continents. The hypsographic curve with point of inflection (symmetry element) on 3 km depth line should be added to these elements. The plankton and benthos communities as well as fauna of taxons are distributed symmetrically according these symmetry elements. Zenkevich model was successfully extrapolated to plankton by K.V. Beklemishev (1967, 1969) and to abyssal benthos by Sokolova M.N. (1986). The plankton communities inhabiting symmetrically located macrocirculations are considered as homologous. The character of circulation determines the trophic structure of plankton and benthos. In the case of high productivity of plankton, benthic grazing animals feed on sedimented particles have bilateral symmetric mouthpart. Otherwise they have to acquire food from water column and use cyclomeric mouthpart. Thus, the symmetry of macrocirculations determines the symmetry distribution of benthic animals with two major symmetries of mouthparts. The peculiarities of organisms' symmetry are discussed in the context of Pierre Curie principle and the ideas of K.V. Beklemishev concerning evolution of morphological axes.
Effect of gravity level fluctuations for rotating fluids in high and low rotating speeds
NASA Technical Reports Server (NTRS)
Hung, R. J.; Tsao, Y. D.; Hong, B. B.; Leslie, F. W.
1989-01-01
Time-dependent evolutions of the profile of the free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been studied. Numerical computations of the dynamics of bubble shapes have been carried out with sinusoidal-function vibration of the gravity environment at high and low cylinder speeds.
From Molecular Point Group Symmetry to Space Group Symmetry.
ERIC Educational Resources Information Center
Hathaway, Brian
1979-01-01
Describes undergraduate chemistry curricula in which the student is asked to either build a model of one asymmetric unit in the unit cell and to indicate the positions of the symmetry-related units by putting in key atoms, or to identify on a prebuild model the asymetric and symmetry-related units. (BB)
Symmetry reduction related with nonlocal symmetry for Gardner equation
NASA Astrophysics Data System (ADS)
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
Symmetry and surface symmetry energies in finite nuclei
Lee, S. J.; Mekjian, A. Z.
2010-12-15
A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of {beta} stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.
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.
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.
New class of locally rotationally symmetric spacetimes with simultaneous rotation and spatial twist
NASA Astrophysics Data System (ADS)
Singh, Sayuri; Ellis, George F. R.; Goswami, Rituparno; Maharaj, Sunil D.
2016-11-01
We establish the existence and find the necessary and sufficient conditions for a new class of solutions of locally rotationally symmetric spacetimes that have nonvanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demands nonvanishing and bounded heat flux and these solutions are self-similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.
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.)
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
PT Symmetry and Spontaneous Symmetry Breaking in a Microwave Billiard
NASA Astrophysics Data System (ADS)
Bittner, S.; Dietz, B.; Günther, U.; Harney, H. L.; Miski-Oglu, M.; Richter, A.; Schäfer, F.
2012-01-01
We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.
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.
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.
Functional Symmetry of Endomembranes
2007-01-01
In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation. PMID:17267686
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.
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.
Symmetry algebras of linear differential equations
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Shirokov, I. V.
1992-07-01
The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.
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.
The rotationally improved Skyrmion, or RISKY
NASA Astrophysics Data System (ADS)
Dorey, N.; Mattis, M. P.
The perceived inability of the Skyrme model to reproduce pseudovector pion-baryon coupling has come to be known as the 'Yukawa problem.' The authors 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(1) symmetry.
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.
REVIEWS OF TOPICAL PROBLEMS: Minimal chaos, stochastic webs, and structures of quasicrystal symmetry
NASA Astrophysics Data System (ADS)
Zaslavskiĭ, G. M.; Sagdeev, Roal'd. Z.; Usikov, D. A.; Chernikov, A. A.
1988-10-01
The relationship between the problem of the symmetry of a plane tiling and the properties of nonintegrable dynamic systems is reviewed. The formation of stochastic layers and a stochastic web in the motion of linear and nonlinear oscillators subjected to a perturbation is discussed in detail. Emphasis is placed on research on the symmetry properties of a stochastic web with a fractal structure of a quasicrystal type. Structures with a quasicrystal symmetry form as a result of an interaction of two types of symmetries: translational and rotational. Various characteristics of structures with a quasicrystal symmetry are discussed: the distributions of stable and unstable points, the state density, and the Fourier spectrum. Quasicrystal structures in solid state physics, hydrodynamics, botany, and ornamental art are discussed.
Electroweak Symmetry Breaking: With Dynamics
Chivukula, R. Sekhar
2005-03-22
In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories.
Classification of spacetimes with symmetry
NASA Astrophysics Data System (ADS)
Hicks, Jesse W.
Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we. i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein's Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov's paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Partial Dynamical Symmetry in Molecules
NASA Astrophysics Data System (ADS)
Ping, Jia-Lun; Chen, Jin-Quan
1997-03-01
It is shown that any Hamiltonian involving only one- and two-bond interactions for a molecule withnbonds and having a point groupPas its symmetry group may have theSn⊃Ppartial dynamical symmetry, i.e., the Hamiltonian can be solved analytically for a part of the states, called the unique states. For example, theXY6molecule has theS6⊃Ohpartial dynamical symmetry. The model of Iachello and Oss forncoupled anharmonic oscillators is revisited in terms of the partial dynamical symmetry. The energies are obtained analytically for the nine unique levels of theXY6molecule and the structures of the eigenstates are disclosed for the first time, while for non-unique states they are obtained by diagonalizing the Hamiltonian in theS6⊃Ohsymmetry adapted basis with greatly reduced dimension.
Metasurfaces inner symmetries: from square lattices to quasicrystalline layouts (presentation video)
NASA Astrophysics Data System (ADS)
Kruk, Sergey S.; Poddubny, Alexander; Helgert, Christian; Decker, Manuel; Staude, Isabelle; Menzel, Christoph; Etrich, Christoph; Rockstuhl, Carsten; Powell, David A.; Pertsch, Thomas; Neshev, Dragomir N.; Kivshar, Yuri S.
2014-09-01
We systematically study both experimentally and theoretically the links between the lattice symmetries of metasurfaces and their optical properties at both normal and oblique illumination. We attribute different symmetry elements to number of polarization phenomena. In particular, we predict analytically and verify experimentally the influence of rotational axes, mirror planes and inversion centres on optical activity, circular dichroism and asymmetric transmission. We fabricate and test nanostructured optical metasurfaces with four different inner structures: square and hexagonal lattices, quasicrystalline layout, and amorphous arrangement. We demonstrate the ability to enhance/suppress particular optical response by appropriate choice of the metasurface's symmetry.
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
Emergent symmetries in atomic nuclei from first principles
NASA Astrophysics Data System (ADS)
Launey, K. D.; Dreyfuss, A. C.; Baker, R. B.; Draayer, J. P.; Dytrych, T.
2015-04-01
An innovative symmetry-guided approach and its applications to light and intermediate-mass nuclei is discussed. This approach, with Sp(3, R) the underpinning group, is based on our recent remarkable finding, namely, we have identified the symplectic Sp(3,R) as an approximate symmetry for low-energy nuclear dynamics. This study presents the results of two complementary studies, one that utilizes realistic nucleon-nucleon interactions and unveils symmetries inherent to nuclear dynamics from first principles (or ab initio), and another study, which selects important components of the nuclear interaction to explain the primary physics responsible for emergent phenomena, such as enhanced collectivity and alpha clusters. In particular, within this symmetry-guided framework, ab initio applications of the theory to light nuclei reveal the emergence of a simple orderly pattern from first principles. This provides a strategy for determining the nature of bound states of nuclei in terms of a relatively small fraction of the complete shell-model space, which, in turn, can be used to explore ultra-large model spaces for a description of alpha-cluster and highly deformed structures together with associated rotations. We find that by using only a fraction of the model space extended far beyond current no-core shell-model limits and a long-range interaction that respects the symmetries in play, the outcome reproduces characteristic features of the low-lying 0+ states in 12C (including the elusive Hoyle state of importance to astrophysics) and agrees with ab initio results in smaller spaces. For these states, we offer a novel perspective emerging out of no-core shell-model considerations, including a discussion of associated nuclear deformation, matter radii, and density distribution. The framework we find is also extensible beyond 12C, namely, to the low-lying 0+ states of 8Be as well as the ground-state rotational band of Ne, Mg, and Si isotopes.
Possible violations of spacetime symmetries
NASA Astrophysics Data System (ADS)
Urrutia, Luis
2016-10-01
The identification of symmetries has played a fundamental role in our understanding of physical phenomena. Nevertheless, in most cases such symmetries constitute only a zeroth-order approximation and they need to be broken so that the predictions of the theory are consistent with experimental observation. In particular, the almost sacred CPT and Lorentz symmetries, which are certainly part of the fundamental ideas of modern physics, need to be probed experimentally. Recently, such efforts have been intensified because different theoretical approaches aiming to understand the microstructure of space-time suggest the possibility that such symmetries could present minute violations. Up to now, and with increasing experimental sensitivities, no signs of violation have been found. Nevertheless, we observe that even the persistence of such negative results will have a profound impact. On one hand, they will provide those symmetries with a firm experimental basis. On the other, they will set stringent experimental bounds to be compared with the possible emergence of such violations in quantum gravity models based upon a discrete structure of space. We present a very general perspective of the research on Lorentz symmetry breaking, together with a review of a few specific topics.
Stellar Rotation Effects in Polarimetric Microlensing
NASA Astrophysics Data System (ADS)
Sajadian, Sedighe
2016-07-01
It is well known that the polarization signal in microlensing events of hot stars is larger than that of main-sequence stars. Most hot stars rotate rapidly around their stellar axes. The stellar rotation creates ellipticity and gravity-darkening effects that break the spherical symmetry of the source's shape and the circular symmetry of the source's surface brightness respectively. Hence, it causes a net polarization signal for the source star. This polarization signal should be considered in polarimetric microlensing of fast rotating stars. For moderately rotating stars, lensing can magnify or even characterize small polarization signals due to the stellar rotation through polarimetric observations. The gravity-darkening effect due to a rotating source star creates asymmetric perturbations in polarimetric and photometric microlensing curves whose maximum occurs when the lens trajectory crosses the projected position of the rotation pole on the sky plane. The stellar ellipticity creates a time shift (i) in the position of the second peak of the polarimetric curves in transit microlensing events and (ii) in the peak position of the polarimetric curves with respect to the photometric peak position in bypass microlensing events. By measuring this time shift via polarimetric observations of microlensing events, we can evaluate the ellipticity of the projected source surface on the sky plane. Given the characterizations of the FOcal Reducer and low dispersion Spectrograph (FORS2) polarimeter at the Very Large Telescope, the probability of observing this time shift is very small. The more accurate polarimeters of the next generation may well measure these time shifts and evaluate the ellipticity of microlensing source stars.
Forced vibration analysis of rotating cyclic structures in NASTRAN
NASA Technical Reports Server (NTRS)
Elchuri, V.; Gallo, A. M.; Skalski, S. C.
1981-01-01
A new capability was added to the general purpose finite element program NASTRAN Level 17.7 to conduct forced vibration analysis of tuned cyclic structures rotating about their axis of symmetry. The effects of Coriolis and centripetal accelerations together with those due to linear acceleration of the axis of rotation were included. The theoretical, user's, programmer's and demonstration manuals for this new capability are presented.
Quantum graphs: PT -symmetry and reflection symmetry of the spectrum
NASA Astrophysics Data System (ADS)
Kurasov, P.; Majidzadeh Garjani, B.
2017-02-01
Not necessarily self-adjoint quantum graphs—differential operators on metric graphs—are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P . If the differential operator is P T -symmetric, then its spectrum has reflection symmetry with respect to the real line. Our goal is to understand whether the opposite statement holds, namely, whether the reflection symmetry of the spectrum of a quantum graph implies that the underlying metric graph possesses a non-trivial automorphism and the differential operator is P T -symmetric. We give partial answer to this question by considering equilateral star-graphs. The corresponding Laplace operator with Robin vertex conditions possesses reflection-symmetric spectrum if and only if the operator is P T -symmetric with P being an automorphism of the metric graph.
Structure and Properties of High Symmetry Composites
1990-07-27
utilizing a 4-directional reinforcement. Reducing the close-to-cubic symmetry concept into practice in our laboratory by a three-dimensional braiding...modelled by utilizing the different elastic strain energy expressions produced by different combinations of symmetry elements. Symmetry in Materials The...rings is insignmicant. Utilizing the above assumptions, numerous textile structures possess holosymmetric cubic symmetry. This symmetry state is found in
Structural Symmetry in Membrane Proteins.
Forrest, Lucy R
2015-01-01
Symmetry is a common feature among natural systems, including protein structures. A strong propensity toward symmetric architectures has long been recognized for water-soluble proteins, and this propensity has been rationalized from an evolutionary standpoint. Proteins residing in cellular membranes, however, have traditionally been less amenable to structural studies, and thus the prevalence and significance of symmetry in this important class of molecules is not as well understood. In the past two decades, researchers have made great strides in this area, and these advances have provided exciting insights into the range of architectures adopted by membrane proteins. These structural studies have revealed a similarly strong bias toward symmetric arrangements, which were often unexpected and which occurred despite the restrictions imposed by the membrane environment on the possible symmetry groups. Moreover, membrane proteins disproportionately contain internal structural repeats resulting from duplication and fusion of smaller segments. This article discusses the types and origins of symmetry in membrane proteins and the implications of symmetry for protein function.
Symmetry Guide to Ferroaxial Transitions
NASA Astrophysics Data System (ADS)
Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.
2016-04-01
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .
Expediting model-based optoacoustic reconstructions with tomographic symmetries
Lutzweiler, Christian; Deán-Ben, Xosé Luís; Razansky, Daniel
2014-01-15
Purpose: Image quantification in optoacoustic tomography implies the use of accurate forward models of excitation, propagation, and detection of optoacoustic signals while inversions with high spatial resolution usually involve very large matrices, leading to unreasonably long computation times. The development of fast and memory efficient model-based approaches represents then an important challenge to advance on the quantitative and dynamic imaging capabilities of tomographic optoacoustic imaging. Methods: Herein, a method for simplification and acceleration of model-based inversions, relying on inherent symmetries present in common tomographic acquisition geometries, has been introduced. The method is showcased for the case of cylindrical symmetries by using polar image discretization of the time-domain optoacoustic forward model combined with efficient storage and inversion strategies. Results: The suggested methodology is shown to render fast and accurate model-based inversions in both numerical simulations andpost mortem small animal experiments. In case of a full-view detection scheme, the memory requirements are reduced by one order of magnitude while high-resolution reconstructions are achieved at video rate. Conclusions: By considering the rotational symmetry present in many tomographic optoacoustic imaging systems, the proposed methodology allows exploiting the advantages of model-based algorithms with feasible computational requirements and fast reconstruction times, so that its convenience and general applicability in optoacoustic imaging systems with tomographic symmetries is anticipated.
Resonantly amplified vibronic symmetry breaking
NASA Astrophysics Data System (ADS)
Poliakoff, E. D.; Rathbone, G. J.; Bozek, J. D.; Lucchese, R. R.
2002-05-01
In photoelectron spectroscopy, it is normally assumed that excitation of a single quantum of a non-totally symmetric vibrational mode is forbidden owing to symmetry constraints. Using vibrationally resolved photoelectron spectroscopy over a broad spectral range, we have shown that a previously overlooked mechanism can lead to these nominally forbidden transitions. Specifically, the photoelectron can mediate the oscillator strength for such a transition via resonantly amplified vibronic symmetry breaking, and this effect results from intrachannel rather than interchannel coupling. In our first experiments, we focused on bending excitation accompanying CO2 photoionization. Photoelectron spectroscopy on the CO_2^+(C^2Σ_g^+) state showed that the excitation of the (010) vibrational mode is mediated by a shape resonant continuum electron. The degree of vibrational excitation can be substantial, and extensions to other types of symmetry breaking are currently being investigated.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Quantum Symmetries and Exceptional Collections
NASA Astrophysics Data System (ADS)
Karp, Robert L.
2011-01-01
We study the interplay between discrete quantum symmetries at certain points in the moduli space of Calabi-Yau compactifications, and the associated identities that the geometric realization of D-brane monodromies must satisfy. We show that in a wide class of examples, both local and compact, the monodromy identities in question always follow from a single mathematical statement. One of the simplest examples is the {{mathbb Z}_5} symmetry at the Gepner point of the quintic, and the associated D-brane monodromy identity.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Chiral symmetry in quarkyonic matter
Kojo, T.
2012-05-15
The 1/N{sub c} expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <{psi}-bar exp (2i{mu}{sub q} z{gamma}{sup 0} {gamma}{sup z}){psi}> . An extension to multiple chiral spirals is also briefly discussed.
Bell Inequalities and Group Symmetry
NASA Astrophysics Data System (ADS)
Bolonek-Lasoń, Katarzyna
2017-03-01
Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr Gűney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S 4 is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.
Nonsupersymmetric Dualities from Mirror Symmetry
NASA Astrophysics Data System (ADS)
Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo; Wang, Huajia
2017-01-01
We study supersymmetry breaking perturbations of the simplest dual pair of (2 +1 )-dimensional N =2 supersymmetric field theories—the free chiral multiplet and N =2 super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals
NASA Astrophysics Data System (ADS)
Yang, Bohm-Jung; Bojesen, Troels Arnfred; Morimoto, Takahiro; Furusaki, Akira
2017-02-01
Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here we show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling.
Translational symmetry breaking and the disintegration of the Hofstadter butterfly
NASA Astrophysics Data System (ADS)
Mishra, Archana; Hassan, S. R.; Shankar, R.
2017-01-01
We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions are prolific and occur at many values of the flux and particle density. The breaking of the translational symmetry introduces a new length scale in the problem and this affects the energy-band diagram resulting in the disintegration of the fractal structure in the energy flux plot, the Hofstadter butterfly. This disintegration increases with increase in the interaction strength. Many of these phase transitions are accompanied with change in the Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly is manifested in the Landau fan diagram also.
Spinor Bose gases: Symmetries, magnetism, and quantum dynamics
NASA Astrophysics Data System (ADS)
Stamper-Kurn, Dan M.; Ueda, Masahito
2013-07-01
Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures, and topological defects, effects of magnetic-dipole interactions, and various nonequilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.
Learning from data to design functional materials without inversion symmetry
NASA Astrophysics Data System (ADS)
Balachandran, Prasanna V.; Young, Joshua; Lookman, Turab; Rondinelli, James M.
2017-02-01
Accelerating the search for functional materials is a challenging problem. Here we develop an informatics-guided ab initio approach to accelerate the design and discovery of noncentrosymmetric materials. The workflow integrates group theory, informatics and density-functional theory to uncover design guidelines for predicting noncentrosymmetric compounds, which we apply to layered Ruddlesden-Popper oxides. Group theory identifies how configurations of oxygen octahedral rotation patterns, ordered cation arrangements and their interplay break inversion symmetry, while informatics tools learn from available data to select candidate compositions that fulfil the group-theoretical postulates. Our key outcome is the identification of 242 compositions after screening ~3,200 that show potential for noncentrosymmetric structures, a 25-fold increase in the projected number of known noncentrosymmetric Ruddlesden-Popper oxides. We validate our predictions for 19 compounds using phonon calculations, among which 17 have noncentrosymmetric ground states including two potential multiferroics. Our approach enables rational design of materials with targeted crystal symmetries and functionalities.
Connections between the dynamical symmetries in the microscopic shell model
NASA Astrophysics Data System (ADS)
Georgieva, A. I.; Drumev, K. P.
2016-03-01
The dynamical symmetries of the microscopic shell model appear as the limiting cases of a symmetry adapted Pairing-Plus-Quadrupole Model /PQM/, with a Hamiltonian containing isoscalar and isovector pairing and quadrupole interactions. We establish a correspondence between each of the three types of pairing bases and Elliott's SU(3) basis, that describes collective rotation of nuclear systems with quadrupole deformation. It is derived from their complementarity to the same LS coupling chain of the shell model number conserving algebra. The probability distribution of the S U(3) basis states within the pairing eigenstates is also obtained through a numerical diagonalization of the PQM Hamiltonian in each limit. We introduce control parameters, which define the phase diagram of the model and determine the role of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
High order accurate finite difference schemes based on symmetry preservation
NASA Astrophysics Data System (ADS)
Ozbenli, Ersin; Vedula, Prakash
2016-11-01
A new algorithm for development of high order accurate finite difference schemes for numerical solution of partial differential equations using Lie symmetries is presented. Considering applicable symmetry groups (such as those relevant to space/time translations, Galilean transformation, scaling, rotation and projection) of a partial differential equation, invariant numerical schemes are constructed based on the notions of moving frames and modified equations. Several strategies for construction of invariant numerical schemes with a desired order of accuracy are analyzed. Performance of the proposed algorithm is demonstrated using analysis of one-dimensional partial differential equations, such as linear advection diffusion equations inviscid Burgers equation and viscous Burgers equation, as our test cases. Through numerical simulations based on these examples, the expected improvement in accuracy of invariant numerical schemes (up to fourth order) is demonstrated. Advantages due to implementation and enhanced computational efficiency inherent in our proposed algorithm are presented. Extension of the basic framework to multidimensional partial differential equations is also discussed.
Rotational Doppler effect in nonlinear optics
NASA Astrophysics Data System (ADS)
Li, Guixin; Zentgraf, Thomas; Zhang, Shuang
2016-08-01
The translational Doppler effect of electromagnetic and sound waves has been successfully applied in measurements of the speed and direction of vehicles, astronomical objects and blood flow in human bodies, and for the Global Positioning System. The Doppler effect plays a key role for some important quantum phenomena such as the broadened emission spectra of atoms and has benefited cooling and trapping of atoms with laser light. Despite numerous successful applications of the translational Doppler effect, it fails to measure the rotation frequency of a spinning object when the probing wave propagates along its rotation axis. This constraint was circumvented by deploying the angular momentum of electromagnetic waves--the so-called rotational Doppler effect. Here, we report on the demonstration of rotational Doppler shift in nonlinear optics. The Doppler frequency shift is determined for the second harmonic generation of a circularly polarized beam passing through a spinning nonlinear optical crystal with three-fold rotational symmetry. We find that the second harmonic generation signal with circular polarization opposite to that of the fundamental beam experiences a Doppler shift of three times the rotation frequency of the optical crystal. This demonstration is of fundamental significance in nonlinear optics, as it provides us with insight into the interaction of light with moving media in the nonlinear optical regime.
Transport of parallel momentum induced by current-symmetry breaking in toroidal plasmas.
Camenen, Y; Peeters, A G; Angioni, C; Casson, F J; Hornsby, W A; Snodin, A P; Strintzi, D
2009-03-27
The symmetry of a physical system strongly impacts on its properties. In toroidal plasmas, the symmetry along a magnetic field line usually constrains the radial flux of parallel momentum to zero in the absence of background flows. By breaking the up-down symmetry of the toroidal currents, this constraint can be relaxed. The parallel asymmetry in the magnetic configuration then leads to an incomplete cancellation of the turbulent momentum flux across a flux surface. The magnitude of the subsequent toroidal rotation increases with the up-down asymmetry and its sign depends on the direction of the toroidal magnetic field and plasma current. Such a mechanism offers new insights in the interpretation and control of the intrinsic toroidal rotation in present day experiments.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra.
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Symmetry-protected topological entanglement
NASA Astrophysics Data System (ADS)
Marvian, Iman
2017-01-01
We propose an order parameter for the symmetry-protected topological (SPT) phases which are protected by Abelian on-site symmetries. This order parameter, called the SPT entanglement, is defined as the entanglement between A and B , two distant regions of the system, given that the total charge (associated with the symmetry) in a third region C is measured and known, where C is a connected region surrounded by A , B , and the boundaries of the system. In the case of one-dimensional systems we prove that in the limit where A and B are large and far from each other compared to the correlation length, the SPT entanglement remains constant throughout a SPT phase, and furthermore, it is zero for the trivial phase while it is nonzero for all the nontrivial phases. Moreover, we show that the SPT entanglement is invariant under the low-depth quantum circuits which respect the symmetry, and hence it remains constant throughout a SPT phase in the higher dimensions as well. Also, we show that there is an intriguing connection between SPT entanglement and the Fourier transform of the string order parameters, which are the traditional tool for detecting SPT phases. This leads to an algorithm for extracting the relevant information about the SPT phase of the system from the string order parameters. Finally, we discuss implications of our results in the context of measurement-based quantum computation.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
From symmetries to number theory
Tempesta, P.
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Resonantly amplified vibronic symmetry breaking
NASA Astrophysics Data System (ADS)
Rathbone, G. J.; Poliakoff, E. D.; Bozek, John D.; Lucchese, R. R.
2001-05-01
The energy dependence of the vibrational branching ratio for exciting one quantum of bending is determined for CO2 4σg-1 photoionization. This nominally forbidden transition becomes allowed for a photoionization transition as a result of instantaneous symmetry breaking due to zero point motion, and is strongly enhanced by a continuum shape resonance.
Hidden local symmetry and beyond
NASA Astrophysics Data System (ADS)
Yamawaki, Koichi
Gerry Brown was a godfather of our hidden local symmetry (HLS) for the vector meson from the birth of the theory throughout his life. The HLS is originated from very nature of the nonlinear realization of the symmetry G based on the manifold G/H, and thus is universal to any physics based on the nonlinear realization. Here, I focus on the Higgs Lagrangian of the Standard Model (SM), which is shown to be equivalent to the nonlinear sigma model based on G/H = SU(2)L ×SU(2)R/SU(2)V with additional symmetry, the nonlinearly-realized scale symmetry. Then, the SM does have a dynamical gauge boson of the SU(2)V HLS, “SM ρ meson”, in addition to the Higgs as a pseudo-dilaton as well as the NG bosons to be absorbed in to the W and Z. Based on the recent work done with Matsuzaki and Ohki, I discuss a novel possibility that the SM ρ meson acquires kinetic term by the SM dynamics itself, which then stabilizes the skyrmion dormant in the SM as a viable candidate for the dark matter, what we call “dark SM skyrmion (DSMS)”.
Monster symmetry and extremal CFTs
NASA Astrophysics Data System (ADS)
Gaiotto, Davide
2012-11-01
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
Rotational excitation of CH4 by He atoms
NASA Astrophysics Data System (ADS)
Yanga, B. H.; Stancil, P. C.
2008-10-01
Quantum close-coupling and coupled-state approximation scattering calculations for rotational energy transfer of rotationally excited CH4 due to collisions with He are presented for collision energies between 10-7 and 3000 cm-1 using the MP4 potential of Calderoni et al. [J. Chem. Phys. 121, 8261 (2004)]. State-to-state cross sections and rate coefficients from selected initial rotational states of CH4 in symmetries A, E, and F are studied from the ultra-cold to the thermal regime. Comparison of the cross sections with available theoretical results and experimental data show good agreement. Applications to astrophysics and cold laboratory environments are briefly addressed.
Symmetry, Statistics and Structure in MHD Turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.
Symmetry Breaking During Drosophila Oogenesis
Roth, Siegfried; Lynch, Jeremy A.
2009-01-01
The orthogonal axes of Drosophila are established during oogenesis through a hierarchical series of symmetry-breaking steps, most of which can be traced back to asymmetries inherent in the architecture of the ovary. Oogenesis begins with the formation of a germline cyst of 16 cells connected by ring canals. Two of these 16 cells have four ring canals, whereas the others have fewer. The first symmetry-breaking step is the selection of one of these two cells to become the oocyte. Subsequently, the germline cyst becomes surrounded by somatic follicle cells to generate individual egg chambers. The second symmetry-breaking step is the posterior positioning of the oocyte within the egg chamber, a process mediated by adhesive interactions with a special group of somatic cells. Posterior oocyte positioning is accompanied by a par gene-dependent repolarization of the microtubule network, which establishes the posterior cortex of the oocyte. The next two steps of symmetry breaking occur during midoogenesis after the volume of the oocyte has increased about 10-fold. First, a signal from the oocyte specifies posterior follicle cells, polarizing a symmetric prepattern present within the follicular epithelium. Second, the posterior follicle cells send a signal back to the oocyte, which leads to a second repolarization of the oocyte microtubule network and the asymmetric migration of the oocyte nucleus. This process again requires the par genes. The repolarization of the microtubule network results in the transport of bicoid and oskar mRNAs, the anterior and posterior determinants, respectively, of the embryonic axis, to opposite poles of the oocyte. The asymmetric positioning of the oocyte nucleus defines a cortical region of the oocyte where gurken mRNA is localized, thus breaking the dorsal–ventral symmetry of the egg and embryo. PMID:20066085
Search for and discovery of chiral symmetry in nuclei
Pasternak, A. A.
2010-08-15
Studies devoted to the discovery and investigation of chiral-symmetry breaking in nuclei are briefly reviewed. Unlike the case of molecules and the macrocosm, where chirality manifests itself in the spatial structure of objects, chirality in nuclei is connected with different relative orientation of valence-quasiparticle spins and the angular momentum of collective rotation of the triaxial core. Decisive arguments in favor of the existence of this effect are based on measurements of lifetimes of high-spin nuclear levels in the picosecond range by Doppler methods of {gamma} spectroscopy.
NASA Technical Reports Server (NTRS)
1976-01-01
The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.
Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator
Del Bino, Leonardo; Silver, Jonathan M.; Stebbings, Sarah L.; Del'Haye, Pascal
2017-01-01
Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) states of light to circulate in the resonator. Equivalently, this effect can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors. PMID:28220865
Symmetry breaking in MAST plasma turbulence due to toroidal flow shear
NASA Astrophysics Data System (ADS)
Fox, M. F. J.; van Wyk, F.; Field, A. R.; Ghim, Y.-c.; Parra, F. I.; Schekochihin, A. A.; the MAST Team
2017-03-01
The flow shear associated with the differential toroidal rotation of tokamak plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by the up–down symmetry of the magnetic equilibrium. Using experimental beam-emission-spectroscopy measurements and gyrokinetic simulations, this symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself as a tilt of the spatial correlation function and a finite skew in the distribution of the fluctuating density field. The tilt is a statistical expression of the ‘shearing’ of the turbulent structures by the mean flow. The skewness of the distribution is related to the emergence of long-lived density structures in sheared, near-marginal plasma turbulence. The extent to which these effects are pronounced is argued (with the aid of the simulations) to depend on the distance from the nonlinear stability threshold. Away from the threshold, the symmetry is effectively restored.
Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator.
Del Bino, Leonardo; Silver, Jonathan M; Stebbings, Sarah L; Del'Haye, Pascal
2017-02-21
Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) states of light to circulate in the resonator. Equivalently, this effect can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
Effective field theory of emergent symmetry breaking in deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2015-09-03
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. In this study, we extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. Lastly, in deformed nuclei these are vibrational modes each of which serves as band head of a rotational band.
Effective field theory of emergent symmetry breaking in deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2015-09-03
Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. In this study, we extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. Lastly, in deformed nuclei these are vibrational modes each of whichmore » serves as band head of a rotational band.« less
Symmetry Breaking of Counter-Propagating Light in a Nonlinear Resonator
NASA Astrophysics Data System (ADS)
Del Bino, Leonardo; Silver, Jonathan M.; Stebbings, Sarah L.; Del'Haye, Pascal
2017-02-01
Spontaneous symmetry breaking is a concept of fundamental importance in many areas of physics, underpinning such diverse phenomena as ferromagnetism, superconductivity, superfluidity and the Higgs mechanism. Here we demonstrate nonreciprocity and spontaneous symmetry breaking between counter-propagating light in dielectric microresonators. The symmetry breaking corresponds to a resonance frequency splitting that allows only one of two counter-propagating (but otherwise identical) states of light to circulate in the resonator. Equivalently, this effect can be seen as the collapse of standing waves and transition to travelling waves within the resonator. We present theoretical calculations to show that the symmetry breaking is induced by Kerr-nonlinearity-mediated interaction between the counter-propagating light. Our findings pave the way for a variety of applications including optically controllable circulators and isolators, all-optical switching, nonlinear-enhanced rotation sensing, optical flip-flops for photonic memories as well as exceptionally sensitive power and refractive index sensors.
The Root Lattice D4 and Planar Quasilattices with Octagonal and Dodecagonal Symmetry
NASA Astrophysics Data System (ADS)
Baake, M.; Joseph, D.; Schlottmann, M.
Quasiperiodic patterns with eight- and twelvefold symmetry are presented which share the root lattice D4, i.e., the 4-D face-centered hypercubic lattice, for their minimal embedding in four-space. We derive the patterns by means of the dualization method and investigate key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction. The generalized point symmetries (and thus the Laue group) of these patterns are the dihedral groups d8 and d12, respectively, which share a common subgroup, d4. We introduce a contiunous one-parameter rotation between the two phases which leaves this subgroup invariant. This should prove useful for modelling alloys like V15Ni10Si where quasicrystalline phases with eight- and twelvefold symmetry coexist.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
An Elementary Course in Mathematical Symmetry.
ERIC Educational Resources Information Center
Rose, Bruce I.; Stafford, Robert D.
1981-01-01
A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)
Model of a rotating magnetic cloud
NASA Technical Reports Server (NTRS)
Farrugia, C. J.; Osherovich, V. A.; Burlaga, L. F.
1992-01-01
The possibility that magnetic clouds rotate while they propagate antisunward was investigated. Magnetic clouds are modeled as magnetic flux ropes which rotate rigidly about the axis of symmetry. An ideal magnetohydrodynamic model, in which the evolution of the magnetic structure is related to the time evolution of the angular frequency, is developed. A class of 'separable' magnetic fields is employed to reduce the problem to a nonlinear ordinary differential equation for the evolution function, and it is solved numerically. The corresponding effective potential gives rise to two modes of evolution--expansion and oscillation--depending on the energy and on the value of a dimensionless parameter, k. Parameter k depends on the gas pressure, the ratio of the magnetic field components, and the frequency of rotation. There is a critical value of k, k(sub c), above which the oscillatory regime disappears and the flux rope invariably expands, regardless of the energy. Below k(sub c) the energy determines whether the configuration is confined or unbounded. Rotation always helps expansion by lowering the potential barrier. A data example was studied and features which are interpreted as signatures of rotation are presented. The angular speed is comparable to the Alfven speed, and the core of the rotating cloud completes on average one full revolution every three days at 1 AU. The parameter k is calculated from observations, and it is found to be close to, but below, critical. Only three out of the nine clouds examined showed signatures of rotation. Theoretical analysis suggests that close to the Sun rotation effects may play a more important role in the evolution of magnetic clouds than 1 AU.
Intrinsic Axial Flows in CSDX and Dynamical Symmetry Breaking in ITG Turbulence
NASA Astrophysics Data System (ADS)
Li, Jiacong; Diamond, P. H.; Hong, R.; Thakur, S. C.; Xu, X. Q.; Tynan, G. R.
2016-10-01
Toroidal plasma rotation can enhance confinement when combined with weak magnetic shear. Also, external rotation drive in future fusion devices (e.g. ITER) will be weak. Together, these two considerations drive us to study intrinsic rotations with weak magnetic shear. In particular, a global transition is triggered in CSDX when magnetic field B exceeds a critical strength threshold. At the transition an ion feature emerges in the core turbulence. Recent studies show that a dynamical symmetry breaking mechanism in drift wave turbulence can drive intrinsic axial flows in CSDX, as well as enhance intrinsic rotations in tokamaks. Here, we focus on what happens when ion features emerge in CSDX, and how ion temperature gradient (ITG) driven turbulence drives intrinsic rotations with weak magnetic shear. The effect of dynamical symmetry breaking in ITG turbulence depends on the stability regime. In a marginally stable regime, dynamical symmetry breaking results in an augmented turbulence viscosity (chi-phi). However, when ITG is far from the stability boundary, a negative increment in turbulent viscosity is induced. This material is based upon work supported by the U.S. Department of Energy, Office of Fusion Energy Sciences, under Award No. DE-FG02-04ER54738.
Time-resolved beam symmetry measurement for VMAT commissioning and quality assurance.
Barnes, Michael P; Greer, Peter B
2016-03-01
In volumetric-modulated arc therapy (VMAT) treatment delivery perfect beam symmetry is assumed by the planning system. This study aims to test this assumption and present a method of measuring time-resolved beam symmetry measurement during a VMAT delivery that includes extreme variations of dose rate and gantry speed. The Sun Nuclear IC Profiler in gantry mount was used to measure time-resolved in-plane and cross-plane profiles during plan delivery from which symmetry could be determined. Time-resolved symmetry measurements were performed throughout static field exposures at cardinal gantry angles, conformal arcs with constant dose rate and gantry speed, and during a VMAT test plan with gantry speed and dose rate modulation. Measurements were performed for both clockwise and counterclockwise gantry rotation and across four Varian 21iX linacs. The symmetry was found to be generally constant throughout the static field exposures to within 0.3% with an exception on one linac of up to 0.7%. Agreement in symmetry between cardinal angles was always within 1.0% and typically within 0.6%. During conformal arcs the results for clockwise and counterclockwise rotation were in agreement to within 0.3%. Both clockwise and counterclockwise tended to vary in similar manner by up to 0.5% during arc consistent with the cardinal gantry angle static field results. During the VMAT test plan the symmetry generally was in agreement with the conformal arc results. Greater variation in symmetry was observed in the low-dose-rate regions by up to 1.75%. All results were within clinically acceptable levels using the tolerances of NCS Report 24 (2015). PACS number(s): 87.55.Qr.
Time-resolved beam symmetry measurement for VMAT commissioning and quality assurance.
Barnes, Michael P; Greer, Peter B
2016-03-08
In volumetric-modulated arc therapy (VMAT) treatment delivery perfect beam symmetry is assumed by the planning system. This study aims to test this assumption and present a method of measuring time-resolved beam symmetry measurement during a VMAT delivery that includes extreme variations of dose rate and gantry speed. The Sun Nuclear IC Profiler in gantry mount was used to measure time-resolved in-plane and cross-plane profiles during plan delivery from which symmetry could be determined. Time-resolved symmetry measurements were performed throughout static field exposures at cardinal gantry angles, conformal arcs with constant dose rate and gantry speed, and during a VMAT test plan with gantry speed and dose rate modulation. Measurements were performed for both clockwise and counterclockwise gantry rotation and across four Varian 21iX lin-acs. The symmetry was found to be generally constant throughout the static field exposures to within 0.3% with an exception on one linac of up to 0.7%. Agreement in symmetry between cardinal angles was always within 1.0% and typically within 0.6%. During conformal arcs the results for clockwise and counterclockwise rotation were in agreement to within 0.3%. Both clockwise and counterclockwise tended to vary in similar manner by up to 0.5% during arc consistent with the cardinal gantry angle static field results. During the VMAT test plan the symmetry generally was in agreement with the conformal arc results. Greater variation in symmetry was observed in the low-dose-rate regions by up to 1.75%. All results were within clinically acceptable levels using the tolerances of NCS Report 24 (2015).
Symmetry perception in humans and macaques.
Beck, Diane M; Pinsk, Mark A; Kastner, Sabine
2005-09-01
The human ability to detect symmetry has been a topic of interest to psychologists and philosophers since the 19th century, yet surprisingly little is known about the neural basis of symmetry perception. In a recent fMRI study, Sasaki and colleagues begin to remedy this situation. By identifying the neural structures that respond to symmetry in both humans and macaques, the authors lay the groundwork for understanding the neural mechanisms underlying symmetry perception.
Flavored Peccei-Quinn symmetry
NASA Astrophysics Data System (ADS)
Ahn, Y. H.
2015-03-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a μ - τ power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the μ - τ power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma≃2.53 ×1 0-5 eV and the axion coupling to photon ga γ γ≃1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.
Control of spin-orbit torques through crystal symmetry in WTe2/ferromagnet bilayers
NASA Astrophysics Data System (ADS)
MacNeill, D.; Stiehl, G. M.; Guimaraes, M. H. D.; Buhrman, R. A.; Park, J.; Ralph, D. C.
2016-11-01
Recent discoveries regarding current-induced spin-orbit torques produced by heavy-metal/ferromagnet and topological-insulator/ferromagnet bilayers provide the potential for dramatically improved efficiency in the manipulation of magnetic devices. However, in experiments performed to date, spin-orbit torques have an important limitation--the component of torque that can compensate magnetic damping is required by symmetry to lie within the device plane. This means that spin-orbit torques can drive the most current-efficient type of magnetic reversal (antidamping switching) only for magnetic devices with in-plane anisotropy, not the devices with perpendicular magnetic anisotropy that are needed for high-density applications. Here we show experimentally that this state of affairs is not fundamental, but rather one can change the allowed symmetries of spin-orbit torques in spin-source/ferromagnet bilayer devices by using a spin-source material with low crystalline symmetry. We use WTe2, a transition-metal dichalcogenide whose surface crystal structure has only one mirror plane and no two-fold rotational invariance. Consistent with these symmetries, we generate an out-of-plane antidamping torque when current is applied along a low-symmetry axis of WTe2/Permalloy bilayers, but not when current is applied along a high-symmetry axis. Controlling spin-orbit torques by crystal symmetries in multilayer samples provides a new strategy for optimizing future magnetic technologies.
Generalized partial dynamical symmetry in nuclei.
Leviatan, A; Isacker, P Van
2002-11-25
We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.
Noether symmetries and duality transformations in cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Symmetry Breaking for Black-Scholes Equations
NASA Astrophysics Data System (ADS)
Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng
2007-06-01
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
CP symmetry in optical systems
NASA Astrophysics Data System (ADS)
Dana, Brenda; Bahabad, Alon; Malomed, Boris A.
2015-04-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Facial symmetry in robust anthropometrics.
Kalina, Jan
2012-05-01
Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.
Symmetry breaking around a wormhole
NASA Astrophysics Data System (ADS)
Choudhury, A. L.
1996-11-01
We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.
Broken symmetries in multilayered perceptrons
NASA Astrophysics Data System (ADS)
Barkai, E.; Hansel, D.; Sompolinsky, H.
1992-03-01
The statistical mechanics of two-layered perceptrons with N input units, K hidden units, and a single output unit that makes a decision based on a majority rule (Committee Machine) are studied. Two architectures are considered. In the nonoverlapping case the hidden units do not share common inputs. In the fully connected case each hidden unit is connected to the entire input layer. In both cases the network realizes a random dichotomy of P inputs. The statistical properties of the space of solutions as a function of P is studied, using the replica method, and by numerical simulations, in the regime where N>>K. In the nonoverlapping architecture with continuously varying weights the capacity, defined as the maximal number of P per weight, (αc) is calculated under a replica-symmetric (RS) ansatz. At large K, αc diverges as K1/2 in contradiction with the rigorous upper bound, αc
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Rotationally resolved infrared spectroscopy of adamantane
NASA Astrophysics Data System (ADS)
Pirali, O.; Boudon, V.; Oomens, J.; Vervloet, M.
2012-01-01
We present the first rotationally resolved spectra of adamantane (C10H16) applying gas-phase Fourier transform infrared (IR) absorption spectroscopy. High-resolution IR spectra are recorded in the 33-4500 cm-1range using as source of IR radiation both synchrotron radiation (at the AILES beamline of the SOLEIL synchrotron) as well as a classical globar. Adamantane is a spherical top molecule with tetrahedral symmetry (Td point group) and has no permanent dipole moment in its vibronic ground state. Of the 72 fundamental vibrational modes in adamantane, only 11 are IR active. Here we present rotationally resolved spectra for seven of them: ν30, ν28, ν27, ν26, ν25, ν24, and ν23. The typical rotational structure of spherical tops is observed and analyzed using the STDS software developed in the Dijon group, which provides the first accurate energy levels and rotational constants for seven fundamental modes. Rotational levels with quantum numbers as high as J = 107 have been identified and included in the fit leading to a typical standard deviation of about 10-3 cm-1.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Fermion mass without symmetry breaking
NASA Astrophysics Data System (ADS)
Catterall, Simon
2016-01-01
We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan [1]. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.
Explaining quantum spontaneous symmetry breaking
NASA Astrophysics Data System (ADS)
Liu, Chuang; Emch, Gérard G.
Two accounts of quantum symmetry breaking (SSB) in the algebraic approach are compared: the representational and the decompositional account. The latter account is argued to be superior for understanding quantum SSB. Two exactly solvable models are given as applications of our account: the Weiss-Heisenberg model for ferromagnetism and the BCS model for superconductivity. Finally, the decompositional account is shown to be more conducive to the causal explanation of quantum SSB.
Dark matter and global symmetries
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.
2016-09-01
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.
Symmetry analysis of talus bone
Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.
2014-01-01
Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391
NASA Astrophysics Data System (ADS)
Doeff, E.; Misiurewicz, M.
1997-11-01
This paper presents results on rotation numbers for orientation-preserving torus homeomorphisms homotopic to a Dehn twist. Rotation numbers and the rotation set for such homeomorphisms have been defined and initially investigated by the first author in a previous paper. Here we prove that each rotation number 0951-7715/10/6/017/img5 in the interior of the rotation set is realized by some compact invariant set, and that there is an ergodic measure on that set with mean rotation number 0951-7715/10/6/017/img5. It is also proved that the function which assigns its rotation set to such a homeomorphism is continuous. Finally, a counterexample is presented that shows that rational extremal points of the shear rotation set do not necessarily correspond to any periodic orbits.
Power Harvesting from Rotation?
ERIC Educational Resources Information Center
Chicone, Carmen; Feng, Z. C.
2008-01-01
We show the impossibility of harvesting power from rotational motions by devices attached to the rotating object. The presentation is suitable for students who have studied Lagrangian mechanics. (Contains 2 figures.)
... to these tendons may result in: Rotator cuff tendinitis, which is irritation and swelling of these tendons ... Brien MJ, Leggin BG, Williams GR. Rotator cuff tendinopathies and tears: surgery and therapy. In: Skirven TM, ...
NASA Technical Reports Server (NTRS)
Randall, Richard L.
1990-01-01
Signal-processing subsystem generates signal indicative of rotation of shaft from output of accelerometer mounted on housing of bearing supporting shaft. Output of subsystem binary signal at frequency of rotation of shaft. Part of assembly of electronic equipment measuring vibrations in rotating machinery. Accelerometer mounted in such way sensitive to vibrations of shaft perpendicular to axis. Output of accelerometer includes noise and components of vibration at frequencies higher than rotational frequency of shaft.
Rotations with Rodrigues' Vector
ERIC Educational Resources Information Center
Pina, E.
2011-01-01
The rotational dynamics was studied from the point of view of Rodrigues' vector. This vector is defined here by its connection with other forms of parametrization of the rotation matrix. The rotation matrix was expressed in terms of this vector. The angular velocity was computed using the components of Rodrigues' vector as coordinates. It appears…
Generalization of Friedberg-Lee symmetry
NASA Astrophysics Data System (ADS)
Huang, Chao-Shang; Li, Tianjun; Liao, Wei; Zhu, Shou-Hua
2008-07-01
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)×U(1) global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)×U(1) flavor symmetry breaking.
Enhanced Facial Symmetry Assessment in Orthodontists.
Jackson, Tate H; Clark, Kait; Mitroff, Stephen R
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff-orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness.
Symmetry constraints on many-body localization
NASA Astrophysics Data System (ADS)
Potter, Andrew C.; Vasseur, Romain
2016-12-01
We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.
Symmetries in nuclei: New methods and applications
NASA Astrophysics Data System (ADS)
Caprio, Mark A.
2011-04-01
When a symmetry is a ``good'' symmetry of the nuclear system, as in the dynamical symmetries of the shell model and interacting boson model, this symmetry can directly give the spectroscopic properties of the nucleus, without the need for involved calculations. However, even if a symmetry is strongly broken, it nonetheless provides a calculational tool, classifying the basis states used in a full computational treatment of the many-body problem and greatly simplifying the underlying computational machinery. The symmetry then serves as the foundation for a physically meaningful truncation scheme for the calculation. This talk will provide an introduction to new applications of symmetry approaches to the nuclear problem, including the required mathematical developments. Supported by the US DOE under grant DE-FG02-95ER-40934 and by the Research Corporation for Science Advancement under a Cottrell Scholar Award.
Enhanced Facial Symmetry Assessment in Orthodontists
Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342
True and false symmetries in the classification of optical scatterers
NASA Astrophysics Data System (ADS)
Crosta, Giovanni F.; Videen, Gorden
2014-05-01
A plane wave is scattered by a potential of bounded support. Translation, rotation and reflection of the potential, q0 induce transformations of the scattered wave. The latter can be represented by means of Born sequences, where q0 appears under the integral sign: non-local formulas are thus derived, the properties of which are discussed. Next, the symmetries induced by the 1st BORN approximation are addressed. Invariance of the squared modulus of the scattering amplitude holds for translation and reflection. The transformation Tɛ := 13 +Σ3ℓ=1ɛℓAℓ, with {ɛℓ;} real and {Aℓ} the generators of rotations in IR3, is investigated. Conditions on the {ɛ ℓ} are derived, by which the scattering amplitude coming from the first BORN approximation is invariant to Tɛ. As an application, these "false symmetries" are compared to those induced by limited angular resolution of a detector in light scattering experiments. Namely, scattering patterns are made available by the TAOS (Two-dimensional Angle-resolved Optical Scattering) method, which consists of detecting single airborne aerosol particles and collecting the intensity of the light they scatter from a pulsed, monochromatic laser beam. The optics and the detector properties determine the resolution at which a pattern is saved. The implications on the performance of TAOS pattern analysis are briefly discussed.
Optimal fold symmetry of LH2 rings on a photosynthetic membrane
Cleary, Liam; Chen, Hang; Chuang, Chern; Silbey, Robert J.; Cao, Jianshu
2013-01-01
An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order. PMID:23650366
Hücker, M; Zimmermann, M V; Debessai, M; Schilling, J S; Tranquada, J M; Gu, G D
2010-02-05
In those cases where charge-stripe order has been observed in cuprates, the crystal structure is such that the average rotational symmetry of the CuO2 planes is reduced from fourfold to twofold. As a result, one could argue that the reduced lattice symmetry is essential to the existence of stripe order. We use pressure to restore the average fourfold symmetry in a single crystal of La1.875Ba0.125CuO4, and show by x-ray diffraction that charge-stripe order still occurs. Thus, electronically driven stripe order can spontaneously break the lattice symmetry.
NASA Astrophysics Data System (ADS)
Hücker, M.; v. Zimmermann, M.; Debessai, M.; Schilling, J. S.; Tranquada, J. M.; Gu, G. D.
2010-02-01
In those cases where charge-stripe order has been observed in cuprates, the crystal structure is such that the average rotational symmetry of the CuO2 planes is reduced from fourfold to twofold. As a result, one could argue that the reduced lattice symmetry is essential to the existence of stripe order. We use pressure to restore the average fourfold symmetry in a single crystal of La1.875Ba0.125CuO4, and show by x-ray diffraction that charge-stripe order still occurs. Thus, electronically driven stripe order can spontaneously break the lattice symmetry.
Dynamical evolution of comet nucleus rotation
NASA Astrophysics Data System (ADS)
Scheeres, D. J.; Sidorenko, V. V.; Neishtadt, A. I.; Vasiliev, A. A.
2002-09-01
The rotational dynamics of outgassing cometary nuclei are investigated analytically. We develop a general theory for the evolution of a comet nucleus' rotation state using averaging theory and assuming that the outgassing torques are a function of solar insolation and heliocentric distance. The resulting solutions are a function of the nucleus inertia ellipsoid, its outgassing properties, its heliocentric orbit, and the assumed distribution of active regions on its surface. We find that the long-term evolution of the comet nucleus rotation is a strong function of the distribution of active regions over its surface. In particular, we find that nuclei with nearly axisymmetric inertia ellipsoids and a uniformly active surface will tend towards a rotation state that has a nutation angle of ~ 55 degrees and its angular momentum perpendicular to the sun-perihelion direction. If such a comet nucleus has only one isolated active region, it will tend towards a zero nutation angle with its approximate symmetry axis and rotational angular momentum aligned parallel to the sun-perihelion direction. In the general case for an inertia ellipsoid that is not close to being axisymmetric we find a much richer set of possible steady-state solutions that are stable, ranging from rotation about the maximum moment of the inertia axis, to SAM and LAM non-principal axis rotation states. The resulting stable rotation states are a strong function of outgassing activity distribution, which we show using a simplified model of the comet Halley nucleus. Also, we demonstrate that comet Borrely observations are consistent with a stable rotation state. Our results can be used to discriminate between competing theories of comet outgassing based on a nucelus' rotation state. They also allow for a range of plausible a priori constraints to be placed on a comet's rotation state to aid in the interpretation of its outgassing structure. This work was supported by the NASA JURRISS program under Grant NAG5
Symmetry Breaking in the Hidden-Order Phase of URu2Si2
NASA Astrophysics Data System (ADS)
Shibauchi, Takasada
2013-03-01
In the heavy fermion compound URu2Si2, the hidden-order transition occurs at 17.5 K, whose nature has posed a long-standing mystery. A second-order phase transition is characterized by spontaneous symmetry breaking, and thus the nature of the hidden order cannot be determined without understanding which symmetry is being broken. Our magnetic torque measurements in small pure crystals reveal the emergence of an in-plane anisotropy of the magnetic susceptibility below the transition temperature, indicating the spontaneous breaking of four-fold rotational symmetry of the tetragonal URu2Si2. In addition, our recent observation of cyclotron resonance allows the full determination of the electron-mass structure of the main Fermi-surface sheets, which implies an anomalous in-plane mass anisotropy consistent with the rotational symmetry breaking. These results impose strong constraints on the symmetry of the hidden order parameter. This work has been done in collaboration with R. Okazaki, S. Tonegawa, K. Hashimoto, K. Ikada, Y. H. Lin, H. Shishido, H. J. Shi, Y. Haga, T. D. Matsuda, E. Yamamoto, Y. Onuki, H. Ikeda, and Y. Matsuda.
NASA Astrophysics Data System (ADS)
Manolopoulou, M.; Plionis, M.
2017-03-01
We study the possible rotation of cluster galaxies, developing, testing, and applying a novel algorithm which identifies rotation, if such does exist, as well as its rotational centre, its axis orientation, rotational velocity amplitude, and, finally, the clockwise or counterclockwise direction of rotation on the plane of the sky. To validate our algorithms we construct realistic Monte Carlo mock rotating clusters and confirm that our method provides robust indications of rotation. We then apply our methodology on a sample of Abell clusters with z ≲ 0.1 with member galaxies selected from the Sloan Digital Sky Survey DR10 spectroscopic data base. After excluding a number of substructured clusters, which could provide erroneous indications of rotation, and taking into account the expected fraction of misidentified coherent substructure velocities for rotation, provided by our Monte Carlo simulation analysis, we find that ∼23 per cent of our clusters are rotating under a set of strict criteria. Loosening the strictness of the criteria, on the expense of introducing spurious rotation indications, we find this fraction increasing to ∼28 per cent. We correlate our rotation indicators with the cluster dynamical state, provided either by their Bautz-Morgan type or by their X-ray isophotal shape and find for those clusters showing rotation within 1.5 h^{-1}_{70} Mpc that the significance of their rotation is related to the dynamically younger phases of cluster formation but after the initial anisotropic accretion and merging has been completed. Finally, finding rotational modes in galaxy clusters could lead to the necessity of correcting the dynamical cluster mass calculations.
Coffman, R.T.
1957-12-10
A seal is described for a rotatable shaft that must highly effective when the shaft is not rotating but may be less effective while the shaft is rotating. Weights distributed about a sealing disk secured to the shaft press the sealing disk against a tubular section into which the shiilt extends, and whem the shaft rotates, the centrifugal forces on the weights relieve the pressurc of the sealing disk against the tubular section. This action has the very desirible result of minimizing the wear of the rotating disk due to contact with the tubular section, while affording maximum sealing action when it is needed.
Visualizing molecular unidirectional rotation
NASA Astrophysics Data System (ADS)
Lin, Kang; Song, Qiying; Gong, Xiaochun; Ji, Qinying; Pan, Haifeng; Ding, Jingxin; Zeng, Heping; Wu, Jian
2015-07-01
We directly visualize the spatiotemporal evolution of a unidirectional rotating molecular rotational wave packet. Excited by two time-delayed polarization-skewed ultrashort laser pulses, the cigar- or disk-shaped rotational wave packet is impulsively kicked to unidirectionally rotate as a quantum rotor which afterwards disperses and exhibits field-free revivals. The rich dynamics can be coherently controlled by varying the timing or polarization of the excitation laser pulses. The numerical simulations very well reproduce the experimental observations and intuitively revivify the thoroughgoing evolution of the molecular rotational wave packet of unidirectional spin.
Spontaneous rotation in a driven mechanical system
NASA Astrophysics Data System (ADS)
Alexander, T. J.
2016-06-01
We show that a mass free to circulate around a shaken pivot point exhibits resonance-like effects and large amplitude dynamics even though there is no natural frequency in the system, simply through driving under geometrical constraint. We find that synchronization between force and mass occurs over a wide range of forcing amplitudes and frequencies, even when the forcing axis is dynamically, and randomly, changed. Above a critical driving amplitude the mass will spontaneously rotate, with a fractal boundary dividing clockwise and anti-clockwise rotations. We show that this has significant implications for energy harvesting, with large output power over a wide frequency range. We examine also the effect of driving symmetry on the resultant dynamics, and show that if the shaking is circular the motion becomes constrained, whereas for anharmonic rectilinear shaking the dynamics may become chaotic, with the system mimicking that of the kicked rotor.
Stochl, Jan; Croudace, Tim
2013-01-01
Why some humans prefer to rotate clockwise rather than anticlockwise is not well understood. This study aims to identify the predictors of the preferred rotation direction in humans. The variables hypothesised to influence rotation preference include handedness, footedness, sex, brain hemisphere lateralisation, and the Coriolis effect (which results from geospatial location on the Earth). An online questionnaire allowed us to analyse data from 1526 respondents in 97 countries. Factor analysis showed that the direction of rotation should be studied separately for local and global movements. Handedness, footedness, and the item hypothesised to measure brain hemisphere lateralisation are predictors of rotation direction for both global and local movements. Sex is a predictor of the direction of global rotation movements but not local ones, and both sexes tend to rotate clockwise. Geospatial location does not predict the preferred direction of rotation. Our study confirms previous findings concerning the influence of handedness, footedness, and sex on human rotation; our study also provides new insight into the underlying structure of human rotation movements and excludes the Coriolis effect as a predictor of rotation.
NASA Astrophysics Data System (ADS)
Hsu, Jong-Ping
2014-02-01
A generalization of the usual gauge symmetry leads to fourth-order gauge field equations, which imply a new constant force independent of distances. The force associated with the new U1 gauge symmetry is repulsive among baryons. Such a constant force based on baryon charge conservation gives a field-theoretic understanding of the accelerated cosmic expansion in the observable portion of the universe dominated by baryon galaxies. In consistent with all conservation laws and known forces, a simple rotating "dumbbell model" of the universe is briefly discussed.
Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state.
Young, A F; Sanchez-Yamagishi, J D; Hunt, B; Choi, S H; Watanabe, K; Taniguchi, T; Ashoori, R C; Jarillo-Herrero, P
2014-01-23
Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases, which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum. Weakly breaking this symmetry generates a gap on the surface, resulting in charge carriers with finite effective mass and exotic spin textures. Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state. Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems, this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states
Symmetry breaking and wake instabilities
NASA Astrophysics Data System (ADS)
Sengupta, Raja
A numerical technique has been developed in the context of spatio-temporal stability analysis. The convective/absolute nature of instability determines the time-asymptotic response of a linearly unstable flow, either in the form an oscillator or in the form of a noise amplifier. This depends on the location of pinch point singularities of the dispersion relations obtained via linear stability analyses. A new and efficient approach to locate such singularities is presented. Local analyticity of the dispersion relations was exploited via the Cauchy-Riemann equations in a quasi-Newton's root- finding procedure employing numerical Jacobians. Initial guesses provided by temporal stability analyses have been shown to converge to the pinch points even in the presence of multiple saddle points for various Falkner- Skan wedge profiles. This effort was motivated by the phenomenon of spontaneous symmetry breaking in flow over a cone. At large enough incidence, a pair of vortices develop on the leeward side of the cone which eventually become asymmetric as the angle of attack is increased further. A conical, thin-layer Navier-Stokes solver was employed to investigate the effect of flowfield saddles in this process. The approximate factorization scheme incorporated in the solver was shown analytically to be symmetric to eliminate possible sources of asymmetry. Local grid resolution studies were performed to demonstrate the importance of correctly computing the leeside saddle point and the secondary separation and reattchment points. Topological studies of the flow field as it loses symmetry agreed well with previous qualitative experimental observations. However, the original goal of this study, to settle an ongoing controversy regarding the nature of the instability responsible for symmetry breaking, could not be realized due to computational inadequacy. It is conjectured that the process is governed by an absolute instability similar to that observed in a flow over a circular
Duality symmetries and G+++ theories
NASA Astrophysics Data System (ADS)
Riccioni, Fabio; Steele, Duncan; West, Peter
2008-02-01
We show that the nonlinear realizations of all the very extended algebras G+++, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G+++2 and we argue that the nonlinear realization of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G+++ algebra.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Han, Seok Jun; Ghosh, Swapnadip; Abudayyeh, Omar K; Hoard, Brittany R; Culler, Ethan C; Bonilla, Jose E; Han, Sang M; Han, Sang Eon
2016-12-26
We introduce a new approach to systematically break the symmetry in periodic nanostructures on a crystalline silicon surface. Our focus is inverted nanopyramid arrays with a prescribed symmetry. The arrangement and symmetry of nanopyramids are determined by etch mask design and its rotation with respect to the [110] orientation of the Si(001) substrate. This approach eliminates the need for using expensive off-cut silicon wafers. We also make use of low-cost, manufacturable, wet etching steps to fabricate the nanopyramids. Our experiment and computational modeling demonstrate that the symmetry breaking can increase the photovoltaic efficiency in thin-film silicon solar cells. For a 10-micron-thick active layer, the efficiency improves from 27.0 to 27.9% by enhanced light trapping over the broad sunlight spectrum. Our computation further reveals that this improvement would increase from 28.1 to 30.0% in the case of a 20-micron-thick active layer, when the unetched area between nanopyramids is minimized with over-etching. In addition to the immediate benefit to solar photovoltaics, our method of symmetry breaking provides a useful experimental platform to broadly study the effect of symmetry breaking on spectrally tuned light absorption and emission.
Cylindrical rotating triboelectric nanogenerator.
Bai, Peng; Zhu, Guang; Liu, Ying; Chen, Jun; Jing, Qingshen; Yang, Weiqing; Ma, Jusheng; Zhang, Gong; Wang, Zhong Lin
2013-07-23
We demonstrate a cylindrical rotating triboelectric nanogenerator (TENG) based on sliding electrification for harvesting mechanical energy from rotational motion. The rotating TENG is based on a core-shell structure that is made of distinctly different triboelectric materials with alternative strip structures on the surface. The charge transfer is strengthened with the formation of polymer nanoparticles on surfaces. During coaxial rotation, a contact-induced electrification and the relative sliding between the contact surfaces of the core and the shell result in an "in-plane" lateral polarization, which drives the flow of electrons in the external load. A power density of 36.9 W/m(2) (short-circuit current of 90 μA and open-circuit voltage of 410 V) has been achieved by a rotating TENG with 8 strip units at a linear rotational velocity of 1.33 m/s (a rotation rate of 1000 r/min). The output can be further enhanced by integrating more strip units and/or applying larger linear rotational velocity. This rotating TENG can be used as a direct power source to drive small electronics, such as LED bulbs. This study proves the possibility to harvest mechanical energy by TENGs from rotational motion, demonstrating its potential for harvesting the flow energy of air or water for applications such as self-powered environmental sensors and wildlife tracking devices.
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Wave Modes Trapped in Rotating Nonlinear Potentials
NASA Astrophysics Data System (ADS)
Li, Yongyao; Pang, Wei; Malomed, Boris A.
We study modes trapped in a rotating ring with the local strength of the nonlinearity modulated as \\cos (2θ ) , where θ is the azimuthal angle. This modulation pattern may be of three different types: self-focusing (SF), self-defocusing (SDF), and alternating SF-SDF. The model, based on the nonlinear Schrödinger (NLS) equation with periodic boundary conditions, applies to the light propagation in a twisted pipe waveguide, and to a Bose-Einstein condensate (BEC) loaded into a toroidal trap, under the action of the rotating nonlinear pseudopotential induced by means of the Feshbach resonance in an inhomogeneous external field. This is the difference from the recently considered similar setting with the rotating linear potential. In the SF, SDF, and alternating regimes, four, three, and five different types of stable trapped modes are identified, respectively: even, odd, second-harmonic (2H), symmetry-breaking, and 2H-breaking ones. The shapes and stability of these modes, together with transitions between them, are investigated in the first rotational Brillouin zone. Ground-state modes are identified in each regime. Boundaries between symmetric and asymmetric modes are also found in an analytical form, by means of a two-mode approximation.
Symmetry energy of dilute warm nuclear matter.
Natowitz, J B; Röpke, G; Typel, S; Blaschke, D; Bonasera, A; Hagel, K; Klähn, T; Kowalski, S; Qin, L; Shlomo, S; Wada, R; Wolter, H H
2010-05-21
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.
Classification of topological phases with reflection symmetry
NASA Astrophysics Data System (ADS)
Yoshida, Tsuneya; Morimoto, Takahiro; Furusaki, Akira
2015-03-01
In Z2 topological band insulators, the time-reversal symmetry protects their topological structure. In these years such a notion is extended to correlated systems including bosonic systems, and these nontrivial phases are referred to as symmetry protected topological (SPT) phases. Parallel to this progress, a topological crystalline insulator, protected by spatial symmetry, is found for SnTe. Thus, SPT phases protected by this type of symmetry are naturally expected, and classifications of such phases are desired. In this article, we address this issue by focusing on a reflection symmetry. Our analysis based on the Chern-Simons approach proposes periodic tables for bosonic and fermionic SPT phases in two dimensions. Besides that, we show an SPT phase with the reflection symmetry is stabilized in a spin model of honeycomb lattice.
Dynamics-dependent symmetries in Newtonian mechanics
NASA Astrophysics Data System (ADS)
Holland, Peter
2014-01-01
We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines the square roots of the kinetic and potential energies and connects solutions of the same dynamical problem (the potential is an invariant function). The other symmetry connects solutions of different dynamical problems (the potential is a scalar function). The existence of corresponding conserved quantities is examined using Noether's theorem and it is shown that the invariant-potential symmetry is correlated with energy conservation. In the Hamilton-Jacobi picture the invariant-potential transformation provides an example of a ‘field-dependent’ symmetry in point mechanics. It is shown that this transformation is not a symmetry of the Schrödinger equation.
Dynamical symmetries of the Kepler problem
NASA Astrophysics Data System (ADS)
Cariglia, Marco; Silva Araújo, Eduardo
2013-09-01
This paper comes from a first-year undergraduate research project on hidden symmetries of the dynamics for classical Hamiltonian systems. For pedagogical reasons the main subject chosen was Kepler’s problem of motion under a central potential, since it is a completely solved system. It is well known that for this problem the group of dynamical symmetries is strictly larger than the isometry group O(3), the extra symmetries corresponding to hidden symmetries of the dynamics. By taking the point of view of examining the group action of the dynamical symmetries on the allowed trajectories, it is possible to teach the basic elements of many important physics subjects in the same project, including the Hamiltonian formalism, hidden symmetries, integrable systems, group theory and the use of manifolds.
Atomic Tests of Symmetry Principles.
NASA Astrophysics Data System (ADS)
Davies, I. O. G.
Available from UMI in association with The British Library. Requires signed TDF. Parity non-conserving effects in atoms due to the neutral weak current interaction can be enhanced in two ways: by exploiting the Z-dependence and by using a near degeneracy between opposite parity states. In this thesis a case where both enhancements are simultaneously present is considered: samarium has Z = 62 and the states 4f^66s6p ^7G_sp{1} {0} and 4f^66d5d ^7F_1 are only 320 GHz apart. A calculation by Gongora and Sandars (1986) yields a value for R = Im
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.
Lie symmetry analysis of the Heisenberg equation
NASA Astrophysics Data System (ADS)
Zhao, Zhonglong; Han, Bo
2017-04-01
The Lie symmetry analysis is performed on the Heisenberg equation from the statistical physics. Its Lie point symmetries and optimal system of one-dimensional subalgebras are determined. The similarity reductions and invariant solutions are obtained. Using the multipliers, some conservation laws are obtained. We prove that this equation is nonlinearly self-adjoint. The conservation laws associated with symmetries of this equation are constructed by means of Ibragimov's method.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
Dynamical evolution of comet nucleus rotation
NASA Astrophysics Data System (ADS)
Scheeres, D. J.; Sidorenko, V. V.; Neishtadt, A. I.; Vasiliev, A. A.
2001-11-01
The rotational dynamics of outgassing cometary nuclei are investigated analytically using dynamical systems theory. We develop a general theory for the averaged evolution of a comet nucleus rotation state assuming that the nucleus is a spheroid (either prolate or oblate) and that the outgassing torques are a function of solar insolation and heliocentric distance. The resulting solutions are a function of the comet outgassing properties, its heliocentric orbit, and the assumed distribution of active regions on its surface. We find that the long-term evolution of the comet nucleus rotation is a strong function of the distribution of active regions over its surface. Specifically, we find that a comet nucleus with a uniformly active surface will tend towards a rotation state with a nutation angle of ~ 55 degrees and an angular momentum perpendicular to the sun-perihelion direction. Conversely, a comet nucleus with an isolated active region will tend towards a zero nutation angle with its symmetry axis and angular momentum aligned parallel to the sun-perihelion direction. For active surface regions between these extremes we find 4 qualitatively different dynamical outcomes. In all cases, the theory predicts that the comet nucleus angular momentum will have a secular increase, a phenomenon that could contribute to nucleus splitting of active comets. These results can be used to discriminate between competing theories of comet outgassing based on a nucelus' rotation state. They also allow for a range of plausible a priori constraints to be placed on a comet's rotation state to aid in the interpretation of its outgassing structure. This work was supported by the NASA JURRISS program under Grant NAG5-8715. AIN, AAV and VVS acknowledge support from Russian Foundation for Basic research via Grants 00-01-00538 and 00-01-0174 respectively. DJS acknowledges support from the PG&G program via Grant NAG5-9017.
Functional ferroic heterostructures with tunable integral symmetry.
Becher, C; Trassin, M; Lilienblum, M; Nelson, C T; Suresha, S J; Yi, D; Yu, P; Ramesh, R; Fiebig, M; Meier, D
2014-07-02
The relation between symmetry and functionality was pinpointed by Pierre Curie who stated that it is the symmetry breaking that creates physical properties. This fundamental principle is nowadays used for engineering heterostructures whose integral symmetry leads to exotic phenomena such as one-way transparency. For switching devices, however, such symmetry-related functionalities cannot be used because the symmetry in conventional heterostructures is immutable once the material has been synthesized. Here we demonstrate a concept for post-growth symmetry control in PbZr0.2Ti0.8O3 and BiFeO3-based heterostructures. A conducting oxide is sandwiched between two ferroelectric layers, and inversion symmetry is reversibly switched on or off by layer-selective electric-field poling. The generalization of our approach to other materials and symmetries is discussed. We thus establish ferroic trilayer structures as device components with reversibly tunable symmetry and demonstrate their use as light emitters that can be activated and deactivated by applying moderate electric voltages.
Discrete gauge symmetry in continuum theories
Krauss, L.M.; Wilczek, F.
1989-03-13
We point out that local symmetries can masquerade as discrete global symmetries to an observer equipped with only low-energy probes. The existence of the underlying local gauge invariance can, however, result in observable Aharonov-Bohm-type effects. Black holes can therefore carry discrete gauge charges: a form of nonclassical ''hair.'' Neither black-hole evaporation, wormholes, nor anything else can violate discrete gauge symmetries. In supersymmetric unified theories such discrete symmetries can forbid proton-decay amplitudes that might otherwise be catastrophic.
Fake conformal symmetry in unimodular gravity
NASA Astrophysics Data System (ADS)
Oda, Ichiro
2016-08-01
We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.
Nonlinear (super)symmetries and amplitudes
NASA Astrophysics Data System (ADS)
Kallosh, Renata
2017-03-01
There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E 7(7) scalar sector symmetries as well as the fermionic goldstino symmetries.
NASA Technical Reports Server (NTRS)
Kley, Wilhelm; Mathews, William G.
1995-01-01
We describe the evolution of the hot interstellar medium in a large, slowly rotating elliptical galaxy. Although the rotation assumed is a small fraction of the circular velocity, in accordance with recent observations, it is sufficient to have a profound influence on the X-ray emission and cooling geometry of the interstellar gas. The hot gas cools into a disk that extends out to approximately 10 kpc. The cool, dusty disks observed in the majority of elliptical galaxies may arise naturally from internal cooling rather than from mergers with gas-rich companions. As a result of angular momentum conservation in the cooling flow, the soft X-ray isophotes are quite noticeably flatter than those of the stellar image. The gas temperature is higer along the rotation axis. The rotational velocity of the gas several kiloparcsecs above the central disk far exceeds the local stellar rotation and approaches the local circular velocity as it flows toward the galactic core. The detailed appearance of the X-ray image and velocity field of the X-ray gas provide information about the global rotational properties of giant ellipticals at radii too distant for optical observations. The overall pattern of rotation in these galaxies retains information about the origin of ellipticals, particularly of their merging history. In ellipticals having radio jets, if the jets are aligned with the rotation axis of the inner cooling flow, rotation within the jet could be sustained by the rotating environment. Since most large ellipticals have modest rotation, the X-ray observations at low spatial resolution, when interpreted with spherical theoretical models, give the impression that hot gas undergoes localized cooling to very low temperatures many kiloparcsecs from the galactic core. We suggest that such apparent cooling can result in a natural way as gas cools onto a rotating disk.
ERIC Educational Resources Information Center
Graham, John P.
2014-01-01
Symmetry properties of molecules are generally introduced in second-year or third-year-level inorganic or physical chemistry courses. Students generally adapt readily to understanding and applying the operations of rotation (C[subscript n]), reflection (s), and inversion (i). However, the two-step operation of improper rotation-reflection…
NASA Astrophysics Data System (ADS)
Serafin, Michal M.; Peebles, Rebecca A.; Peebles, Sean A.
2008-07-01
The rotational spectrum of the normal isotopic species of the HCF 3-CO 2 weakly bound complex has been measured by Fourier-transform microwave (FTMW) spectroscopy. All transitions are split into A and E states by internal rotation of the trifluoromethane subunit. A global fit of these states gives rotational constants that are consistent with a structure predicted by an MP2/6-311++G(2d,2p) ab initio calculation in which the axes of the monomers are coplanar, with the hydrogen atom of the trifluoromethane angled toward one of the oxygen atoms of the CO 2. Measured dipole moment components ( μa = 0.431(6) D, μb = 0, μc = 1.436(6) D, μtotal = 1.499(6) D) confirm the ab initio prediction of an ac plane of symmetry; however, the very near-prolate nature of the complex ( κ = -0.997), combined with the relatively high barrier to internal rotation (˜30 cm -1) leads to asymmetry splittings and internal rotation splittings of similar magnitude, resulting in the observation of dipole forbidden b-type E-state transitions in addition to the expected a- and c-type lines. Although this effect has been observed previously in several monomer spectra, this appears to be one of few examples for a weakly bound complex.
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
Vortex patterns in moderately rotating Bose-condensed gas
NASA Astrophysics Data System (ADS)
Imran, Mohd; Ahsan, M. A. H.
2017-02-01
Using exact diagonalization, we investigate the many-body ground state for regular vortex patterns in a rotating Bose-condensed gas of N spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The N-body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum L z , to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta 4N≤slant {L}z< 5N for N = 16 bosons. In response to externally impressed rotation, the patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete p-fold rotational symmetry with p = 5 and p = 6 are observed. The hexagonal vortex pattern with p = 6 symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.
Inflation, symmetry, and B-modes
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
2015-05-01
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by envoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with a cosmological constant and a massless scalar carries conformal symmetry. They claim this conformal symmetry is hidden when the action is written in the Einstein frame, and so has not been fully appreciated in the literature. They further claim that such a theory carries another hidden symmetry; a global SO (1 , 1) symmetry. By deforming around the global SO (1 , 1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend to give rise to B-modes with small amplitude. Here we explain that standard Einstein gravity does not in fact possess conformal symmetry. Instead these authors are merely introducing a redundancy into the description, not an actual conformal symmetry. Furthermore, we explain that the only real (global) symmetry in these models is not at all hidden, but is completely manifest when expressed in the Einstein frame; it is in fact the shift symmetry of a scalar field. When analyzed systematically as an effective field theory, deformations do not generally produce asymptotically flat potentials and small B-modes as suggested in these recent papers. Instead, deforming around the shift symmetry systematically, tends to produce models of inflation with B-modes of appreciable amplitude. Such simple models typically
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.
Mirror symmetry for Enriques surfaces
NASA Astrophysics Data System (ADS)
Lakuriqi, Enkeleida
In this thesis, we investigate three separate but related projects. In the first one, we describe the geometric backgrounds of Type II string theory which are given by Enriques surfaces and their mirrors. We also study the effect of various string dualities on such backgrounds, in particular phase change in Gauged Linear Sigma Models and mirror symmetry. In the second project, we investigate special Kahler geometry in order to find canonical coordinates on the moduli of generalised Calabi-Yau spaces and the associated (2, 2) superconformal field theories. In the third project, we develop a general technique for computing the massless spectrum of (0, 2) quantum field theory compactified on a proper stack or an orbifold. We produce general formulas for the contribution of the twisted sectors and compute specific examples of compactifications on gerbes on projective spaces and Calabi-Yau threefolds.
Permutation symmetry for theta functions
Carlson, B.C.
2011-01-21
This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.
Rotation of plasma membrane proteins measured by polarized fluorescence depletion
NASA Astrophysics Data System (ADS)
Barisas, B. George; Rahman, Noorul A.; Yoshida, Thomas M.; Roess, Deborah A.
1990-05-01
We have implemented a new laser microscopic method, polarized fluorescence depletion (PFD), for measuring the rotational dynamics of functional membrane proteins on individual, microscopically selected cells under physiological conditions. This method combines the long lifetimes of triplet-state probes with the sensitivity of fluorescence detection to measure macromolecular rotational correlation times from 10 microsec to > 1 ms. As examples, the rotational correlation time of Fc receptors (FcR) on the surface of 2H3 rat basophilic leukemia cells is 79.9 4.4 microsec at 4°C when labeled with eosin conjugates of IgE. This value is consistent with the known 100 kDa receptor size. When labeled with intact F4 anti-FcR monoclonal antibody, the rotational correlation time for FcER is increased about 2-fold to 170.8 +/- 6.5 microsec, consistent with receptor dimer formation on the plasma membrane and with the ability of this antibody to form FcER dimers on 2H3 cell surfaces. We have also examined the rotational diffusion of the luteinizing hormone receptor on plasma membranes of small ovine luteal cells. Luteinizing hormone receptors (LHR), when occupied by ovine luteinizing hormone (oLH), have a rotational correlation time of 20.5 +/- 0.1 microsec at 4°C. When occupied by human chorionic gonadotropin (hCG), LHR have a rotational correlation time of 46.2 +/- 0.4 microsec suggesting that binding of hCG triggers additional LHR interactions with plasma membrane proteins. Together these studies suggest the utility of PFD measurements in assessing molecular size and molecular association of membrane proteins on individual cells. Relative advantages of time- and frequency-domain implementations of PFD are also discussed.
Formation and local symmetry of the Holstein polaron in the t-J model
NASA Astrophysics Data System (ADS)
Ma, Han; Lee, T. K.; Chen, Yan
2013-04-01
The formation and local symmetry of a spin-lattice polaron has been investigated semiclassically in planar Holstein t-J-like models within the exact diagonalization method. Due to the interplay of strong correlations and electron-lattice interaction, the doped hole may either move freely or lead to the localized spin-lattice distortion and form a Holstein polaron. The formation of a polaron breaks the translational symmetry by suppression of antiferromagnetic correlations and inducement of ferromagnetic correlations locally. Moreover, the breaking of local rotational symmetry around the polaron has been shown. The ground state is generically a parity singlet and the first excited state may be a parity doublet. Further consequences of the density of states spectra for comparison with scanning tunneling microscopy experiments are discussed.
Rare Isotopes and Fundamental Symmetries
NASA Astrophysics Data System (ADS)
Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy
2009-01-01
Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.
Neutrino properties and fundamental symmetries
Bowles, T.J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.
Flavor symmetries and fermion masses
Rasin, Andrija
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V_{ub}/V_{cb} = √m_{u}/m_{c} and V_{td}/V_{ts} = √m_{d}/m_{s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay β → sγ constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tanβ, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Ripple rotation in epitaxial growth of MnAs(1100)
Vidal, F.; Etgens, V. H.; Salles, B. Rache; Eddrief, M.; Fernandes, V.
2011-03-15
Rippled states formation driven by kinetic instability is evidenced in the case of MnAs(1100) hetero- and homoepitaxial growth in a narrow multistable range of growth parameters. The evolution of the surface morphology in this range, comprising slope selection and ripple rotation, maps the kinetic phase diagram recently predicted [A. Levandovsky and L. Golubovic, Phys. Rev. E 76, 041605 (2007)] for growth on rectangular symmetry surfaces, including Ehrlich-Schwoebel instability and effects related to vertical asymmetry.
Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi
2013-08-23
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
Diamagnetism of rotating plasma
Young, W. C.; Hassam, A. B.; Romero-Talamas, C. A.; Ellis, R. F.; Teodorescu, C.
2011-11-15
Diamagnetism and magnetic measurements of a supersonically rotating plasma in a shaped magnetic field demonstrate confinement of plasma pressure along the magnetic field resulting from centrifugal force. The Grad-Shafranov equation of ideal magnetohydrodynamic force balance, including supersonic rotation, is solved to confirm that the predicted angular velocity is in agreement with spectroscopic measurements of the Doppler shifts.
NASA Astrophysics Data System (ADS)
Pochernyaev, V. N.
1993-06-01
Rotating junctions of coaxial-waveguide and waveguide type with a traveling wave coefficient exceeding 0.8 in a wide frequency range are considered. The design of these junctions is based on a method of the theory of electrodynamic circuits. Numerical results are obtained for rotating junctions of partially filled rectangular waveguide type and their particular cases.
The Weighted Oblimin Rotation.
ERIC Educational Resources Information Center
Lorenzo-Seva, Urbano
2000-01-01
Demonstrates that the weighting procedure proposed by E. Cureton and S. Mulaik (1975) can be applied to the Direct Oblimin approach of D. Clarkson and R. Jennrich (1988) to provide good results. The rotation method obtained is called Weighted Oblimin. Compared this method to other rotation methods with favorable results. (SLD)
NASA Technical Reports Server (NTRS)
Le Vine, David
2016-01-01
Faraday rotation is a change in the polarization as signal propagates through the ionosphere. At L-band it is necessary to correct for this change and measurements are made on the spacecraft of the rotation angle. These figures show that there is good agreement between the SMAP measurements (blue) and predictions based on models (red).
Rotatable shear plate interferometer
Duffus, Richard C.
1988-01-01
A rotatable shear plate interferometer comprises a transparent shear plate mounted obliquely in a tubular supporting member at 45.degree. with respect to its horizontal center axis. This tubular supporting member is supported rotatably around its center axis and a collimated laser beam is made incident on the shear plate along this center axis such that defocus in different directions can be easily measured.
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Symmetry is less than meets the eye.
Apthorp, Deborah; Bell, Jason
2015-03-30
Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6].
Symmetry in Critical Random Boolean Networks Dynamics
NASA Astrophysics Data System (ADS)
Bassler, Kevin E.; Hossein, Shabnam
2014-03-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.
Symmetry in critical random Boolean network dynamics
NASA Astrophysics Data System (ADS)
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Order in the Universe: The Symmetry Principle.
ERIC Educational Resources Information Center
Foundation for Integrative Education, Inc., New York, NY.
The first two papers in this booklet provide a review of the pervasiveness of symmetry in nature and art, discussing how symmetry can be traced through every domain open to our understanding, from all aspects of nature to the special provinces of man; the checks and balances of government, the concept of equal justice, and the aesthetic ordering…
Partial dynamical symmetry in a fermion system
Escher; Leviatan
2000-02-28
The relevance of the partial dynamical symmetry concept for an interacting fermion system is demonstrated. Hamiltonians with partial SU(3) symmetry are presented in the framework of the symplectic shell model of nuclei and shown to be closely related to the quadrupole-quadrupole interaction. Implications are discussed for the deformed light nucleus 20Ne.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Continuous point symmetries in group field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2017-03-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on group field theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.
Topological symmetry breaking by quantum wormholes
Mignemi, S.; Moss, I. )
1993-10-15
In multiply connected spacetimes which contain quantum wormholes it may be possible to break gauge symmetries without the usual Higgs fields. In a simple model, symmetry breaking is favored by the quantum effects of Dirac Fermions and leads to vector boson masses related to the wormhole separation.
The role of symmetry in nuclear physics
NASA Astrophysics Data System (ADS)
Iachello, Francesco
2015-02-01
The role of discrete symmetries in nuclear physics is briefly reviewed within the context of the algebraic cluster model (ACM). The symmetries D3 (triangle) for 3α and Td (tetrahedron) for 4α are discussed and evidence shown for their occurrence in 12C (D3) and 16O (Td).
Symmetries in flat space-times
Duncan, D.C.
1989-01-01
In the following flat spacetimes with a high degree of symmetry are studied. The first part completes the classification of all homogeneous flat spacetimes begun by Wolf. The second part explores classification of flat spacetimes with symmetry groups having codimension one orbits. In this case attention is restricted to spacetimes which model a centrally symmetric gravitational field.
A nilpotent symmetry of quantum gauge theories
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
NOTE: Circular symmetry in topologically massive gravity
NASA Astrophysics Data System (ADS)
Deser, S.; Franklin, J.
2010-05-01
We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.
Electroweak symmetry breaking: Top quard condensates
Bardeen, W.A.
1990-12-01
The fundamental mechanisms for the dynamical breaking of the electroweak gauge symmetries remain a mystery. This paper examines the possible role of heavy fermions, particularly the top quark, in generating the observed electroweak symmetry breaking, the masses of the W and Z bosons and the masses of all observed quarks and leptons. 27 refs., 10 figs., 4 tabs.
XU Gong-ou
1985-01-01
In order to preserve all the symmetry properties for the effective collective Hamiltonian obtained with the generator coordinate method, it is necessary for the trial wave function to have proper transformation properties. The generator coordinates should then transform in the same way as the represented collective operators. Also, the center-of-mass motion should be independent of the internal motion in conformity with the invariance of the nuclear Hamiltonian with respect to space rotation and Galilean transformation.
Schluessel, V; Beil, O; Weber, T; Bleckmann, H
2014-09-01
Several species have been shown to perceive symmetry as a measure of superior genetic quality, useful for assessing potential mates or mediating other visual activities such as the selection of food sources. The current study assessed whether Pseudotropheus sp. and Chiloscyllium griseum, two fish species from distantly related groups, possess symmetry perception. In alternative two choice experiments, individuals were tested for spontaneous preferences and trained to discriminate between abstract symmetrical and asymmetrical stimulus pairs. Pair discriminations were followed by extensive categorization experiments. Transfer tests elucidated whether bilaterally symmetrical and rotationally symmetrical stimuli could be distinguished. Sharks were also tested for the degree of dissimilarity between two symbols that could still be detected. While sharks showed both a spontaneous preference for symmetry as well as remarkable discrimination abilities by succeeding in all of the presented tasks, cichlids showed no spontaneous preference, had difficulties in discriminating between symbols and performed poorly in the categorization experiments. Sharks distinguished between bilaterally and rotationally symmetrical stimuli and easily differentiated between a four-armed cross (all arms 90° apart) and a cross where one of the arms was only 45° spaced from the one next to it. Performance did not decline when the separation was extended to 70°, but was significantly reduced at an 80° separation. Results indicate that the ability for symmetry perception varies across fish species and individuals, whereby some can detect even subtle differences in this respect.
Sevec, John B.
1978-01-01
A protective device to provide a warning if a piece of rotating machinery slows or stops comprises a pair of hinged weights disposed to rotate on a rotating shaft of the equipment. When the equipment is rotating, the weights remain in a plane essentially perpendicular to the shaft and constitute part of an electrical circuit that is open. When the shaft slows or stops, the weights are attracted to a pair of concentric electrically conducting disks disposed in a plane perpendicular to the shaft and parallel to the plane of the weights when rotating. A disk magnet attracts the weights to the electrically conducting plates and maintains the electrical contact at the plates to complete an electrical circuit that can then provide an alarm signal.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
NASA Astrophysics Data System (ADS)
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Natural Electroweak Breaking from a Mirror Symmetry
Chacko, Z.; Goh, Hock-Seng; Harnik, Roni
2006-06-16
We present ''twin Higgs models,'' simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.
Bilateral symmetry breaking in nonlinear circular cylinders.
Yuan, Lijun; Lu, Ya Yan
2014-12-01
Symmetry breaking is a common phenomenon in nonlinear systems, it refers to the existence of solutions that do not preserve the original symmetries of the underlying system. In nonlinear optics, symmetry breaking has been previously investigated in a number of systems, usually based on simplified model equations or temporal coupled mode theories. In this paper, we analyze the scattering of an incident plane wave by one or two circular cylinders with a Kerr nonlinearity, and show the existence of solutions that break a lateral reflection symmetry. Although symmetry breaking is a known phenomenon in nonlinear optics, it is the first time that this phenomenon was rigorously studied in simple systems with one or two circular cylinders.
Symmetries in geology and geophysics
Turcotte, Donald L.; Newman, William I.
1996-01-01
Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters. PMID:11607719
On Gauging Symmetry of Modular Categories
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-12-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4}-obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G.; Pegoraro, F.; Ceccherini, F.
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
Seol, J; Lee, S G; Park, B H; Lee, H H; Terzolo, L; Shaing, K C; You, K I; Yun, G S; Kim, C C; Lee, K D; Ko, W H; Kwak, J G; Kim, W C; Oh, Y K; Kim, J Y; Kim, S S; Ida, K
2012-11-09
It is observed that the magnitude of the toroidal rotation speed is reduced by the central electron cyclotron resonance heating (ECRH) regardless of the direction of the toroidal rotation. The magnetohydrodynamics activities generally appear with the rotation change due to ECRH. It is shown that the internal kink mode is induced by the central ECRH and breaks the toroidal symmetry. When the magnetohydrodynamics activities are present, the toroidal plasma viscosity is not negligible. The observed effects of ECRH on the toroidal plasma rotation are explained by the neoclassical toroidal viscosity in this Letter. It is found that the neoclassical toroidal viscosity torque caused by the internal kink mode damps the toroidal rotation.
NASA Astrophysics Data System (ADS)
Penotti, Fabio E.; Cooper, David L.
2015-07-01
We examine the symmetry properties of spin-coupled (or full generalised valence bond) wavefunctions for C2H2 and N2. The symmetry-separated (σ,π) and bent-bond (ω) solutions are totally symmetric only in the D4h and D3h subgroups of D∞h, respectively. Two fairly different strategies are explored for imposing full cylindrical symmetry, with one of them (small nonorthogonal configuration interaction calculations involving rotated versions of the wavefunction) turning out to be somewhat preferable on energetic grounds to the other one (application of additional spin constraints to a single spatial configuration). It is also shown that mixing together the cylindrically symmetric symmetry-separated and bent-bond spin-coupled models leads to relatively small energy improvements unless the valence orbitals in each type of configuration are reoptimised.
Quasi-periodic continuation along a continuous symmetry
NASA Astrophysics Data System (ADS)
Salomone, Matthew David
Given a system of differential equations which admits a continuous group of symmetries and possesses a periodic solution, we show that under certain nondegeneracy assumptions there always exists a continuous family containing infinitely many periodic and quasi-periodic trajectories. This generalizes the continuation method of Poincaré to orbits which are not necessarily periodic. We apply these results in the setting of the Lagrangian N -body problem of homogeneous potential to characterize an infinite family of rotating nonplanar "hip-hop" orbits in the four-body problem of equal masses, and show how some other trajectories in the N -body theory may be extended to infinite families of periodic and quasi-periodic trajectories.
Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition
NASA Astrophysics Data System (ADS)
Baity-Jesi, Marco; Goodrich, Carl P.; Liu, Andrea J.; Nagel, Sidney R.; Sethna, James P.
2017-01-01
We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.
Prospects for Fundamental Symmetry Tests with Polyatomic Molecules
NASA Astrophysics Data System (ADS)
Berger, Robert; Isaev, Timur
2013-06-01
Special features of polyatomic molecules make them attractive candidates for search for violation of fundamental symmetries and variation of fundamental constants [1, 2]. We discuss the possibility of searching for nuclear spin-dependent space-parity violating (NSD-PV) interaction in closed-shell and open-shell polyatomic molecules. The parameter W_{a} of the effective molecular spin-rotational Hamiltonian characterising the strength of NSD-PV interaction in open-shell linear molecules is discussed and approaches for its calculation outlined. In addition, possibilities for detecting NSD-PV in chiral molecules via NMR and MW spectroscopy are presented. REFERENCES: C. Stoeffler et al, Phys. Chem. Chem. Phys., 13 (3), 2011; M. Quack, J. Stohner and M. Willeke, Ann. Rev. Phys. Chem., 59, 2008 J. Bagdonaite et al, Science, 339 (6115), 2013.
Symmetry in chemistry from the hydrogen atom to proteins
Kellman, Michael E.
1996-01-01
The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules. PMID:8962040
Surprises and pitfalls arising from (pseudo)symmetry
Zwart, Peter H.; Grosse-Kunstleve, Ralf W.; Lebedev, Andrey A.; Murshudov, Garib N.; Adams, Paul D.
2008-01-01
The presence of pseudosymmetry can cause problems in structure determination and refinement. The relevant background and representative examples are presented. It is not uncommon for protein crystals to crystallize with more than a single molecule per asymmetric unit. When more than a single molecule is present in the asymmetric unit, various pathological situations such as twinning, modulated crystals and pseudo translational or rotational symmetry can arise. The presence of pseudosymmetry can lead to uncertainties about the correct space group, especially in the presence of twinning. The background to certain common pathologies is presented and a new notation for space groups in unusual settings is introduced. The main concepts are illustrated with several examples from the literature and the Protein Data Bank.
Rotatable seal assembly. [Patent application; rotating targets
Logan, C.M.; Garibaldi, J.L.
1980-11-12
An assembly is provided for rotatably supporting a rotor on a stator so that vacuum chambers in the rotor and stator remain in communication while the chambers are sealed from ambient air, which enables the use of a ball bearing or the like to support most of the weight of the rotor. The apparatus includes a seal device mounted on the rotor to rotate therewith, but shiftable in position on the rotor while being sealed to the rotor as by an O-ring. The seal device has a flat face that is biased towards a flat face on the stator, and pressurized air is pumped between the faces to prevent contact between them while spacing them a small distance apart to avoid the inflow of large amounts of air between the faces and into the vacuum chambers.
NASA Technical Reports Server (NTRS)
Roberts, Glyn O.
1991-01-01
Undesired gravitational effects such as convection or sedimentation in a fluid can sometimes be avoided or decreased by the use of a closed chamber uniformly rotated about a horizontal axis. In a previous study, the spiral orbits of a heavy or buoyant particle in a uniformly rotating fluid were determined. The particles move in circles, and spiral in or out under the combined effects of the centrifugal force and centrifugal buoyancy. A optimization problem for the rotation rate of a cylindrical reactor rotated about its axis and containing distributed particles was formulated and solved. Related studies in several areas are addressed. A computer program based on the analysis was upgraded by correcting some minor errors, adding a sophisticated screen-and-printer graphics capability and other output options, and by improving the automation. The design, performance, and analysis of a series of experiments with monodisperse polystyrene latex microspheres in water were supported to test the theory and its limitations. The theory was amply confirmed at high rotation rates. However, at low rotation rates (1 rpm or less) the assumption of uniform solid-body rotation of the fluid became invalid, and there were increasingly strong secondary motions driven by variations in the mean fluid density due to variations in the particle concentration. In these tests the increase in the mean fluid density due to the particles was of order 0.015 percent. To a first approximation, these flows are driven by the buoyancy in a thin crescent-shaped depleted layer on the descending side of the rotating reactor. This buoyancy distribution is balanced by viscosity near the walls, and by the Coriolis force in the interior. A full analysis is beyond the scope of this study. Secondary flows are likely to be stronger for buoyant particles, which spiral in towards the neutral point near the rotation axis under the influence of their centrifugal buoyancy. This is because the depleted layer is
Micromagnetic investigation of low-symmetry 3D particles
NASA Astrophysics Data System (ADS)
Blachowicz, T.; Ehrmann, A.
2017-02-01
Investigating the anisotropies of magnetic nanoparticles is crucial for further development of magnetic data storage media, MRAM, magnetic logical circuits, or magnetic quantum cellular automata. Former theoretical and experimental examinations have revealed the possibility to gain highly symmetric nanoparticles with increased numbers of magnetic states per storage element. In a recent project, we have investigated low-symmetry T-shaped 2D and 3D particles from iron using the micromagnetic simulation software MAGPAR which is based on solving the Landau-Lifshitz-Gilbert (LLG) equation of motion for a mesh built from tetrahedral finite elements. To examine the influence of the reduced symmetry, simulations were performed on the 3D double-T particle with the field applied in different directions in the x-y base plane, ranging from 0 to 180° in 5° steps. Additionally, the external magnetic field was rotated laterally under different angles with respect to the x-y plane, i.e. 5°, 22.5°, and 45°. Similar simulations were executed for the 2D single-T particle. Our results show the strong impact of the shape anisotropy and the respective possibility to tailor magnetic anisotropies according to the desired behaviour by modifying the nanoparticles’ form.
Macroscopic Behavior of Nematics with D2d Symmetry
NASA Astrophysics Data System (ADS)
Pleiner, Harald; Brand, Helmut R.
2010-03-01
We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is non-polar. While this phase could resemble the classic D∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to non-polar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.
Learning from data to design functional materials without inversion symmetry
Balachandran, Prasanna V.; Young, Joshua; Lookman, Turab; Rondinelli, James M.
2017-01-01
Accelerating the search for functional materials is a challenging problem. Here we develop an informatics-guided ab initio approach to accelerate the design and discovery of noncentrosymmetric materials. The workflow integrates group theory, informatics and density-functional theory to uncover design guidelines for predicting noncentrosymmetric compounds, which we apply to layered Ruddlesden-Popper oxides. Group theory identifies how configurations of oxygen octahedral rotation patterns, ordered cation arrangements and their interplay break inversion symmetry, while informatics tools learn from available data to select candidate compositions that fulfil the group-theoretical postulates. Our key outcome is the identification of 242 compositions after screening ∼3,200 that show potential for noncentrosymmetric structures, a 25-fold increase in the projected number of known noncentrosymmetric Ruddlesden-Popper oxides. We validate our predictions for 19 compounds using phonon calculations, among which 17 have noncentrosymmetric ground states including two potential multiferroics. Our approach enables rational design of materials with targeted crystal symmetries and functionalities. PMID:28211456
Symmetry Breaking in a Model for Nodal Cilia
NASA Astrophysics Data System (ADS)
Brokaw, Charles J.
2005-03-01
Nodal cilia are very short cilia found in the embryonic node on the ventral surface of early mammalian embryos. They create a right to left fluid flow that is responsible for determining the normal asymmetry of the internal organs of the mammalian body. To do this, the distal end of the cilium must circle in a counterclockwise sense. Computer simulations with 3-dimensional models of flagella allow examination of 3-dimensional movements such as those of nodal cilia. 3-dimensional circling motions of short cilia can be achieved with velocity controlled models, in which dynein activity is regulated by sliding velocity. If dyneins on one outer doublet are controlled by the sliding velocity experienced by that doublet, the system is symmetric, and the 3-dimensional models can show either clockwise or counterclockwise circling. My computer simulations have examined two possible symmetry breaking mechanisms: 1) dyneins on doublet N are regulated by a mixture of the sliding velocities experienced by doublets N and N+1 (numbered in a clockwise direction, looking from the base). or 2) symmetry is broken by an off-axis force that produces a right-handed twist of the axoneme, consistent with observations that some dyneins can rotate their substrate microtubules in a clockwise direction.
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
Gungordu, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; ...
2016-02-24
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices withmore » fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. As a result, we find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.« less
Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets
Gungordu, Utkan; Nepal, Rabindra; Tretiakov, Oleg A.; Belashchenko, Kirill; Kovalev, Alexey A.
2016-02-24
Recently there has been substantial interest in realizations of skyrmions, in particular in quasi-two-dimensional (2D) systems due to increased stability resulting from reduced dimensionality. A stable skyrmion, representing the smallest realizable magnetic texture, could be an ideal element for ultradense magnetic memories. Here we use the most general form of the quasi-2D free energy with Dzyaloshinskii-Moriya interactions constructed from general symmetry considerations reflecting the underlying system. We predict that the skyrmion phase is robust and it is present even when the system lacks the in-plane rotational symmetry. In fact, the lowered symmetry leads to increased stability of vortex-antivortex lattices with fourfold symmetry and in-plane spirals, in some instances even in the absence of an external magnetic field. Our results relate different hexagonal and square cell phases to the symmetries of materials used for realizations of skyrmions. This will give clear directions for experimental realizations of hexagonal and square cell phases, and will allow engineering of skyrmions with unusual properties. We also predict striking differences in gyrodynamics induced by spin currents for isolated skyrmions and for crystals where spin currents can be induced by charge carriers or by thermal magnons. As a result, we find that under certain conditions, isolated skyrmions can move along the current without a side motion which can have implications for realizations of magnetic memories.
Laws of conservation as related to brain growth, aging, and evolution: symmetry of the minicolumn.
Casanova, Manuel F; El-Baz, Ayman; Switala, Andrew
2011-01-01
Development, aging, and evolution offer different time scales regarding possible anatomical transformations of the brain. This article expands on the perspective that the cerebral cortex exhibits a modular architecture with invariant properties in regards to these time scales. These properties arise from morphometric relations of the ontogenetic minicolumn as expressed in Noether's first theorem, i.e., that for each continuous symmetry there is a conserved quantity. Whenever minicolumnar symmetry is disturbed by either developmental or aging processes the principle of least action limits the scope of morphometric alterations. Alternatively, local and global divergences from these laws apply to acquired processes when the system is no longer isolated from its environment. The underlying precepts to these physical laws can be expressed in terms of mathematical equations that are conservative of quantity. Invariant properties of the brain include the rotational symmetry of minicolumns, a scaling proportion or "even expansion" between pyramidal cells and core minicolumnar size, and the translation of neuronal elements from the main axis of the minicolumn. It is our belief that a significant portion of the architectural complexity of the cerebral cortex, its response to injury, and its evolutionary transformation, can all be captured by a small set of basic physical laws dictated by the symmetry of minicolumns. The putative preservations of parameters related to the symmetry of the minicolumn suggest that the development and final organization of the cortex follows a deterministic process.
NASA Technical Reports Server (NTRS)
Binzel, R. P.; Green, J. R.; Opal, C. B.
1986-01-01
Thomas et al. (1984) analyzed 14 Voyager 2 images of Saturn's satellite Hyperion and interpreted them to be consistent with a coherent (nonchaotic) rotation period of 13.1 days. This interpretation was criticized by Peale and Wisdom (1984), who argued that the low sampling frequency of Voyager data does not allow chaotic or nonchaotic rotation to be distinguished. New observations obtained with a higher sampling frequency are reported here which conclusively show that the 13.1 day period found by Thomas et al. was not due to coherent rotation.
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Symmetry and range limits in importance indices.
Seifan, Tal; Seifan, Merav
2015-10-01
Recently, Mingo has analyzed the properties of I imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maximum performance of the organism in ideal conditions. Because of this structure, importance indices can hardly ever achieve symmetry along the whole range of potential performances. We discuss the limitation of the symmetry range for different symmetry types and for both additive and multiplicative indices. We conclude that importance indices, as other interactions indices, are practical tools for interpreting ecological outcomes, especially while comparing between studies. Nevertheless, the current structure of importance indices prevents symmetry along their whole range. While the lack of "perfect" symmetry may call for the development of more sophisticated importance metrics, the current indices are still helpful for the understanding of biological systems and should not be discarded before better alternatives are well established. To prevent potential confusion, we suggest that ecologists present the relevant index symmetry range in addition to their results, thus minimizing the probability of misinterpretation.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.
Sufficient symmetry conditions for Topological Quantum Order.
Nussinov, Zohar; Ortiz, Gerardo
2009-10-06
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order.
Symmetries and "simple" solutions of the classical n-body problem
NASA Astrophysics Data System (ADS)
Chenciner, Alain
2006-03-01
The Lagrangian of the classical n-body problem has well known symmetries: isometries of the ambient Euclidean space (translations, rotations, reflexions) and changes of scale coming from the homogeneity of the potential. To these symmetries are associated "simple" solutions of the problem, the so-called homographic motions, which play a basic role in the global understanding of the dynamics. The classical subproblems (planar, isosceles) are also consequences of the existence of symmetries: invariance under reflexion through a plane in the first case, invariance under exchange of two equal masses in the second. In these two cases, the symmetry acts at the level of the "shape space" (the oriented one in the first case) whose existence is the main difference between the 2-body problem and the (n ≥ 3)-body problem. These symmetries of the Lagrangian imply symmetries of the action functional, which is defined on the space of regular enough loops of a given period in the configuration space of the problem. Minimization of the action under well-chosen symmetry constraints leads to remarkable solutions of the n-body problem which may also be called simple and could play after the homographic ones the role of organizing centers in the global dynamics. In [13] and [16], I have given a survey of the new classes of solutions which had been obtained in this way, mainly choreographies of n equal masses in a plane or in space and generalized Hip-Hops of at least 4 arbitrary masses in space. I give here an updated overview of the results and a quick glance at the methods of proofs.
General criteria for determining rotation or oscillation in a two-dimensional axisymmetric system
NASA Astrophysics Data System (ADS)
Koyano, Yuki; Yoshinaga, Natsuhiko; Kitahata, Hiroyuki
2015-07-01
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.
Molecular collisions. 11: Semiclassical approximation to atom-symmetric top rotational excitation
NASA Technical Reports Server (NTRS)
Russell, D.; Curtiss, C. F.
1973-01-01
In a paper of this series a distorted wave approximation to the T matrix for atom-symmetric top scattering was developed which is correct to first order in the part of the interaction potential responsible for transitions in the component of rotational angular momentum along the symmetry axis of the top. A semiclassical expression for this T matrix is derived by assuming large values of orbital and rotational angular momentum quantum numbers.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Exploring Symmetry to Assist Alzheimer's Disease Diagnosis
NASA Astrophysics Data System (ADS)
Illán, I. A.; Górriz, J. M.; Ramírez, J.; Salas-Gonzalez, D.; López, M.; Padilla, P.; Chaves, R.; Segovia, F.; Puntonet, C. G.
Alzheimer's disease (AD) is a progressive neurodegenerative disorder first affecting memory functions and then gradually affecting all cognitive functions with behavioral impairments and eventually causing death. Functional brain imaging as Single-Photon Emission Computed Tomography (SPECT) is commonly used to guide the clinician's diagnosis. The essential left-right symmetry of human brains is shown to play a key role in coding and recognition. In the present work we explore the implications of this symmetry in AD diagnosis, showing that recognition may be enhanced when considering this latent symmetry.
Duality and symmetry lost in solid mechanics
NASA Astrophysics Data System (ADS)
Bui, Huy Duong
2008-01-01
Some conservation laws in Solids and Fracture Mechanics present a lack of symmetry between kinematic and dynamic variables. It is shown that Duality is the right tool to re-establish the symmetry between equations and variables and to provide conservation laws of the pure divergence type which provide true path independent integrals. The loss of symmetry of some energetic expressions is exploited to derive a new method for solving some inverse problems. In particular, the earthquake inverse problem is solved analytically. To cite this article: H.D. Bui, C. R. Mecanique 336 (2008).
Homogeneous sphere packings with triclinic symmetry.
Fischer, W; Koch, E
2002-11-01
All homogeneous sphere packings with triclinic symmetry have been derived by studying the characteristic Wyckoff positions P -1 1a and P -1 2i of the two triclinic lattice complexes. These sphere packings belong to 30 different types. Only one type exists that has exclusively triclinic sphere packings and no higher-symmetry ones. The inherent symmetry of part of the sphere packings is triclinic for 18 types. Sphere packings of all but six of the 30 types may be realized as stackings of parallel planar nets.
NASA Technical Reports Server (NTRS)
Gregory, T. J.
1977-01-01
Apparatus holds remotely piloted arm that accelerates until launching speed is reached. Then vehicle and counterweight at other end of arm are released simultaneously to avoid structural damage from unbalanced rotating forces.
ERIC Educational Resources Information Center
Greenslade, Thomas B., Jr.
1981-01-01
Discusses theory of the rotating mirror, its use in measuring the velocity of the electrical signal in wires, and the velocity of light. Concludes with a description of the manometric flame apparatus developed for analyzing sound waves. (SK)
... cuff are common. They include tendinitis, bursitis, and injuries such as tears. Rotator cuff tendons can become ... cuff depends on age, health, how severe the injury is, and how long you've had the ...
Miller RH III, Azar FM, Throckmorton TW. Shoulder and elbow injuries. In: Canale ST, Beaty JH, eds. ... Krishnan SG. Rotator cuff and impingement lesions. In: Miller MD, Thompson SR, eds. DeLee and Drez's Orthopaedic ...
Rotator cuff repair - slideshow
... presentations/100229.htm Rotator cuff repair - series—Normal anatomy To use the sharing features on this page, ... Bethesda, MD 20894 U.S. Department of Health and Human Services National Institutes of Health Page last updated: ...
Chen, Lixiang; She, Weilong
2008-09-15
We demonstrate that single photons from a rotating q-plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift (RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift deltaomega = Omega((delta)s + deltal) , where s, l and Omega are quantum numbers of spin, orbital angular momentum, and rotating velocity of the q-plate, respectively. Of interest is that the rotational Doppler shift directly reflects the rotational symmetry of q-plates and can be also expressed as deltaomega = (Omega)n , where n = 2(q-1) denotes the fold number of rotational symmetry. Besides, based on this single-photon spin-orbit-RDS entanglement, we propose an experimental scheme to sort photons of different frequency shifts according to individual orbital angular momentum.
Crusher, R H
2000-07-01
Different types of rotator cuff injuries frequently present to Accident and Emergency departments and minor injury units but can be difficult to differentiate clinically. This brief case study describes the examination and diagnosis of related shoulder injuries, specifically rotator cuff tears/disruption and calcifying supraspinatus tendinitis. The relevant anatomy and current therapies for these injuries is also discussed to enable the emergency nurse practitioner to have a greater understanding of the theory surrounding their diagnosis and treatments.
Hunter, Steven L.
2002-01-01
A rate sensor for angular/rotational acceleration includes a housing defining a fluid cavity essentially completely filled with an electrolyte fluid. Within the housing, such as a toroid, ions in the fluid are swept during movement from an excitation electrode toward one of two output electrodes to provide a signal for directional rotation. One or more ground electrodes within the housing serve to neutralize ions, thus preventing any effect at the other output electrode.
Rotational spectrum of phenylglycinol
NASA Astrophysics Data System (ADS)
Simão, Alcides; Peña, Isabel; Cabezas, Carlos; Alonso, José L.
2014-11-01
Solid samples of phenylglycinol were vaporized by laser ablation and investigated through rotational spectroscopy in a supersonic expansion using two different techniques: chirped pulse Fourier transform microwave spectroscopy and narrow band molecular beam Fourier transform microwave spectroscopy. One conformer, bearing an O-H···N and an N-H···π intramolecular hydrogen bonds, could be successfully identified by comparison of the experimental rotational and 14N nuclear quadruple coupling constants with those predicted theoretically.
Whealton, John H.; Tsai, Chin-Chi
2003-05-27
A spark plug device includes a structure for modification of an arc, the modification including arc rotation. The spark plug can be used in a combustion engine to reduce emissions and/or improve fuel economy. A method for operating a spark plug and a combustion engine having the spark plug device includes the step of modifying an arc, the modifying including rotating the arc.
Instability in Rotating Machinery
NASA Technical Reports Server (NTRS)
1985-01-01
The proceedings contain 45 papers on a wide range of subjects including flow generated instabilities in fluid flow machines, cracked shaft detection, case histories of instability phenomena in compressors, turbines, and pumps, vibration control in turbomachinery (including antiswirl techniques), and the simulation and estimation of destabilizing forces in rotating machines. The symposium was held to serve as an update on the understanding and control of rotating machinery instability problems.
Electromagnetic rotational actuation.
Hogan, Alexander Lee
2010-08-01
There are many applications that need a meso-scale rotational actuator. These applications have been left by the wayside because of the lack of actuation at this scale. Sandia National Laboratories has many unique fabrication technologies that could be used to create an electromagnetic actuator at this scale. There are also many designs to be explored. In this internship exploration of the designs and fabrications technologies to find an inexpensive design that can be used for prototyping the electromagnetic rotational actuator.
García-Senz, D.; Cabezón, R. M.; Thielemann, F. K.; Domínguez, I. E-mail: ruben.cabezon@unibas.ch
2016-03-10
Currently the number of models aimed at explaining the phenomena of type Ia supernovae is high and distinguishing between them is a must. In this work we explore the influence of rotation on the evolution of the nuclear flame that drives the explosion in the so-called gravitational confined detonation models. Assuming that the flame starts in a pointlike region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very dependent on the angle between the rotational axis and the line connecting the initial bubble of burned material with the center of the WD at the moment of ignition. The impact of rotation is larger for angles close to 90° because the Coriolis force on a floating element of fluid is maximum and its principal effect is to break the symmetry of the deflagration. Such symmetry breaking weakens the convergence of the nuclear flame at the antipodes of the initial ignition volume, changing the environmental conditions around the convergence region with respect to non-rotating models. These changes seem to disfavor the emergence of a detonation in the compressed volume at the antipodes and may compromise the viability of the so-called gravitational confined detonation mechanism.
NASA Astrophysics Data System (ADS)
García-Senz, D.; Cabezón, R. M.; Domínguez, I.; Thielemann, F. K.
2016-03-01
Currently the number of models aimed at explaining the phenomena of type Ia supernovae is high and distinguishing between them is a must. In this work we explore the influence of rotation on the evolution of the nuclear flame that drives the explosion in the so-called gravitational confined detonation models. Assuming that the flame starts in a pointlike region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very dependent on the angle between the rotational axis and the line connecting the initial bubble of burned material with the center of the WD at the moment of ignition. The impact of rotation is larger for angles close to 90° because the Coriolis force on a floating element of fluid is maximum and its principal effect is to break the symmetry of the deflagration. Such symmetry breaking weakens the convergence of the nuclear flame at the antipodes of the initial ignition volume, changing the environmental conditions around the convergence region with respect to non-rotating models. These changes seem to disfavor the emergence of a detonation in the compressed volume at the antipodes and may compromise the viability of the so-called gravitational confined detonation mechanism.
Symmetry energy III: Isovector skins
NASA Astrophysics Data System (ADS)
Danielewicz, Paweł; Singh, Pardeep; Lee, Jenny
2017-02-01
Isoscalar density is a sum of neutron and proton densities and isovector is a normalized difference. Here, we report the experimental evidence for the displacement of the isovector and isoscalar surfaces in nuclei, by ∼ 0.9 fm from each other. We analyze data on quasielastic (QE) charge exchange (p,n) reactions, concurrently with proton and neutron elastic scattering data for the same target nuclei, following the concepts of the isoscalar and isovector potentials combined into Lane optical potential. The elastic data largely probe the geometry of the isoscalar potential and the (p,n) data largely probe a relation between the geometries of the isovector and isoscalar potentials. The targets include 48Ca, 90Zr, 120Sn and 208Pb and projectile incident energy values span the range of (10-50) MeV. In our fit to elastic and QE charge-exchange data, we allow the values of isoscalar and isovector radii, diffusivities and overall potential normalizations to float away from those in the popular Koning and Delaroche parametrization. We find that the best-fit isovector radii are consistently larger than isoscalar and the best-fit isovector surfaces are steeper. Upon identifying the displacement of the potential surfaces with the displacement of the surfaces for the densities in the Skyrme-Hartree-Fock calculations, and by supplementing the results with those from analyzing excitation energies to isobaric analog states in the past, we arrive at the slope and value of the symmetry energy at normal density of 70 < L < 101 MeV and 33.5 < aaV < 36.4 MeV, respectively.
Symmetry and the Cosmic Microwave Background
NASA Technical Reports Server (NTRS)
Wollock, Edward J.
2012-01-01
A brief historical introduction to the development of observational astronomy and cosmology will be presented. The close relationship between the properties of light, symmetry, and our understanding the contents of our universe will be explored.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
FJRW-Rings and Mirror Symmetry
NASA Astrophysics Data System (ADS)
Krawitz, Marc; Priddis, Nathan; Acosta, Pedro; Bergin, Natalie; Rathnakumara, Himal
2010-05-01
The Landau-Ginzburg Mirror Symmetry Conjecture states that for an invertible quasi-homogeneous singularity W and its maximal group G of diagonal symmetries, there is a dual singularity W T such that the orbifold A-model of W/ G is isomorphic to the B-model of W T . The Landau-Ginzburg A-model is the Frobenius algebra {fancyscript{H}_{W,G}} constructed by Fan, Jarvis, and Ruan, and the B-model is the orbifold Milnor ring of W T . We verify the Landau-Ginzburg Mirror Symmetry Conjecture for Arnol’d’s list of unimodal and bimodal quasi-homogeneous singularities with G the maximal diagonal symmetry group, and include a discussion of eight axioms which facilitate the computation of FJRW-rings.
Spontaneous chiral symmetry breaking in metamaterials.
Liu, Mingkai; Powell, David A; Shadrivov, Ilya V; Lapine, Mikhail; Kivshar, Yuri S
2014-07-18
Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains.
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Noether symmetries and the Swinging Atwood Machine
NASA Astrophysics Data System (ADS)
Moreira, I. C.; Almeida, M. A.
1991-07-01
In this work we apply the Noether theorem with generalised symmetries for discussing the integrability of the Swinging Atwood Machine (SAM) model. We analyse also the limitations of this procedure and compare it with the Yoshida method.
Soliton surfaces in the generalized symmetry approach
NASA Astrophysics Data System (ADS)
Grundland, A. M.
2016-09-01
We investigate some features of generalized symmetries of integrable systems aiming to obtain the Fokas-Gel'fand formula for the immersion of two-dimensional soliton surfaces in Lie algebras. We show that if there exists a common symmetry of the zero-curvature representation of an integrable partial differential equation and its linear spectral problem, then the Fokas-Gel'fand immersion formula is applicable in its original form. In the general case, we show that when the symmetry of the zero-curvature representation is not a symmetry of its linear spectral problem, then the immersion function of the two-dimensional surface is determined by an extended formula involving additional terms in the expression for the tangent vectors. We illustrate these results with examples including the elliptic ordinary differential equation and the C P N-1 sigma-model equation.
Rotating superconductor magnet for producing rotating lobed magnetic field lines
Hilal, Sadek K.; Sampson, William B.; Leonard, Edward F.
1978-01-01
This invention provides a rotating superconductor magnet for producing a rotating lobed magnetic field, comprising a cryostat; a superconducting magnet in the cryostat having a collar for producing a lobed magnetic field having oppositely directed adjacent field lines; rotatable support means for selectively rotating the superconductor magnet; and means for energizing the superconductor magnet.
Vortex formation in a fast rotating Bose-Einstein condensate
Ghosh, Tarun Kanti
2004-04-01
We study rotational motion of an interacting atomic Bose-Einstein condensate confined in a quadratic-plus-quartic potential. We calculate the lowest energy surface mode frequency and show that a symmetric trapped (harmonic and quartic) Bose-Einstein condensate breaks the rotational symmetry of the Hamiltonian when rotational frequency is greater than one-half of the lowest energy surface mode frequency. We argue that the formation of a vortex is not possible in a noninteracting as well as in an attractive Bose-Einstein condensate confined in a harmonic trap due to the absence of the spontaneous shape deformation, but it can occur which leads to the vortex formation if we add an additional quartic potential. Moreover, the spontaneous shape deformation and consequently the formation of a vortex in an attractive system depends on the strengths of the two-body interaction and the quartic potential.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Spontaneously broken spacetime symmetries and Goldstone's theorem.
Low, Ian; Manohar, Aneesh V
2002-03-11
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincaré and conformal invariance.
Noether symmetries in the phase space
NASA Astrophysics Data System (ADS)
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Leptogenesis with Friedberg-Lee Symmetry
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Geng, C. Q.
We consider the µ - τ symmetric Friedberg-Lee (FL) symmetry for the neutrino sector and show that a specific FL translation leads to the tribimaximal mixing pattern of the Maki-Nakagawa-Sakata (MNS) matrix. We also apply the symmetry to the type-I seesaw framework and address the baryon asymmetry of the universe through the leptogenesis mechanism. We try to establish a relation between the net baryon asymmetry and CP phases included in the MNS matrix.
Symmetry breaking of quasihelical stellarator equilibria
Weening, R.H. )
1993-04-01
A mean-field Ohm's law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm's law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.
Density dependence of nuclear symmetry energy
NASA Astrophysics Data System (ADS)
Behera, B.; Routray, T. R.; Tripathy, S. K.
2016-10-01
High density behavior of nuclear symmetry energy is studied on the basis of the stiffest density dependence of asymmetric contribution to energy per nucleon in charge neutral n + p + e + μ matter under beta equilibrium. The density dependence of nuclear symmetry energy obtained in this way is neither very stiff nor soft at high densities and is found to be in conformity with recent observations of neutron stars.
Fluency Expresses Implicit Knowledge of Tonal Symmetry
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
Symmetry calculation for molecules and transition states.
Vandewiele, Nick M; Van de Vijver, Ruben; Van Geem, Kevin M; Reyniers, Marie-Françoise; Marin, Guy B
2015-01-30
The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three-dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label-stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules.
A new paradigm for animal symmetry.
Holló, Gábor
2015-12-06
My aim in this article is to soften certain rigid concepts concerning the radial and bilateral symmetry of the animal body plan, and to offer a more flexible framework of thinking for them, based on recent understandings of how morphogenesis is regulated by the mosaically acting gene regulatory networks. Based on general principles of the genetic regulation of morphogenesis, it can be seen that the difference between the symmetry of the whole body and that of minor anatomical structures is only a question of a diverse timing during development. I propose that the animal genome, as such, is capable of expressing both radial and bilateral symmetries, and deploys them according to the functional requirements which must be satisfied by both the anatomical structure and body as a whole. Although it may seem paradoxical, this flexible view of symmetry, together with the idea that symmetry is strongly determined by function, bolsters the concept that the presence of the two main symmetries in the animal world is not due to chance: they are necessary biological patterns emerging in evolution.
Fluency Expresses Implicit Knowledge of Tonal Symmetry.
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences.
Exploring symmetry in near-vacuum hohlraums
NASA Astrophysics Data System (ADS)
Berzak Hopkins, L.; Le Pape, S.; Divol, L.; Meezan, N.; MacKinnon, A.; Ho, D. D.; Jones, O.; Khan, S.; Ma, T.; Milovich, J.; Pak, A.; Ross, J. S.; Thomas, C.; Turnbull, D.; Amendt, P.; Wilks, S.; Zylstra, A.; Rinderknecht, H.; Sio, H.; Petrasso, R.
2015-11-01
Recent experiments with near-vacuum hohlraums, which utilize a minimal but non-zero helium fill, have demonstrated performance improvements relative to conventional gas-filled (0.96 - 1.6 mg/cc helium) hohlraums: minimal backscatter, reduced capsule drive degradation, and minimal suprathermal electron generation. Because this is a low laser-plasma interaction platform, implosion symmetry is controlled via pulse-shaping adjustments to laser power balance. Extending this platform to high-yield designs with high-density carbon capsules requires achieving adequate symmetry control throughout the pulse. In simulations, laser propagation is degraded suddenly by hohlraum wall expansion interacting with ablated capsule material. Nominal radiation-hydrodynamics simulations have not yet proven predictive on symmetry of the final hotspot, and experiments show more prolate symmetry than preshot calculations. Recent efforts have focused on understanding the discrepancy between simulated and measured symmetry and on alternate designs for symmetry control through varying cone fraction, trade-offs between laser power and energy, and modifications to case-to-capsule ratio. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
Symmetry energy in cold dense matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
A new paradigm for animal symmetry
Holló, Gábor
2015-01-01
My aim in this article is to soften certain rigid concepts concerning the radial and bilateral symmetry of the animal body plan, and to offer a more flexible framework of thinking for them, based on recent understandings of how morphogenesis is regulated by the mosaically acting gene regulatory networks. Based on general principles of the genetic regulation of morphogenesis, it can be seen that the difference between the symmetry of the whole body and that of minor anatomical structures is only a question of a diverse timing during development. I propose that the animal genome, as such, is capable of expressing both radial and bilateral symmetries, and deploys them according to the functional requirements which must be satisfied by both the anatomical structure and body as a whole. Although it may seem paradoxical, this flexible view of symmetry, together with the idea that symmetry is strongly determined by function, bolsters the concept that the presence of the two main symmetries in the animal world is not due to chance: they are necessary biological patterns emerging in evolution. PMID:26640644
Spherical shell model description of rotational motion
NASA Astrophysics Data System (ADS)
Zuker, A. P.; Retamosa, J.; Poves, A.; Caurier, E.
1995-10-01
Exact diagonalizations with a realistic interaction show that configurations with four neutrons in a major shell and four protons in another-or the same-major shell, behave systematically as backbending rotors. The dominance of the q.q component of the interaction is related to an approximate ``quasi-SU3'' symmetry. It is suggested that the onset of rotational motion in the rare earth nuclei is due to the promotion of the eight particle blocks to the major shells above the ones currently filling. Assuming a ``pseudo-SU3'' coupling for the particles in the lower orbits, it is possible to account remarkably well for the observed B(E2) rates at the beginning of the region.
Spontaneous Core Rotation in Ferrofluid Pipe Flow
NASA Astrophysics Data System (ADS)
Krekhov, Alexei; Shliomis, Mark
2017-03-01
Ferrofluid flow along a tube of radius R in a constant axial magnetic field is revisited. Our analytical solution and numerical simulations predict a transition from an initially axial flow to a steady swirling one. The swirl dynamo arises above some critical pressure drop and magnetic field strength. The new flow pattern consists of two phases of different symmetry: The flow in the core resembles Poiseuille flow in a rotating tube of the radius r*
Determination of the rotation of Mercury from satellite gravimetry
NASA Astrophysics Data System (ADS)
Cicalò, S.; Milani, A.
2012-11-01
Space missions can have as a goal the determination of the interior structure of a planet: this is the case for the ESA BepiColombo mission to Mercury. Very precise range and range-rate tracking from the Earth and onboard accelerometry will provide a huge amount of data, from which it will be possible to study the gravity field of Mercury and other parameters of interest. Gravity can be used to constrain the interior structure, but cannot uniquely determine the interior mass distribution. A much stronger constraint on the interior can be given by also determining the rotation state of the planet. If the planet is asymmetric enough, the gravity field as measured by an orbiting probe tracked from the Earth contains signatures from the rotation. Are these enough to solve for the rotation state, to the required accuracy, from tracking data alone, without measurements of the surface? In order to reach some result analytically, a simplified analytical model is developed, and the symmetry breaking, occurring when the shape of the planet deviates from spherical symmetry, is characterized by explicit formulae. Moreover, a full cycle numerical simulation of the Radio Science Experiment is performed, including the generation of simulated tracking and accelerometer data and the determination, by least-squares fit, of the Mercury-centric initial conditions of the probe, of Mercury's gravity field and its rotation state, together with other parameters affecting the dynamics. The conclusion is that there is no reason of principle prohibiting the determination of the rotation from gravimetry, and the sensitivity of the measurements and the coverage are good enough to perform the experiment at the required level of accuracy. This will be important also in ensuring independent terms of comparison for the rotation experiment performed with a high-resolution camera. The mission is currently under development and much care has to be taken in guaranteeing the scientific goals even if
Rapidly rotating superfluid neutron stars in Newtonian dynamics
NASA Astrophysics Data System (ADS)
Yoshida, Shijun; Eriguchi, Yoshiharu
2004-01-01
We develop a formulation for constructing and examining rapidly rotating Newtonian neutron star models that contain two superfluids, taking account of the effect of the rotation velocity difference between two superfluids. We assume neutron stars to be composed of the superfluid neutrons and a mixture of the superfluid protons and the normal fluid electrons. To describe Newtonian dynamics of the two superfluids, the Newtonian version of the so-called two-fluid formalism is employed. The effect of the rotation velocity difference on the structure of equilibrium state is treated as a small perturbation to rapidly rotating superfluid stars whose angular velocities of two superfluids are assumed to be exactly the same. We derive basic equations for the perturbed structures of rapidly rotating superfluid stars due to the rotation velocity difference between two superfluids. Assuming the superfluids to obey a simple analytical equation of state proposed by Prix, Comer and Andersson, we obtain numerical solutions for the perturbations and find that the density distributions of the superfluids are strongly dependent on the parameter σ, which appears in the analytical equation of state and characterizes the so-called symmetry energy. It is also found that if the analytical equation of state of Prix et al. is assumed, the perturbations can be represented in terms of the universal functions that are independent of the parameters of the equation of state.
Optical spatial phase retarder/modulator by a rotating freely suspended LC film
NASA Astrophysics Data System (ADS)
Saghaei, Tayebeh; Feiz, Mohammad-Sadegh; Amjadi, Ahmad
2016-12-01
This study presents a new method to develop a thin controllable retarder/modulator with spatial axial symmetry by rotating a freely suspended of 4-Cyano-4-n-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA) liquid crystal films using mechanical method or as a liquid film motor.
Floppy Molecules with Internal Rotation and Inversion
NASA Astrophysics Data System (ADS)
Kreglewski, Marek
2016-06-01
There are different ways to analyze rovibrational structure of molecules having several large amplitude motions of different type, like internal rotation and inversion or ring-puckering. In my research group we have developed and used methods starting from potential surfaces for large amplitude motions but also applied purely effective Hamiltonians, where tunneling splittings were key parameters. Whatever is the method the following problems must be solved when addressing a rovibrational problem with large amplitude vibrations: 1) a definition of the permutation-inversion molecular symmetry group, 2) a choice of the internal coordinates and their transformation in the symmetry group, 3) derivation of the Hamiltonian in chosen coordinates, 4) calculation of the Hamiltonian matrix elements in a symmetrized basis set. These points will be discussed. The advantage of methods which start from the geometry and potential surface for large amplitude vibrations give much clearer picture of internal dynamics of molecules but generally the fit to experimental data is much poorer. The fitting procedure is strongly non-linear and the iteration procedure much longer. The effective Hamiltonians the fit is generally much better since almost all optimized parameters are linear but the parameters have no clear physical meaning. This method is very useful in the assignment of experimental spectra. Results of the application of both method to methylamine and hydrazine will be presented.
NASA Astrophysics Data System (ADS)
Mitchell, Justin Chadwick
2011-12-01
Using light to probe the structure of matter is as natural as opening our eyes. Modern physics and chemistry have turned this art into a rich science, measuring the delicate interactions possible at the molecular level. Perhaps the most commonly used tool in computational spectroscopy is that of matrix diagonalization. While this is invaluable for calculating everything from molecular structure and energy levels to dipole moments and dynamics, the process of numerical diagonalization is an opaque one. This work applies symmetry and semi-classical techniques to elucidate numerical spectral analysis for high-symmetry molecules. Semi-classical techniques, such as the Potential Energy Surfaces, have long been used to help understand molecular vibronic and rovibronic spectra and dynamics. This investigation focuses on newer semi-classical techniques that apply Rotational Energy Surfaces (RES) to rotational energy level clustering effects in high-symmetry molecules. Such clusters exist in rigid rotor molecules as well as deformable spherical tops. This study begins by using the simplicity of rigid symmetric top molecules to clarify the classical-quantum correspondence of RES semi-classical analysis and then extends it to a more precise and complete theory of modern high-resolution spectra. RES analysis is extended to molecules having more complex and higher rank tensorial rotational and rovibrational Hamiltonians than were possible to understand before. Such molecules are shown to produce an extraordinary range of rotational level clusters, corresponding to a panoply of symmetries ranging from C4v to C2 and C1 (no symmetry) with a corresponding range of new angular momentum localization and J-tunneling effects. Using RES topography analysis and the commutation duality relations between symmetry group operators in the lab-frame to those in the body-frame, it is shown how to better describe and catalog complex splittings found in rotational level clusters. Symmetry
STRUCTURE OF UNIFORMLY ROTATING STARS
Deupree, Robert G.
2011-07-10
Zero-age main-sequence models of uniformly rotating stars have been computed for 10 masses between 1.625 and 8 M{sub sun} and for 21 rotation rates from zero to nearly critical rotation. The surface shape is used to distinguish rotation rather than the surface equatorial velocity or the rotation rate. Using the surface shape is close, but not quite equivalent, to using the ratio of the rotation rate to the critical rotation rate. Using constant shape as the rotation variable means that it and the mass are separable, something that is not true for either the rotation rate or surface equatorial velocity. Thus, a number of properties, including the ratio of the effective temperature anywhere on the surface to the equatorial temperature, are nearly independent of the mass of the model, as long as the rotation rate changes in such a way as to keep the surface shape constant.
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
NASA Technical Reports Server (NTRS)
2000-01-01
During its 1979 flyby, Voyager 2 observed Io only from a distance. However, the volcanic activity discovered by Voyager 1 months earlier was readily visible. This sequence of nine color images was collected using the Blue, Green and Orange filters from about 1.2 million kilometers. A 2.5 hour period is covered during which Io rotates 7 degrees.
Rotating into view over the limb of Io are the plumes of the volcanoes Amirani (top) and Maui (lower). These plumes are very distinct against the black sky because they are being illuminated from behind. Notice that as Io rotates, the proportion of Io which is sunlit decreases greatly. This changing phase angle is because Io is moving between the spacecraft and the Sun.
This time-lapse movie was produced at JPL by the Image Processing Laboratory in 1985.
Rusnak, Brian; Hall, James M.; Shen, Stewart; Wood, Richard L.
2005-01-18
A rotating aperture system includes a low-pressure vacuum pumping stage with apertures for passage of a deuterium beam. A stator assembly includes holes for passage of the beam. The rotor assembly includes a shaft connected to a deuterium gas cell or a crossflow venturi that has a single aperture on each side that together align with holes every rotation. The rotating apertures are synchronized with the firing of the deuterium beam such that the beam fires through a clear aperture and passes into the Xe gas beam stop. Portions of the rotor are lapped into the stator to improve the sealing surfaces, to prevent rapid escape of the deuterium gas from the gas cell.
Chiral rotational spectroscopy
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Götte, Jörg B.; Barnett, Stephen M.
2016-09-01
We introduce chiral rotational spectroscopy, a technique that enables the determination of the orientated optical activity pseudotensor components BX X, BY Y, and BZ Z of chiral molecules, in a manner that reveals the enantiomeric constitution of a sample and provides an incisive signal even for a racemate. Chiral rotational spectroscopy could find particular use in the analysis of molecules that are chiral solely by virtue of their isotopic constitution and molecules with multiple chiral centers. A basic design for a chiral rotational spectrometer together with a model of its functionality is given. Our proposed technique offers the more familiar polarizability components αX X, αY Y, and αZ Z as by-products, which could see it find use even for achiral molecules.
Lattice QCD in rotating frames.
Yamamoto, Arata; Hirono, Yuji
2013-08-23
We formulate lattice QCD in rotating frames to study the physics of QCD matter under rotation. We construct the lattice QCD action with the rotational metric and apply it to the Monte Carlo simulation. As the first application, we calculate the angular momenta of gluons and quarks in the rotating QCD vacuum. This new framework is useful to analyze various rotation-related phenomena in QCD.
Relativistic symmetries in nuclear single-particle spectra
NASA Astrophysics Data System (ADS)
Guo, Jian-You; Liang, Hao Zhao; Meng, Jie; Zhou, Shan-Gui
Symmetry is a fundamental concept in quantum physics. The quasi-degeneracy between single-particle orbitals (n, l, j = l + 1/2) and (n -1, l + 2, j = l + 3/2) indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry. Since the pseudospin symmetry was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry for anti-nucleons, and many new concepts have been introduced. In this Chapter, we will illustrate the schematic picture of spin and pseudospin symmetries, derive the basic formalism, highlight the recent progress from several different aspects, and discuss selected open issues in this topic.
Rotating bubble membrane radiator
Webb, Brent J.; Coomes, Edmund P.
1988-12-06
A heat radiator useful for expelling waste heat from a power generating system aboard a space vehicle is disclosed. Liquid to be cooled is passed to the interior of a rotating bubble membrane radiator, where it is sprayed into the interior of the bubble. Liquid impacting upon the interior surface of the bubble is cooled and the heat radiated from the outer surface of the membrane. Cooled liquid is collected by the action of centrifical force about the equator of the rotating membrane and returned to the power system. Details regarding a complete space power system employing the radiator are given.
Pepper, W.B.
1984-05-09
A rotating parachute for decelerating objects travelling through atmosphere at subsonic or supersonic deployment speeds includes a circular canopy having a plurality of circumferentially arranged flexible panels projecting radially from a solid central disk. A slot extends radially between adjacent panels to the outer periphery of the canopy. Upon deployment, the solid disk diverts air radially to rapidly inflate the panels into a position of maximum diameter. Air impinging on the panels adjacent the panel slots rotates the parachute during its descent. Centrifugal force flattens the canopy into a constant maximum diameter during terminal descent for maximum drag and deceleration.
The effect of femoral component rotation and asymmetry in total knee replacements.
Worland, Richard L; Jessup, Douglas E; Vazquez-Vela Johnson, Gonzalo; Alemparte, Jose Antonio; Tanaka, Sakae; Rex, Francisco Soza; Keenan, Jonathan
2002-10-01
Between April 1999 and February 2000, femoral component rotation and asymmetry (universal versus anatomic) were studied in a prospective randomized control trial in 101 consecutive patients undergoing total knee replacement. Patients were randomly assigned to four groups. The same surgical technique was used in all patients except for femoral component symmetry and rotational alignment. Universal femoral components provide a cheaper and equally reliable solution compared to anatomic compo nents. External rotation of the femoral component or using an anatomic femoral component did not statistically reduce the need for lateral release or improve patellar tracking.
Unconventional pairings and radial line nodes in inversion symmetry broken superconductors
NASA Astrophysics Data System (ADS)
Hakioğlu, T.; Günay, Mehmet
2016-09-01
Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C∞v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C∞v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology.
Turbulent Compressible Convection with Rotation. 2; Mean Flows and Differential Rotation
NASA Technical Reports Server (NTRS)
Brummell, Nicholas H.; Hurlburt, Neal E.; Toomre, Juri
1998-01-01
with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.
Ge, Liang; Jones, S Casey; Sotiropoulos, Fotis; Healy, Timothy M; Yoganathan, Ajit P
2003-10-01
A numerical method is developed for simulating unsteady, 3-D, laminar flow through a bileaflet mechanical heart valve with the leaflets fixed. The method employs a dual-time-stepping artificial-compressibility approach together with overset (Chimera) grids and is second-order accurate in space and time. Calculations are carried out for the full 3-D valve geometry under steady inflow conditions on meshes with a total number of nodes ranging from 4 x 10(5) to 1.6 x 10(6). The computed results show that downstream of the leaflets the flow is dominated by two pairs of counter-rotating vortices, which originate on either side of the central orifice in the aortic sinus and rotate such that the common flow of each pair is directed away from the aortic wall. These vortices intensify with Reynolds number, and at a Reynolds number of approximately 1200 their complex interaction leads to the onset of unsteady flow and the break of symmetry with respect to both geometric planes of symmetry. Our results show the highly 3-D structure of the flow; question the validity of computationally expedient assumptions of flow symmetry; and demonstrate the need for highly resolved, fully 3-D simulations if computational fluid dynamics is to accurately predict the flow in prosthetic mechanical heart valves.
Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics
NASA Astrophysics Data System (ADS)
Ball, Justin; Parra, Felix I.; Barnes, Michael
2016-04-01
A poloidal tilting symmetry of the local nonlinear δ f gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using up-down asymmetry.
ERIC Educational Resources Information Center
Fuchigami, Kei; Schrandt, Matthew; Miessler, Gary L.
2016-01-01
A hands-on symmetry project is proposed as an innovative way of teaching point groups to undergraduate chemistry students. Traditionally, courses teaching symmetry require students to identify the point group of a given object. This project asks the reverse: students are instructed to identify an object that matches each point group. Doing so…
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar γ ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar γ ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar γ ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(ℓ)(L)\\uparrowG. A cluster-(ℓ) has one E(epsilon)-level labeled by G species (epsilon) for each L species (ℓ) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar γ ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar γ ^i-parameters are redundant or zero and directly determine d(ℓ)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and
Effect of rotation on a rotating hot-wire sensor
NASA Technical Reports Server (NTRS)
Hah, C.; Lakshminarayana, B.
1978-01-01
An investigation was conducted to discern the effects of centrifugal and Coriolis forces on a rotating hot-wire. The probe was calibrated in a wind tunnel as well as in a rotating mode. The effect of rotation was found to be negligibly small. A small change in cold resistance (1.5%) was observed in the rotating wire. The rotation seems to have a negligible effect on the fluid mechanics, heat transfer and material characteristics of the wire. This is a significant conclusion in view of the potential application of the hot-wire probe in a rotating passage (such as turbomachinery).
The symmetries of the Carroll superparticle
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric; Gomis, Joaquim; Parra, Lorena
2016-05-01
Motivated by recent applications of Carroll symmetries we investigate, using the method of nonlinear realizations, the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case. In the supersymmetric case we study the dynamics of the { N }=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z = 0. We also discuss in the flat case the extension to { N }=2 supersymmetry and show that the flat { N }=2 superparticle is equivalent to the (non-moving) { N }=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry. In an appendix we discuss the { N }=2 curved case in three-dimensions only and show that there are two { N }=2 theories that are physically different.
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Axisymmetric photonic structures with PT-symmetry
NASA Astrophysics Data System (ADS)
Ahmed, Waqas W.; Herrero, Ramon; Botey, Muriel; Staliunas, Kestutis
2016-09-01
PT-symmetric structures in photonic crystals, combining refractive index and gain-loss modulations is becoming a research field with increasing interest due to the light directionality induced by these particular potentials. Here, we consider PT-symmetric potentials with axial symmetry to direct light to the crystal central point obtaining a localization effect. The axial and PT-symmetric potential intrinsically generates an exceptional central point in the photonic crystal by the merge of both symmetries. This particular point in the crystal lattice causes field amplitude gradients with exponential slopes around the crystal center. The field localization strongly depends on the phase of the central point and on the complex amplitude of the PT-potential. The presented work analyzes in a first stage 1D linear PT-axisymmetric crystals and the role of the central point phase that determines the defect character, i.e. refractive index defect, gain-loss defect or a combination of both. The interplay of the directional light effect induced by the PT-symmetry and the light localization around the central point through the axial symmetry enhances localization and allows higher field concentration for certain phases. The linearity of the studied crystals introduces an exponential growth of the field that mainly depends on the complex amplitude of the potential. The work is completed by the analysis of 2D PT-axisymmetric potentials showing different spatial slopes and growth rates caused by symmetry reasons.
Graph fibrations and symmetries of network dynamics
NASA Astrophysics Data System (ADS)
Nijholt, Eddie; Rink, Bob; Sanders, Jan
2016-11-01
Dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking. A methodology for classifying patterns of synchrony in networks was developed by Golubitsky and Stewart. They showed that the robustly synchronous dynamics of a network is determined by its quotient networks. This result was recently reformulated by DeVille and Lerman, who pointed out that the reduction from a network to a quotient is an example of a graph fibration. The current paper exploits this observation and demonstrates the importance of self-fibrations of network graphs. Self-fibrations give rise to symmetries in the dynamics of a network. We show that every network admits a lift with a semigroup or semigroupoid of self-fibrations. The resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking. Also, when the network has a trivial symmetry groupoid, then every robust synchrony in the lift is determined by symmetry. We finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks.
Seiberg duality versus hidden local symmetry
NASA Astrophysics Data System (ADS)
Abel, Steven; Barnard, James
2012-05-01
It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU( N) SQCD. We deduce the Kähler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the ρ-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter a. Its value continuously interpolates between a = 2 on the baryonic branch of moduli space — corresponding to "vector meson dominance" — and a = 1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further applied to SO and Sp groups, where the usual Seiberg duals are recovered, as well as adjoint SQCD. Finally we discuss some possible future applications, including (naturally) the unitarisation of composite W scattering, blended Higgs/technicolour models, real world QCD and non-supersymmetric dualities.
Exploring the limits of broadband 90° and 180° universal rotation pulses.
Kobzar, Kyryl; Ehni, Sebastian; Skinner, Thomas E; Glaser, Steffen J; Luy, Burkhard
2012-12-01
90° and 180° universal rotation (UR) pulses are two of the most important classes of pulses in modern NMR spectroscopy. This article presents a systematic study characterizing the achievable performance of these pulses as functions of bandwidth, pulse length, and tolerance to B(1)-field inhomogeneity/miscalibration. After an evaluation of different quality factors employed in pulse design algorithms based on optimal control theory, resulting pulses are discussed in detail with a special focus on pulse symmetry. The vast majority of resulting BURBOP (broadband universal rotations by optimal control) pulses are either fully symmetric or have one symmetric and one antisymmetric Cartesian rf component, where the importance of the first symmetry has not been demonstrated yet and the latter one matches the symmetry that results from a previously derived construction principle of universal rotation pulses out of point-to-point pulses [3]. Optimized BURBOP pulses are shown to perform better than previously reported UR pulses, resulting in shorter pulse durations for the same quality of broadband rotations. From a comparison of qualities of effective universal rotations, we find that the application of a single optimal refocusing pulse matches or improves the performance of two consecutive inversion pulses in INEPT-like pulse sequence elements of the same total duration.
Compact rotating cup anemometer
NASA Technical Reports Server (NTRS)
Wellman, J. B.
1968-01-01
Compact, collapsible rotating cup anemometer is used in remote locations where portability and durability are factors in the choice of equipment. This lightweight instrument has a low wind-velocity threshold, is capable of withstanding large mechanical shocks while in its stowed configuration, and has fast response to wind fluctuations.
Rotationally Actuated Prosthetic Hand
NASA Technical Reports Server (NTRS)
Norton, William E.; Belcher, Jewell G., Jr.; Carden, James R.; Vest, Thomas W.
1991-01-01
Prosthetic hand attached to end of remaining part of forearm and to upper arm just above elbow. Pincerlike fingers pushed apart to degree depending on rotation of forearm. Simpler in design, simpler to operate, weighs less, and takes up less space.
ERIC Educational Resources Information Center
Hogg, Loretta A.
1980-01-01
Described is a science classroom program with centralized materials, and assistance and workshops for teachers. Classroom materials on one of five topics rotate every six weeks among five schools. Teachers plan specific units to match the arrival of the materials in their schools. (Author/DS)
Rotational Dynamics with Tracker
ERIC Educational Resources Information Center
Eadkhong, T.; Rajsadorn, R.; Jannual, P.; Danworaphong, S.
2012-01-01
We propose the use of Tracker, freeware for video analysis, to analyse the moment of inertia ("I") of a cylindrical plate. Three experiments are performed to validate the proposed method. The first experiment is dedicated to find the linear coefficient of rotational friction ("b") for our system. By omitting the effect of such friction, we derive…
Technology Transfer Automated Retrieval System (TEKTRAN)
Crop rotations have been a part of civilization since the Middle Ages. With colonization of what would become the United States came new crops of tobacco, cotton, and corn, the first two of which would play significant roles in both the economic beginnings and social fabric of the new country, how ...
NASA Astrophysics Data System (ADS)
Povall, Timothy; McBride, Andrew; Govender, Indresan
2015-11-01
An anisotropic relationship between the stress and the strain rate has been observed in two-dimensional simulations of rotating drums. The objective of this work is to investigate the structure of the constitutive relation using three-dimensional discrete-element-method simulations of a rotating drum containing identical rigid spheres for a range of rotational speeds. Anisotropy is quantified from the alignment of the stress and strain rate tensors, with the strain rate computed using a least-squares fit. It is shown that in certain regions there is a strong anisotropic relationship, regardless of the speed of rotation. The effective friction coefficient is examined in order to determine the phase space in which the μ (I) rheology is valid. Lastly, a depth-averaged approach through the flowing layer is employed to determine the relationship between the velocity tangential to the equilibrium surface and the height of the flowing layer. A power-law relationship that approaches linear at high speeds is observed. Supported by NRF/DST Scarce Skills (South Africa).
ERIC Educational Resources Information Center
Rueckner, Wolfgang; And Others
1995-01-01
Describes a demonstration in which a ball is placed in an unstable position on a saddle shape. The ball becomes stable when it is rotated above some threshold angular velocity. The demonstration is a mechanical analog of confining a particle in a "Paul Trap". (DDR)
Deveney, Joseph E.; Sanderson, Stephen N.
1984-01-01
A valve stem and lock include a housing surrounding a valve stem, a solenoid affixed to an interior wall of the housing, an armature affixed to the valve stem and a locking device for coupling the armature to the housing body. When the solenoid is energized, the solenoid moves away from the housing body, permitting rotation of the valve stem.
Deveney, J.E.; Sanderson, S.N.
1981-10-27
A valve stem and lock is disclosed which includes a housing surrounding a valve stem, a solenoid affixed to an interior wall of the housing, an armature affixed to the valve stem and a locking device for coupling the armature to the housing body. When the solenoid is energized, the solenoid moves away from the housing body, permitting rotation of the valve stem.
ERIC Educational Resources Information Center
Connors, G. Patrick
Many baseball players suffer from shoulder injuries related to the rotator cuff muscles. These injuries may be classified as muscular strain, tendonitis or tenosynovitis, and impingement syndrome. Treatment varies from simple rest to surgery, so it is important to be seen by a physician as soon as possible. In order to prevent these injuries, the…
NASA Astrophysics Data System (ADS)
Pravec, Petr; Harris, A. W.; Warner, B. D.
2007-05-01
Of nearly 3900 near-Earth asteroids known in June 2006, 325 have got estimated rotation periods. NEAs with sizes down to 10 meters have been sampled. Observed spin distribution shows a major changing point around D=200 m. Larger NEAs show a barrier against spin rates >11 d-1 (period P~2.2 h) that shifts to slower rates with increasing equatorial elongation. The spin barrier is interpreted as a critical spin rate for bodies held together by self-gravitation only, suggesting that NEAs larger than 200 m are mostly strenghtless bodies (i.e., with zero tensile strength), so called `rubble piles'. The barrier disappears at D<200 m where most objects rotate too fast to be held together by self-gravitation only, so a non-zero cohesion is implied in the smaller NEAs. The distribution of NEA spin rates in the `rubble pile' range (D>0.2 km) is non-Maxwellian, suggesting that other mechanisms than just collisions worked there. There is a pile up in front of the barrier (P of 2-3 h). It may be related to a spin up mechanism crowding asteroids to the barrier. An excess of slow rotators is seen at P>30 h. The spin-down mechanism has no clear lower limit on spin rate; periods as long as tens of days occur. Most NEAs appear to be in basic spin states with rotation around the principal axis. Excited rotations are present among and actually dominate in slow rotators with damping timescales >4.5 byr. A few tumblers observed among fast rotating coherent objects consistently appear to be more rigid or younger than the larger, rubble-pile tumblers. An abundant population of binary systems among NEAs has been found. The fraction of binaries among NEAs larger than 0.3 km has been estimated to be 15 +/-4%. Primaries of the binary systems concentrate at fast spin rates (periods 2-3 h) and low amplitudes, i.e., they lie just below the spin barrier. The total angular momentum content in the binary systems suggests that they formed at the critical spin rate, and that little or no angular
Direct terrestrial test of Lorentz symmetry in electrodynamics to 10−18
Nagel, Moritz; Parker, Stephen R.; Kovalchuk, Evgeny V.; Stanwix, Paul L.; Hartnett, John G.; Ivanov, Eugene N.; Peters, Achim; Tobar, Michael E.
2015-01-01
Lorentz symmetry is a foundational property of modern physics, underlying the standard model of particles and general relativity. It is anticipated that these two theories are low-energy approximations of a single theory that is unified and consistent at the Planck scale. Many unifying proposals allow Lorentz symmetry to be broken, with observable effects appearing at Planck-suppressed levels; thus, precision tests of Lorentz invariance are needed to assess and guide theoretical efforts. Here we use ultrastable oscillator frequency sources to perform a modern Michelson–Morley experiment and make the most precise direct terrestrial test to date of Lorentz symmetry for the photon, constraining Lorentz violating orientation-dependent relative frequency changes Δν/ν to 9.2±10.7 × 10−19 (95% confidence interval). This order of magnitude improvement over previous Michelson–Morley experiments allows us to set comprehensive simultaneous bounds on nine boost and rotation anisotropies of the speed of light, finding no significant violations of Lorentz symmetry. PMID:26323989