Discrete minimal flavor violation
Zwicky, Roman; Fischbacher, Thomas
2009-10-01
We investigate the consequences of replacing the global flavor symmetry of minimal flavor violation (MFV) SU(3){sub Q}xSU(3){sub U}xSU(3){sub D}x{center_dot}{center_dot}{center_dot} by a discrete D{sub Q}xD{sub U}xD{sub D}x{center_dot}{center_dot}{center_dot} symmetry. Goldstone bosons resulting from the breaking of the flavor symmetry generically lead to bounds on new flavor structure many orders of magnitude above the TeV scale. The absence of Goldstone bosons for discrete symmetries constitute the primary motivation of our work. Less symmetry implies further invariants and renders the mass-flavor basis transformation observable in principle and calls for a hierarchy in the Yukawa matrix expansion. We show, through the dimension of the representations, that the (discrete) symmetry in principle does allow for additional {delta}F=2 operators. If though the {delta}F=2 transitions are generated by two subsequent {delta}F=1 processes, as, for example, in the standard model, then the four crystal-like groups {sigma}(168){approx_equal}PSL(2,F{sub 7}), {sigma}(72{phi}), {sigma}(216{phi}) and especially {sigma}(360{phi}) do provide enough protection for a TeV-scale discrete MFV scenario. Models where this is not the case have to be investigated case by case. Interestingly {sigma}(216{phi}) has a (nonfaithful) representation corresponding to an A{sub 4} symmetry. Moreover we argue that the, apparently often omitted, (D) groups are subgroups of an appropriate {delta}(6g{sup 2}). We would like to stress that we do not provide an actual model that realizes the MFV scenario nor any other theory of flavor.
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.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
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.
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.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Neutrino mass and mixing with discrete symmetry.
King, Stephen F; Luhn, Christoph
2013-05-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A₄, S₄ and Δ(96).
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Superheavy dark matter with discrete gauge symmetries
NASA Astrophysics Data System (ADS)
Hamaguchi, K.; Nomura, Yasunori; Yanagida, T.
1998-11-01
We show that there are discrete gauge symmetries which naturally protect heavy X particles from decaying into ordinary light particles in the supersymmetric standard model. This makes the proposal that superheavy X particles constitute part of the dark matter in the present universe very attractive. It is more interesting that there is a class of discrete gauge symmetries which naturally accommodates a long-lived unstable X particle. We find that in some discrete Z10 models, for example, a superheavy X particle has a lifetime of τX~=1011-1026 yr for a mass of MX~=1013-1014 GeV. This long lifetime is guaranteed by the absence of lower dimensional operators (of light particles) coupled to the X. We briefly discuss a possible explanation for the recently observed ultrahigh-energy cosmic ray events by the decay of this unstable X particle.
Long lived superheavy dark matter with discrete gauge symmetries
NASA Astrophysics Data System (ADS)
Hamaguchi, K.; Nomura, Yasunori; Yanagida, T.
1999-03-01
The recently observed ultrahigh energy (UHE) cosmic rays beyond the Greisen-Zatsepin-Kuzmin bound can be explained by the decays of some superheavy X particles forming a part of dark matter in our universe. We consider various discrete gauge symmetries ZN to ensure the required long lifetime (τX~=1010-1022 yr) of the X particle to explain the UHE cosmic rays in the minimal supersymmetric standard model (MSSM) with massive Majorana neutrinos. We show that there is no anomaly-free discrete gauge symmetry to make the lifetime of the X particle sufficiently long in the MSSM with the X particle. We find, however, possible solutions to this problem especially by enlarging the particle contents in the MSSM. We show a number of solutions introducing an extra pair of singlets Y and Y¯ which have fractional ZN(N=2,3) charges. The present experimental constraints on the X particle are briefly discussed.
Spontaneous Breaking of Lie Groups to Discrete Symmetries
NASA Astrophysics Data System (ADS)
Rachlin, Bradley; Kephart, Thomas
2017-01-01
Many models of beyond Standard Model physics connect flavor symmetry with a discrete group. Having this symmetry arise spontaneously from a gauge theory maintains compatibility with quantum gravity and prevents anomalies. We detail ways to set up Higgs potentials to break gauge groups to discrete symmetries of interest. The scalar mass spectra are examined. Research Assistantship funded by Department of Energy (DOE).
Minimal but non-minimal inflation and electroweak symmetry breaking
Marzola, Luca; Racioppi, Antonio
2016-10-07
We consider the most minimal scale invariant extension of the standard model that allows for successful radiative electroweak symmetry breaking and inflation. The framework involves an extra scalar singlet, that plays the rôle of the inflaton, and is compatibile with current experimental bounds owing to the non-minimal coupling of the latter to gravity. This inflationary scenario predicts a very low tensor-to-scalar ratio r≈10{sup −3}, typical of Higgs-inflation models, but in contrast yields a scalar spectral index n{sub s}≃0.97 which departs from the Starobinsky limit. We briefly discuss the collider phenomenology of the framework.
Cosmology of biased discrete symmetry breaking
NASA Technical Reports Server (NTRS)
Gelmini, Graciela B.; Gleiser, Marcelo; Kolb, Edward W.
1988-01-01
The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.
Nonlocal symmetries, spectral parameter and minimal surfaces in AdS/CFT
NASA Astrophysics Data System (ADS)
Klose, Thomas; Loebbert, Florian; Münkler, Hagen
2017-03-01
We give a general account of nonlocal symmetries in symmetric space models and their relation to the AdS/CFT correspondence. In particular, we study a master symmetry which generates the spectral parameter and acts as a level-raising operator on the classical Yangian generators. The master symmetry extends to an infinite tower of symmetries with nonlocal Casimir elements as associated conserved charges. We discuss the algebraic properties of these symmetries and establish their role in explaining the recently observed one-parameter deformation of holographic Wilson loops. Finally, we provide a numerical framework, in which discretized minimal surfaces and their master symmetry deformation can be calculated.
Symmetry induced compression of discrete phase space
NASA Astrophysics Data System (ADS)
Krawczyk, Małgorzata J.
2011-06-01
A compressed representation is described of the state space of discrete systems with some kind of symmetry of its states. An initial state space is represented as a network of states. Two states are linked if some single process leads from one state to another. The network can be compressed by a grouping of states into classes. States in the same class are represented by nodes of equal degree. Further, subclasses are defined: states belong to the same subclass if their neighbouring states belong to the same subclasses. The goal is that the equilibrium probability distribution of states in the initial network can be found from the probability of subclasses in the compressed network. The approach is applied to three exemplary systems: two pieces of a triangular lattice (25 and 36 nodes) with Ising spins at the lattice nodes, and a roundabout with three access roads and three exit roads. The compression is from 3630 ground states to 12 subclasses, from 263 640 ground states to 409 subclasses, and from 729 states to 55 subclasses, respectively.
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.
Anomalous discrete symmetries in three dimensions and group cohomology.
Kapustin, Anton; Thorngren, Ryan
2014-06-13
We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G(1) × G(2) such that gauging G(1) necessarily breaks G(2) and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.
On discrete symmetries for a whole Abelian model
Chauca, J.; Doria, R.
2012-09-24
Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {l_brace}D{sub {mu}},X{sup i}{sub {mu}}{r_brace} and the physical basis {l_brace}G{sub {mu}I}{r_brace}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws driven for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {l_brace}G{sub {mu}I}{r_brace} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.
PREFACE: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Mavromatos, Nick E.; Mitsou, Vasiliki A.; Skliros, Dimitri P.
2015-07-01
The DISCRETE 2014: Fourth Symposium in the Physics of Discrete Symmetries took place at King's College London, Strand Campus, London WC2R 2LS, from Tuesday, December 2 2014 till Saturday, December 6 2014. This is the fourth Edition of the DISCRETE conference series, which is a biannual event, having been held previously in Valencia (Discrete'08), Rome (Discrete2010) and Lisbon (Discrete2012). The topics covered at the DISCRETE series of conferences are: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence and entangled states, Lorentz symmetry breaking (phenomenology and current bounds); neutrino mass and mixing; implications for cosmology and astroparticle physics, dark matter searches; experimental prospects at LHC, new facilities. In DISCRETE 2014 we have also introduced two new topics: cosmological aspects of non-commutative space-times as well as PT symmetric Hamiltonians (non-Hermitian but with real eigenvalues), a topic that has wide applications in particle physics and beyond. The conference was opened by the King's College London Vice Principal on Research and Innovation, Mr Chris Mottershead, followed by a welcome address by the Chair of DISCRETE 2014 (Professor Nick E. Mavromatos). After these introductory talks, the scientific programme of the DISCRETE 2014 symposium started. Following the tradition of DISCRETE series of conferences, the talks (138 in total) were divided into plenary-review talks (25), invited research talks (50) and shorter presentations (63) — selected by the conveners of each session in consultation with the organisers — from the submitted abstracts. We have been fortunate to have very high-quality, thought stimulating and interesting talks at all levels, which, together with the discussions among the participants, made the conference quite enjoyable. There were 152 registered participants for the event.
NASA Astrophysics Data System (ADS)
Luo, Lin
2017-02-01
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation, the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory. Supported by the National Science Foundation of China under Grant No. 11371244 and the Applied Mathematical Subject of SSPU under Grant No. XXKPY1604
Self-assembled fibre optoelectronics with discrete translational symmetry
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel
2016-01-01
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout. PMID:27698454
Self-assembled fibre optoelectronics with discrete translational symmetry.
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F; Joannopoulos, John; Fink, Yoel
2016-10-04
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ∼10(4) self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.
Self-assembled fibre optoelectronics with discrete translational symmetry
NASA Astrophysics Data System (ADS)
Rein, Michael; Levy, Etgar; Gumennik, Alexander; Abouraddy, Ayman F.; Joannopoulos, John; Fink, Yoel
2016-10-01
Fibres with electronic and photonic properties are essential building blocks for functional fabrics with system level attributes. The scalability of thermal fibre drawing approach offers access to large device quantities, while constraining the devices to be translational symmetric. Lifting this symmetry to create discrete devices in fibres will increase their utility. Here, we draw, from a macroscopic preform, fibres that have three parallel internal non-contacting continuous domains; a semiconducting glass between two conductors. We then heat the fibre and generate a capillary fluid instability, resulting in the selective transformation of the cylindrical semiconducting domain into discrete spheres while keeping the conductive domains unchanged. The cylindrical-to-spherical expansion bridges the continuous conducting domains to create ~104 self-assembled, electrically contacted and entirely packaged discrete spherical devices per metre of fibre. The photodetection and Mie resonance dependent response are measured by illuminating the fibre while connecting its ends to an electrical readout.
Generalized gaugino condensation in super Yang-Mills theories: Discrete R symmetries and vacua
NASA Astrophysics Data System (ADS)
Kehayias, John
2010-12-01
One can define generalized models of gaugino condensation as theories that dynamically break a discrete R symmetry but do not break supersymmetry. We consider general examples consisting of gauge and matter fields and the minimal number of gauge-singlet fields to avoid flat directions in the potential. We explore which R symmetries can arise and their spontaneous breaking. In general, we find that the discrete symmetry is Z2b0R, and the number of supersymmetric vacua is b0, where b0 is the coefficient of the one-loop beta function. Results are presented for various groups, including SU(Nc), SO(Nc), Sp(2Nc), and G2, for various numbers of flavors, Nf, by several methods. This analysis can also apply to the other exceptional groups and, thus, all simple Lie groups. We also comment on model-building applications where a discrete R symmetry, broken by the singlet vacuum expectation values, can account for μ-type terms and allow a realistic Higgs spectrum naturally.
Families of Quintic Calabi Yau 3 Folds with Discrete Symmetries
NASA Astrophysics Data System (ADS)
Doran, Charles; Greene, Brian; Judes, Simon
2008-06-01
At special loci in their moduli spaces, Calabi Yau manifolds are endowed with discrete symmetries. Over the years, such spaces have been intensely studied and have found a variety of important applications. As string compactifications they are phenomenologically favored, and considerably simplify many important calculations. Mathematically, they provided the framework for the first construction of mirror manifolds, and the resulting rational curve counts. Thus, it is of significant interest to investigate such manifolds further. In this paper, we consider several unexplored loci within familiar families of Calabi Yau hypersurfaces that have large but unexpected discrete symmetry groups. By deriving, correcting, and generalizing a technique similar to that of Candelas, de la Ossa and Rodriguez Villegas, we find a calculationally tractable means of finding the Picard Fuchs equations satisfied by the periods of all 3 forms in these families. To provide a modest point of comparison, we then briefly investigate the relation between the size of the symmetry group along these loci and the number of nonzero Yukawa couplings. We include an introductory exposition of the mathematics involved, intended to be accessible to physicists, in order to make the discussion self contained.
The Friedberg-Lee symmetry and minimal seesaw model
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Liao, Wei
2009-11-01
The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field q to q + ξz. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N - 1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.
Breaking discrete symmetries in the effective field theory of inflation
Cannone, Dario; Gong, Jinn-Ouk; Tasinato, Gianmassimo
2015-08-03
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.
Breaking discrete symmetries in the effective field theory of inflation
Cannone, Dario; Gong, Jinn-Ouk; Tasinato, Gianmassimo E-mail: jinn-ouk.gong@apctp.org
2015-08-01
We study the phenomenon of discrete symmetry breaking during the inflationary epoch, using a model-independent approach based on the effective field theory of inflation. We work in a context where both time reparameterization symmetry and spatial diffeomorphism invariance can be broken during inflation. We determine the leading derivative operators in the quadratic action for fluctuations that break parity and time-reversal. Within suitable approximations, we study their consequences for the dynamics of linearized fluctuations. Both in the scalar and tensor sectors, we show that such operators can lead to new direction-dependent phases for the modes involved. They do not affect the power spectra, but can have consequences for higher correlation functions. Moreover, a small quadrupole contribution to the sound speed can be generated.
Proton Stability in Grand Unified Theories and Discrete Gauge Symmetries
Mohapatra, R. N.
2008-05-13
Most supersymmetric grand unified theories face the problem of rapid proton decay coming either from R-parity violating interactions and/or from Planck scale induced R-parity conserving operators, possibly induced by non-perturbative Planck scale effects such as black holes or wormholes. In this talk, I argue in favor of the possibility that a natural way to resolve this problem is to assume that there are new discrete or continuous gauge symmetries accompanying these theories that resolve these problems while at the same time allowing enough flexibility to have a viable model. I discuss this for left-right and SO(10) theories and discuss the profound impact such considerations have on the construction of realistic GUT models. I then discuss a recently proposed SO(10) model which has only apparently string inspired multiplets and has enough structure to be a realistic model.
PREFACE: DISCRETE '08: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Bernabéu, José; Botella, Francisco J.; Mavromatos, Nick E.; Mitsou, Vasiliki A.
2009-07-01
The Symposium DISCRETE'08 on Prospects in the Physics of Discrete Symmetries was held at the Instituto de Física Corpuscular (IFIC) in Valencia, Spain from 11 to 16 December 2008. IFIC is a joint centre of the Consejo Superior de Investigaciones Científicas (CSIC) and the Universitat de València (UVEG). The aim of the Symposium was to bring together experts on the field of Discrete Symmetries in order to discuss its prospects on the eve of the LHC era. The general state of the art for CP, T and CPT symmetries was reviewed and their interplay with Baryogenesis, Early Cosmology, Quantum Gravity, String Theory and the Dark Sector of the Universe was emphasised. Connections with physics beyond the Standard Model, in particular Supersymmetry, were investigated. Experimental implications in current and proposed facilities received particular attention. The scientific programme consisted of 24 invited Plenary Talks and 93 contributions selected among the submitted papers. Young researchers, in particular, were encouraged to submit an abstract. The Special Lecture on ''CERN and the Future of Particle Physics'', given by the CERN Director General Rolf-Dieter Heuer to close the Symposium, was of particular relevance. On the last day of the Symposium, an open meeting took place between Professor Heuer and the Spanish community of particle physics. The Symposium covered recent developments on the subject of Discrete Symmetries in the following topics: Quantum Vacuum Entanglement, Symmetrisation Principle CPT in Quantum Gravity and String Theory, Decoherence, Lorentz Violation Ultra-high-energy Messengers Time Reversal CP violation in the SM and beyond Neutrino Mass, Mixing and CP Baryogenesis, Leptogenesis Family Symmetries Supersymmetry and other searches Experimental Prospects: LHC, Super-B Factories, DAΦNE-2, Neutrino Beams The excellence of most of the presentations during the Symposium was pointed out by many participants. The broad spectrum of topics under the
PREFACE: DISCRETE 2012 - Third Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Branco, G. C.; Emmanuel-Costa, D.; González Felipe, R.; Joaquim, F. R.; Lavoura, L.; Palomares-Ruiz, S.; Rebelo, M. N.; Romão, J. C.; Silva, J. P.
2013-07-01
The Third Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2012) was held at Instituto Superior Técnico, Portugal, from 3-7 December 2012 and was organised by Centro de Física Teórica de Partículas (CFTP) of Instituto Superior Técnico, Universidade Técnica de Lisboa. This is the sequel to the Symposia that was successfully organised in Valéncia in 2008 and in Rome in 2010. The topics covered included: T, C, P, CP symmetries CPT symmetry, decoherence, Lorentz symmetry breaking Discrete symmetries and models of flavour mixing Baryogenesis, leptogenesis Neutrino physics Electroweak symmetry breaking and physics beyond the Standard Model Accidental symmetries (B, L conservation) Experimental prospects at LHC Dark matter searches Super flavour factories, and other new experimental facilities The Symposium was organised in plenary sessions with a total of 24 invited talks, and parallel sessions with a total of 70 talks, including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Ignatios Antoniadis, Abdelhak Djouadi, Rabindra Mohapatra, André Rubbia, Alexei Yu Smirnov, José Bernabéu, Marco Cirelli, Apostolos Pilaftsis, Antonio Di Domenico, Robertus Potting, João Varela, Frank Rathmann, Michele Gallinaro, Dumitru Ghilencea, Neville Harnew, John Walsh, Patrícia Conde Muíño, Juan Aguilar-Saavedra, Nick Mavromatos, Ulrich Nierste, Ferruccio Feruglio, Vasiliki Mitsou, Masanori Yamauchi, and Marcello Giorgi. The Symposium was attended by about 140 participants. Among the social events, there was a social dinner in the historical Associação Comercial de Lisboa, which included a musical performance of 'Fado', the traditional music from Lisbon. The next symposium of the series will be organised by King's College, London University, UK, from 1-5 December 2014. Guest Editors G C Branco, D Emmanuel-Costa, R González Felipe, F R Joaquim, L Lavoura, S Palomares-Ruiz, M N Rebelo, J C
Flocking with discrete symmetry: The two-dimensional active Ising model.
Solon, A P; Tailleur, J
2015-10-01
We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a two-dimensional lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density-velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density-temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular, we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.
PREFACE: DISCRETE 2010: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Bini, Cesare; Bloise, Caterina; Bossi, Fabio; Faccini, Riccardo; Gauzzi, Paolo; Isidori, Gino; Lipari, Paolo; Ludovici, Lucio; Silvestrini, Luca
2011-12-01
The Symposium DISCRETE2010 on Prospects in the Physics of Discrete Symmetries was held at the Sapienza Universitàa di Roma, Italy from 6-11 December 2010. This second edition, after the successful one in Valencia in 2008, covered all theoretical and experimental progress in the field, and aimed at a thorough discussion on the latest developments. The topics covered included: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence, Lorentz symmetry breaking; neutrino mass and mixing; cosmology and astroparticles, dark matter searches; experimental prospects at LHC, Super flavor factories, and new facilities. The Symposium was organized in plenary sessions with a total of 23 invited talks, and parallel sessions with a total of 80 talks including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Achille Stocchi, Andreas Weiler, Kevin Pitts, Tim Gershon, Marco Sozzi, Neal Weiner, Vasiliki Mitsou, Bernard Sadoulet, Gianfranco Bertone, J. Eric Grove, Mauro Mezzetto, Alexei Yu Smirnov, Oliviero Cremonesi, Antonio Riotto, Reno Mandolesi, Brett Altschul, Jose Bernabeu, Lawrence Hall, Marco Grassi, Yannis K. Semertzidis, Riccardo Barbieri, Gigi Rolandi, Luciano Maiani. The Symposium venue was the CNR (Consiglio Nazionale delle Ricerche) headquarter building, close to the Sapienza University. At the end of the Symposium a special open session, devoted to a wider audience, was held at the Pontifical University of the Holy Cross, in the historical center of Rome. The symposium was attended by about 140 participants, about half coming from Italy, and the rest mainly from other European countries and United States. Among the social events was a concert at the Aula Magna of the Sapienza University, and a social dinner in the historical Palazzo Pallavicini-Rospigliosi on the Quirinale Hill. The next symposium of the series will be organised by IST, Universidade Tàecnica de Lisboa
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.
NASA Astrophysics Data System (ADS)
Low, Catherine I.; Volkas, Raymond R.
2003-08-01
Neutrino oscillation experiments (excluding the Liquid Scintillator Neutrino Detector experiment) suggest a tribimaximal form for the lepton mixing matrix. This form indicates that the mixing matrix is probably independent of the lepton masses, and suggests the action of an underlying discrete family symmetry. Using these hints, we conjecture that the contrasting forms of the quark and lepton mixing matrices may both be generated by such a discrete family symmetry. This idea is that the diagonalization matrices out of which the physical mixing matrices are composed have large mixing angles, which cancel out due to a symmetry when the CKM matrix is computed, but do not do so in the MNS case. However, in the cases where the Higgs bosons are singlets under the symmetry, and the family symmetry commutes with SU(2)L, we prove a no-go theorem: no discrete unbroken family symmetry can produce the required mixing patterns. We then suggest avenues for future research.
Symmetry breaking of localized discrete matter waves induced by spin-orbit coupling
NASA Astrophysics Data System (ADS)
Salerno, M.; Abdullaev, F. Kh.
2015-10-01
We study localized nonlinear excitations of a dilute Bose-Einstein condensate (BEC) with spin-orbit coupling in a deep optical lattice (OL). For this we introduce a tight-binding model that includes the spin-orbit coupling (SOC) at the discrete level in the form of a generalized discrete nonlinear Schrödinger equation. Existence and stability of discrete solitons of different symmetry types is demonstrated. Quite interestingly, we find three distinctive regions in which discrete solitons undergo spontaneously symmetry breaking, passing from on-site to inter-site and to asymmetric, simply by varying the interatomic interactions. Existence ranges of discrete solitons with inter-site symmetry depend on SOC and shrink to zero as the SOC parameter is increased. Asymmetric discrete solitons appear as novel excitations specific of the SOC. Possible experimental implementation of these results is briefly discussed.
Maximal neutrino mixing from a minimal flavor symmetry
Aranda, A.; Carone, C.D.; Lebed, R.F.
2000-02-01
The authors study a number of models, based on a non-Abelian discrete group, that successfully reproduce the simple and predictive Yukawa textures usually associated with U(2) theories of flavor. These models allow for solutions to the solar and atmospheric neutrino problems that do not require altering successful predictions for the charged fermions or introducing sterile neutrinos. Although Yukawa matrices are hierarchical in the models they consider, the mixing between second- and third-generation neutrinos is naturally large. They first present a quantitative analysis of a minimal model proposed in earlier work, consisting of a global fit to fermion masses and mixing angles, including the most important renormalization group effects. They then propose two new variant models: The first reproduces all important features of the SU(5) x U(2) unified theory with neither SU(5) nor U(2). The second demonstrates that discrete subgroups of SU(2) can be used in constructing viable supersymmetric theories of flavor without scalar universality even though SU(2) by itself cannot.
Multi-Target Tracking by Discrete-Continuous Energy Minimization.
Milan, Anton; Schindler, Konrad; Roth, Stefan
2016-10-01
The task of tracking multiple targets is often addressed with the so-called tracking-by-detection paradigm, where the first step is to obtain a set of target hypotheses for each frame independently. Tracking can then be regarded as solving two separate, but tightly coupled problems. The first is to carry out data association, i.e., to determine the origin of each of the available observations. The second problem is to reconstruct the actual trajectories that describe the spatio-temporal motion pattern of each individual target. The former is inherently a discrete problem, while the latter should intuitively be modeled in continuous space. Having to deal with an unknown number of targets, complex dependencies, and physical constraints, both are challenging tasks on their own and thus most previous work focuses on one of these subproblems. Here, we present a multi-target tracking approach that explicitly models both tasks as minimization of a unified discrete-continuous energy function. Trajectory properties are captured through global label costs, a recent concept from multi-model fitting, which we introduce to tracking. Specifically, label costs describe physical properties of individual tracks, e.g., linear and angular dynamics, or entry and exit points. We further introduce pairwise label costs to describe mutual interactions between targets in order to avoid collisions. By choosing appropriate forms for the individual energy components, powerful discrete optimization techniques can be leveraged to address data association, while the shapes of individual trajectories are updated by gradient-based continuous energy minimization. The proposed method achieves state-of-the-art results on diverse benchmark sequences.
Discrete and continuous symmetries in multi-Higgs-doublet models
Ferreira, P. M.; Silva, Joao P.
2008-12-01
We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis-invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.
Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries
Haldar, K.; Lagoudas, D. C.
2014-01-01
A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials. PMID:25197247
Constitutive modelling of magnetic shape memory alloys with discrete and continuous symmetries.
Haldar, K; Lagoudas, D C
2014-09-08
A free energy-based constitutive formulation is considered for magnetic shape memory alloys. Internal state variables are introduced whose evolution describes the transition from reference state to the deformed and transformed one. We impose material symmetry restrictions on the Gibbs free energy and on the evolution equations of the internal state variables. Discrete symmetry is considered for single crystals, whereas continuous symmetry is considered for polycrystalline materials.
Discretized energy minimization in a wave guide with point sources
NASA Technical Reports Server (NTRS)
Propst, G.
1994-01-01
An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.
Non-Abelian discrete flavor symmetries of 10D SYM theory with magnetized extra dimensions
NASA Astrophysics Data System (ADS)
Abe, Hiroyuki; Kobayashi, Tatsuo; Ohki, Hiroshi; Sumita, Keigo; Tatsuta, Yoshiyuki
2014-06-01
We study discrete flavor symmetries of the models based on a ten-dimensional supersymmetric Yang-Mills (10D SYM) theory compactified on magnetized tori. We assume non-vanishing non-factorizable fluxes as well as the orbifold projections. These setups allow model-building with more various flavor structures. Indeed, we show that there exist various classes of non-Abelian discrete flavor symmetries. In particular, we find that S 3 flavor symmetries can be realized in the framework of the magnetized 10D SYM theory for the first time.
A minimal discrete model for toroidal moments and its experimental realization
NASA Astrophysics Data System (ADS)
Xiang, Hong; Ge, Lixin; Liu, Liang; Jiang, Tianshu; Zhang, Z. Q.; Chan, C. T.; Han, Dezhuan
2017-01-01
It is well known that a closed loop of magnetic dipoles can give rise to the rather elusive toroidal moment. However, artificial structures required to generate the necessary magnetic moments in metamaterials are typically optically large, complex to make, and easily compromised by the kinetic inductance at high frequencies. Instead of using magnetic dipoles, we propose a minimal model based on just three aligned discrete electric dipoles in which the occurrence of resonant toroidal modes is guaranteed by symmetry. The advantage of this model is its simplicity and the same model supports toroidal moments from the microwave regime up to optical frequencies as exemplified by a three-antenna array and a system consisting of three nanosized plasmonic particles. Both the microwave and high-frequency configurations exhibit nonradiating "anapoles." Experiments in the microwave regime confirm the theoretical predictions.
Integrability test for discrete equations via generalized symmetries
Levi, D.; Yamilov, R. I.
2010-12-23
In this article we present some integrability conditions for partial difference equations obtained using the formal symmetries approach. We apply them to find integrable partial difference equations contained in a class of equations obtained by the multiple scale analysis of the general multilinear dispersive difference equation defined on the square.
BOOK REVIEW: Discrete Symmetries and CP Violation: From Experiment to Theory (Oxford Graduate Texts)
NASA Astrophysics Data System (ADS)
Fösel, A.
2009-03-01
Discrete Symmetries and CP Violation: From Experiment to Theory by Marco Sozzi discusses C(harge conjugation), P(arity) and T(ime reversal) discrete symmetries and of course CP symmetry in microscopic (atomic, nuclear and particle) physics. It includes a detailed description of key or representative experiments, and major achievements and recent developments are also mentioned. Though lots of excellent textbooks already exist which cover the basics of discrete symmetries and CP violation in theory and experiment, Sozzi has fully achieved the goal of presenting a book that describes the basics of this subject in detail, from an experimental point of view as well as from theory. He also succeeds in finding links between experiments and theory, leading to a better understanding of the subject. Besides, as an experimentalist, discrete symmetries and CP violation appear to the author as ideal subjects to convey the depth and excitement of experimental `beautiful' physics, which Marco S Sozzi - in my opinion - has managed to do brilliantly. Though mainly addressed to graduate students, the book may also be useful to undergraduates (by skipping some of the more advanced sections and utilizing the brief introduction to some topics in the appendices) and to young researchers looking for a wider modern overview of the issues related to CP symmetry. At the end of each chapter, further reading sections are conveniently provided for the reader to find relevant literature for further studies. Problems to solve at the end of each chapter act as 'little tests'. Unfortunately, their solutions are currently absent: perhaps a publication that includes them is planned in the near future. To conclude, the book succeeds in being a complete and self-consistent text describing in up-to-date detail the investigation of discrete symmetries in sub-atomic physics. It also emphasizes the concepts and ingenuity behind many delicate, careful, and by all means 'beautiful' experiments.
Discrete-time quantum walks: Continuous limit and symmetries
NASA Astrophysics Data System (ADS)
di Molfetta, G.; Debbasch, F.
2012-12-01
The continuous limit of one-dimensional discrete-time quantum walks with time-and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks do. All families (1-jets) admitting a continuous limit are identified. The continuous limit is described by a Dirac-like equation or, alternately, a couple of Klein-Gordon equations. Variational principles leading to these equations are also discussed, together with local invariance properties.
Model for neutrino masses and dark matter with a discrete gauge symmetry
NASA Astrophysics Data System (ADS)
Chang, We-Fu; Wong, Chi-Fong
2012-01-01
A simple renormalizable U(1) gauge model is constructed to explain the smallness of the active neutrino masses and provide the stable cold dark matter candidate simultaneously. The local U(1) symmetry is assumed to be spontaneously broken by a scalar field around the TeV scale. The active neutrino masses are then generated at one-loop level. This model contains several cold dark matter candidates whose stability is guaranteed by a residual discrete gauge Z2 symmetry à la the Krauss-Wilczek mechanism. Unlike the other dark matter models, no further global discrete or continuous symmetry is introduced. Moreover, the masses of all fermionic degrees of freedom beyond the standard model are closely related to the scale of spontaneous breaking of U(1); thus they could be probed at or below the TeV scale. The possible cosmological and phenomenological consequences are briefly discussed.
NASA Astrophysics Data System (ADS)
Moskal, P.; Alfs, D.; Bednarski, T.; Białas, P.; Curceanu, C.; Czerwiński, E.; Dulski, K.; Gajos, A.; Głowacz, B.; Gupta-Sharma, N.; Gorgol, M.; Hiesmayr, B. C.; Jasińska, B.; Kamińska, D.; Khreptak, O.; Korcyl, G.; Kowalski, P.; Krzemień, W.; Krawczyk, N.; Kubicz, E.; Mohammed, M.; Niedźwiecki, Sz.; Pawlik-Niedńwiecka, M.; Raczyński, L.; Rudy, Z.; Silarski, M.; Smyrski, J.; Wieczorek, A.; Wiślicki, W.; Zgardzińska, B.; Zieliński, M.
2016-11-01
Discrete symmetries such as parity (P), charge-conjugation (C) and time reversal (T) are of fundamental importance in physics and cosmology. Breaking of charge conjugation symmetry (C) and its combination with parity (CP) constitute necessary conditions for the existence of the asymmetry between matter and antimatter in the observed Universe. The presently known sources of discrete symmetries violations can account for only a tiny fraction of the excess of matter over antimatter. So far CP and T symmetries violations were observed only for systems involving quarks and they were never reported for the purely leptonic objects. In this article we describe briefly an experimental proposal for the test of discrete symmetries in the decays of positronium atom which is made exclusively of leptons. The experiments are conducted by means of the Jagiellonian Positron Emission Tomograph (J-PET) which is constructed from strips of plastic scintillators enabling registration of photons from the positronium annihilation. J-PET tomograph together with the positronium target system enable to measure expectation values for the discrete symmetries odd operators constructed from (i) spin vector of the ortho-positronium atom, (ii) momentum vectors of photons originating from the decay of positronium, and (iii) linear polarization direction of annihilation photons. Linearly polarized positronium will be produced in the highly porous aerogel or polymer targets, exploiting longitudinally polarized positrons emitted by the sodium 22Na isotope. Information about the polarization vector of orthopositronium will be available on the event by event basis and will be reconstructed from the known position of the positron source and the reconstructed position of the orthopositronium annihilation. In 2016 the first tests and calibration runs are planned, and the data collection with high statistics will commence in the year 2017.
Dynamics of symmetry breaking during quantum real-time evolution in a minimal model system.
Heyl, Markus; Vojta, Matthias
2014-10-31
One necessary criterion for the thermalization of a nonequilibrium quantum many-particle system is ergodicity. It is, however, not sufficient in cases where the asymptotic long-time state lies in a symmetry-broken phase but the initial state of nonequilibrium time evolution is fully symmetric with respect to this symmetry. In equilibrium, one particular symmetry-broken state is chosen as a result of an infinitesimal symmetry-breaking perturbation. From a dynamical point of view the question is: Can such an infinitesimal perturbation be sufficient for the system to establish a nonvanishing order during quantum real-time evolution? We study this question analytically for a minimal model system that can be associated with symmetry breaking, the ferromagnetic Kondo model. We show that after a quantum quench from a completely symmetric state the system is able to break its symmetry dynamically and discuss how these features can be observed experimentally.
Residual Z 2 symmetries and leptonic mixing patterns from finite discrete subgroups of U(3)
NASA Astrophysics Data System (ADS)
Joshipura, Anjan S.; Patel, Ketan M.
2017-01-01
We study embedding of non-commuting Z 2 and Z m , m ≥ 3 symmetries in discrete subgroups (DSG) of U(3) and analytically work out the mixing patterns implied by the assumption that Z 2 and Z m describe the residual symmetries of the neutrino and the charged lepton mass matrices respectively. Both Z 2 and Z m are assumed to be subgroups of a larger discrete symmetry group G f possessing three dimensional faithful irreducible representation. The residual symmetries predict the magnitude of a column of the leptonic mixing matrix U PMNS which are studied here assuming G f as the DSG of SU(3) designated as type C and D and large number of DSG of U(3) which are not in SU(3). These include the known group series Σ(3 n 3), T n ( m), Δ(3 n 2, m), Δ(6 n 2, m) and Δ'(6 n 2, j, k). It is shown that the predictions for a column of | U PMNS| in these group series and the C and D types of groups are all contained in the predictions of the Δ(6 N 2) groups for some integer N. The Δ(6 N 2) groups therefore represent a sufficient set of G f to obtain predictions of the residual symmetries Z 2 and Z m .
SAR image regularization with fast approximate discrete minimization.
Denis, Loïc; Tupin, Florence; Darbon, Jérôme; Sigelle, Marc
2009-07-01
Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle noise. Markov random field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges. Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving nonconvex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the alpha -expansion) is too heavy specially when considering joint regularization of several images. We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut-based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.
Alternative schemes of predicting lepton mixing parameters from discrete flavor and C P symmetry
NASA Astrophysics Data System (ADS)
Lu, Jun-Nan; Ding, Gui-Jun
2017-01-01
We suggest two alternative schemes to predict lepton mixing angles as well as C P violating phases from a discrete flavor symmetry group combined with C P symmetry. In the first scenario, the flavor and C P symmetry is broken to the residual groups of the structure Z2×C P in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters θν and θl. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant C P transformation, all lepton mixing parameters are determined in terms of three free parameters θ1 ,2 ,3. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters θν ,l and θ1 ,2 ,3 is taken into account. We have studied the lepton mixing patterns arising from the flavor group S4 and C P symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
6d dual conformal symmetry and minimal volumes in AdS
NASA Astrophysics Data System (ADS)
Bhattacharya, Jyotirmoy; Lipstein, Arthur E.
2016-12-01
The S-matrix of a theory often exhibits symmetries which are not manifest from the viewpoint of its Lagrangian. For instance, powerful constraints on scattering amplitudes are imposed by the dual conformal symmetry of planar 4d N=4 super Yang-Mills theory and the ABJM theory. Motivated by this, we investigate the consequences of dual conformal symmetry in six dimensions, which may provide useful insight into the worldvolume theory of M5-branes (if it enjoys such a symmetry). We find that 6d dual conformal symmetry uniquely fixes the integrand of the one-loop 4-point amplitude, and its structure suggests a Lagrangian with more than two derivatives. On integrating out the loop momentum in 6 - 2 ɛ dimensions, the result is very similar to the corresponding amplitude of N=4 super Yang-Mills theory. We confirm this result holographically by generalizing the Alday-Maldacena solution for a minimal area string in Anti-de Sitter space to a minimal volume M2-brane ending on a pillow-shaped surface in the boundary whose seams correspond to a null-polygon. This involves careful treatment of a prefactor which diverges as 1/ ɛ, and we comment on its possible interpretation. We also study 2-loop 4-point integrands with 6d dual conformal symmetry and speculate on the existence of an all-loop formula for the 4-point amplitude.
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.
Baksic, Alexandre; Ciuti, Cristiano
2014-05-02
We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the nonstandard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We show that such an unusual coupling scheme can be implemented in circuit QED systems, where artificial Josephson atoms are coupled both capacitively and inductively to a superconducting resonator. We demonstrate that it is possible to pass from a discrete, paritylike Z(2) symmetry to a continuous U(1) with the appearance of photonic Goldstone and amplitude modes above a critical point even in the ultrastrong coupling regime (where the rotating wave approximation for the interaction between field and two-level systems is no longer applicable). We determine the rich phase diagram showing "superradiant" phases with different symmetries and phase boundaries of both first and second order.
Discrete flavor symmetries for degenerate solar neutrino pair and their predictions
NASA Astrophysics Data System (ADS)
Joshipura, Anjan S.; Patel, Ketan M.
2014-08-01
Flavor symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group Gf. Gf can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3) divided into the two classes, called type C and D in Miller et al. [Theory and Applications of Finite Groups (John Wiley & Sons, New York, 1916)]. The main results are (a) All the SU(3) subgroups of type C fail in simultaneously giving correct θ13 and θ23. (b) All the groups of type D can predict a relation cos2θ13sin2θ23=1/3 among the mixing angles which appears to be a good zeroth order approximation. Among these, various Δ(6n2) groups with n ≥8 can simultaneously lead also to sin2θ13 in agreement with global fit at 3σ. (c) The group Σ(168)≅PSL(2,7) predicts near to the best fit value for θ13 and θ23 within the 1σ range. All discrete subgroups of U(3) with order <512 and having three-dimensional irreducible representation are considered as possible Gf when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict θ13 and/or θ23. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables is discussed in the context of several groups which offer good leading order predictions.
A Vector-Like Fourth Generation with A Discrete Symmetry From Split-UED
Kong, Kyoungchul; Park, Seong Chan; Rizzo, Thomas G.; /SLAC
2011-08-19
Split-UED allows for the possibility that the lowest lying KK excitations of the Standard Model fermions can be much lighter than the corresponding gauge or Higgs KK states. This can happen provided the fermion bulk masses are chosen to be large, in units of the inverse compactification radius, 1/R, and negative. In this setup, all of the other KK states would be effectively decoupled from low energy physics. Such a scenario would then lead to an apparent vector-like fourth generation with an associated discrete symmetry that allows us to accommodate a dark matter candidate. In this paper the rather unique phenomenology presented by this picture will be examined.
Multi-Higgs model with Abelian and non-Abelian discrete symmetries
NASA Astrophysics Data System (ADS)
Machado, A. C. B.; Pleitez, V.
2008-11-01
-handed fermions, singlet under the gauge symmetry, transforming as triplet or singlet of A4. The predictive power is a consequence of the discrete symmetries imposed to the model: A4 otimes Z3 otimes Z'3 otimes Z''3. In conclusions, the mass matrices obtained, which arise because of the symmetry of the model, give appropriate insight concerning the solution of the flavor problem. Of course, it is necessary to explain how these symmetries are realized from a more fundamental theory.
On a discrete symmetry of the Bremsstrahlung function in {N} = 4 SYM
NASA Astrophysics Data System (ADS)
Beccaria, Matteo; Macorini, Guido
2013-07-01
We consider the quark anti-quark potential on the three sphere in planar {N} = 4 SYM and the associated vacuum potential in the near BPS limit with L units of R-charge. The associated Bremsstrahlung function B L has been recently computed analytically by means of the Thermodynamical Bethe Ansatz. We discuss it at strong coupling by computing it at large but finite L. We provide strong support to a special symmetry of the Bremsstrahlung function under the formal discrete {{{Z}}_2} symmetry L → -1 - L. In this context, it is the counterpart of the reciprocity invariance discovered in the past in the spectrum of various gauge invariant composite operators. The {{{Z}}_2} symmetry has remarkable consequences in the scaling limit where L is taken to be large with fixed ratio to the 't Hooft coupling. This limit organizes in inverse powers of the coupling and resembles the semiclassical expansion of the dual string theory which is indeed known to capture the leading classical term. We show that the various higher-order contributions to the Bremsstrahlung function obey several constraints and, in particular, the next-to-leading term, formally associated with the string one-loop correction, is completely determined by the classical contribution. The large L limit at strong coupling is also discussed.
Interplay between Fano resonance and PT symmetry in non-Hermitian discrete systems
NASA Astrophysics Data System (ADS)
Zhu, Baogang; Lü, Rong; Chen, Shu
2015-04-01
We study the effect of PT -symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT -symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT -symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the perfect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.
Discrete symmetry enhancement in non-Abelian models and the existence of asymptotic freedom
NASA Astrophysics Data System (ADS)
Patrascioiu, Adrian; Seiler, Erhard
2001-09-01
We study the universality between a discrete spin model with icosahedral symmetry and the O(3) model in two dimensions. For this purpose we study numerically the renormalized two-point functions of the spin field and the four point coupling constant. We find that those quantities seem to have the same continuum limits in the two models. This has far reaching consequences, because the icosahedron model is not asymptotically free in the sense that the coupling constant proposed by Lüscher, Weisz, and Wolff [Nucl. Phys. B359, 221 (1991)] does not approach zero in the short distance limit. By universality this then also applies to the O(3) model, contrary to the predictions of perturbation theory.
2014-01-01
Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP), which aims to minimize total service time, and proposes an iterated greedy (IG) algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set. PMID:25295295
Lin, Shih-Wei; Ying, Kuo-Ching; Wan, Shu-Yen
2014-01-01
Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP), which aims to minimize total service time, and proposes an iterated greedy (IG) algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set.
Non-minimal CW inflation, electroweak symmetry breaking and the 750 GeV anomaly
NASA Astrophysics Data System (ADS)
Marzola, L.; Racioppi, A.; Raidal, M.; Urban, F. R.; Veermäe, H.
2016-03-01
We study whether the hinted 750 GeV resonance at the LHC can be a Coleman-Weinberg inflaton which is non-minimally coupled to gravity. Since the inflaton must couple to new charged and coloured states to reproduce the LHC diphoton signature, the same interaction can generate its effective potential and trigger the electroweak symmetry breaking via the portal coupling to the Higgs boson. This inflationary scenario predicts a lower bound on the tensor-to-scalar ratio of r ≳ 0.006, where the minimal value corresponds to the measured spectral index n s ≃ 0.97. However, we find that the compatibility with the LHC diphoton signal requires exotic new physics at energy scales accessible at the LHC. We study and quantify the properties of the predicted exotic particles.
Minimally allowed beta beata 0_nu rates from approximate flavor symmetries
Jenkins, James
2008-01-01
Neutrinoless double beta decay ({beta}{beta}0{nu}) is the only realistic probe of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to m{sub ee} , the e - e element of the Majorana mass matrix. This is expected to hold true for small {beta}{beta}{nu} rates ({Gamma}{sub {beta}{beta}0{nu}}), even in the presence of new physics. Naively, current data allows for vanishing m{sub ee} , but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. Hence, Majorana neutrinos imply nonzero {Gamma}{sub {beta}{beta}0{nu}}. I perform a spurion analysis to break all possible abelian symmetries that guarantee {Gamma}{sub {beta}{beta}0{nu}} = 0 and search for minimally allowed m{sub ee} values. Specifically, I survey 259 broken structures to yield m{sub ee} values and current phenomenological constraints under a variety of scenarios. This analysis also extracts predictions for both neutrino oscillation parameters and kinematic quantities. Assuming reasonable tuning levels, I find that m{sub ee} > 4 x 10{sup -6} eV at 99% confidence. Bounds below this value would indicate the Dirac neutrino nature or the existence of new light (eV-MeV scale) degrees of freedom that can potentially be probed elsewhere. This limit can be raised by improvements in neutrino parameter measurements, particularly of the reactor mixing angle, depending on the best fit parameter values. Such improvements will also significantly constrain the available model space and aid in future constructions.
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Fidkowski, Lukasz
2016-09-01
We construct exactly solved commuting projector Hamiltonian lattice models for all known (2+1)-dimensional (2+1D) fermionic symmetry protected topological phases (SPTs) with on-site unitary symmetry group Gf=G ×Z2f , where G is finite and Z2f is the fermion parity symmetry. In particular, our models transcend the class of group supercohomology models, which realize some, but not all, fermionic SPTs in 2+1D. A natural ingredient in our construction is a discrete form of the spin structure of the 2D spatial surface M on which our model is defined, namely a "Kasteleyn" orientation of a certain graph associated with the lattice. As a special case, our construction yields commuting projector models for all eight members of the Z8 classification of 2D fermionic SPTs with G =Z2 .
as the flavor symmetry in a non-minimal SUSY model
NASA Astrophysics Data System (ADS)
Gómez-Izquierdo, J. C.; González-Canales, F.; Mondragon, M.
2015-05-01
We present a non-minimal renormalizable SUSY model, with extended Higgs sector and right-handed neutrinos, where the flavor sector exhibits a flavor symmetry. We analyzed the simplest version of this model, in which R-parity is conserved and the right-handed neutrino masses in the flavor doublet are considered with and without degeneracy. We find the generic form of the mass matrices both in the quark and lepton sectors. We reproduce, according to current data, the mixing in the CKM matrix. In the leptonic sector, in the general case where the right-handed neutrino masses are not degenerate, we find that the values for the solar, atmospheric, and reactor mixing angles are in very good agreement with the experimental data, both for a normal and an inverted hierarchy. In the particular case where the right-handed neutrinos masses are degenerate, the model predicts a strong inverted hierarchy spectrum and a sum rule among the neutrino masses. In this case the atmospheric and solar angles are in very good agreement with experimental data, and the reactor one is different from zero, albeit too small (). This value constitutes a lower bound for in the general case. We also find the range of the values for the neutrino masses in each case.
Selecting discrete and continuous features based on neighborhood decision error minimization.
Hu, Qinghua; Pedrycz, Witold; Yu, Daren; Lang, Jun
2010-02-01
Feature selection plays an important role in pattern recognition and machine learning. Feature evaluation and classification complexity estimation arise as key issues in the construction of selection algorithms. To estimate classification complexity in different feature subspaces, a novel feature evaluation measure, called the neighborhood decision error rate (NDER), is proposed, which is applicable to both categorical and numerical features. We first introduce a neighborhood rough-set model to divide the sample set into decision positive regions and decision boundary regions. Then, the samples that fall within decision boundary regions are further grouped into recognizable and misclassified subsets based on class probabilities that occur in neighborhoods. The percentage of misclassified samples is viewed as the estimate of classification complexity of the corresponding feature subspaces. We present a forward greedy strategy for searching the feature subset, which minimizes the NDER and, correspondingly, minimizes the classification complexity of the selected feature subset. Both theoretical and experimental comparison with other feature selection algorithms shows that the proposed algorithm is effective for discrete and continuous features, as well as their mixture.
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.
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.
Mass minimization of a discrete regenerative fuel cell (RFC) system for on-board energy storage
NASA Astrophysics Data System (ADS)
Li, Xiaojin; Xiao, Yu; Shao, Zhigang; Yi, Baolian
RFC combined with solar photovoltaic (PV) array is the advanced technologic solution for on-board energy storage, e.g. land, sky, stratosphere and aerospace applications, due to its potential of achieving high specific energy. This paper focuses on mass modeling and calculation for a RFC system consisting of discrete electrochemical cell stacks (fuel cell and electrolyzer), together with fuel storage, a PV array, and a radiator. A nonlinear constrained optimization procedure is used to minimize the entire system mass, as well as to study the effect of operating conditions (e.g. current densities of fuel cell and electrolyzer) on the system mass. According to the state-of-the-art specific power of both electrochemical stacks, an energy storage system has been designed for the conditions of stratosphere applications and a rated power output of 12 kW. The calculation results show that the optimization of the current density of both stacks is of importance in designing the light weight on-board energy system.
NASA Astrophysics Data System (ADS)
Hiesmayr, Beatrix C.
2015-07-01
About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem (“why do we observe no tables in superposition?”) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.
Theory of the lattice Boltzmann equation: symmetry properties of discrete velocity sets.
Rubinstein, Robert; Luo, Li-Shi
2008-03-01
The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested.
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory
Purvine, Emilie AH; Monson, Kyle E.; Jurrus, Elizabeth R.; Star, Keith T.; Baker, Nathan A.
2016-09-01
There are several applications in computational biophysics which require the optimization of discrete interacting states; e.g., amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial-time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of maximum flow-minimum cut graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein, and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial-time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.
ERIC Educational Resources Information Center
Kellen, David; Klauer, Karl Christoph
2014-01-01
A classic discussion in the recognition-memory literature concerns the question of whether recognition judgments are better described by continuous or discrete processes. These two hypotheses are instantiated by the signal detection theory model (SDT) and the 2-high-threshold model, respectively. Their comparison has almost invariably relied on…
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory.
Purvine, Emilie; Monson, Kyle; Jurrus, Elizabeth; Star, Keith; Baker, Nathan A
2016-08-25
There are several applications in computational biophysics that require the optimization of discrete interacting states, for example, amino acid titration states, ligand oxidation states, or discrete rotamer angles. Such optimization can be very time-consuming as it scales exponentially in the number of sites to be optimized. In this paper, we describe a new polynomial time algorithm for optimization of discrete states in macromolecular systems. This algorithm was adapted from image processing and uses techniques from discrete mathematics and graph theory to restate the optimization problem in terms of "maximum flow-minimum cut" graph analysis. The interaction energy graph, a graph in which vertices (amino acids) and edges (interactions) are weighted with their respective energies, is transformed into a flow network in which the value of the minimum cut in the network equals the minimum free energy of the protein and the cut itself encodes the state that achieves the minimum free energy. Because of its deterministic nature and polynomial time performance, this algorithm has the potential to allow for the ionization state of larger proteins to be discovered.
Symmetry, dark matter, and LHC phenomenology of the minimal νSM
NASA Astrophysics Data System (ADS)
He, Xiao-Gang; Li, Tong; Liao, Wei
2010-02-01
A sterile neutrino with a mass of a few keV can play the role of warm dark matter (DM). This can be realized in seesaw models with 3 left- and 3 right-handed neutrinos. It is possible to identify the keV neutrino to be one of the right-handed neutrinos leaving the other two to be much more heavier, the νSM model. We show that with this realization of keV neutrino DM, the model has an approximate Friedberg-Lee symmetry providing a natural explanation for the lightness of the right-handed neutrino. We also find that in this model the mixing parameters couple light and heavy neutrinos are strongly correlated, and can be large enough to have testable effects at the LHC for the two heavy right-handed neutrinos to be in the hundred-GeV range.
Discrete artificial bee colony algorithm for lot-streaming flowshop with total flowtime minimization
NASA Astrophysics Data System (ADS)
Sang, Hongyan; Gao, Liang; Pan, Quanke
2012-09-01
Unlike a traditional flowshop problem where a job is assumed to be indivisible, in the lot-streaming flowshop problem, a job is allowed to overlap its operations between successive machines by splitting it into a number of smaller sub-lots and moving the completed portion of the sub-lots to downstream machine. In this way, the production is accelerated. This paper presents a discrete artificial bee colony (DABC) algorithm for a lot-streaming flowshop scheduling problem with total flowtime criterion. Unlike the basic ABC algorithm, the proposed DABC algorithm represents a solution as a discrete job permutation. An efficient initialization scheme based on the extended Nawaz-Enscore-Ham heuristic is utilized to produce an initial population with a certain level of quality and diversity. Employed and onlooker bees generate new solutions in their neighborhood, whereas scout bees generate new solutions by performing insert operator and swap operator to the best solution found so far. Moreover, a simple but effective local search is embedded in the algorithm to enhance local exploitation capability. A comparative experiment is carried out with the existing discrete particle swarm optimization, hybrid genetic algorithm, threshold accepting, simulated annealing and ant colony optimization algorithms based on a total of 160 randomly generated instances. The experimental results show that the proposed DABC algorithm is quite effective for the lot-streaming flowshop with total flowtime criterion in terms of searching quality, robustness and effectiveness. This research provides the references to the optimization research on lot-streaming flowshop.
NASA Astrophysics Data System (ADS)
Setare, M. R.; Adami, H.
2016-09-01
We consider the Generalized Minimal Massive Gravity (GMMG) model in the first order formalism. We show that all the solutions of the Einstein gravity with negative cosmological constants solve the equations of motion of considered model. Then we find an expression for the off-shell conserved charges of this model. By considering the near horizon geometry of a three dimensional black hole in the Gaussian null coordinates, we find near horizon conserved charges and their algebra. The obtained algebra is centrally extended. By writing the algebra of conserved charges in terms of Fourier modes and considering the BTZ black hole solution as an example, one can see that the charge associated with rotations along Y0 coincides exactly with the angular momentum, and the charge associated with time translations T0 is the product of the black hole entropy and its temperature. As we expect, in the limit when the GMMG tends to the Einstein gravity, all the results we obtain in this paper reduce to the results of the paper [1].
2012-01-01
Subjects were tested for their ability to identify objects that were represented by an array of dots that marked the major contours, usually only the outer boundary. Each dot was briefly flashed to make its position known, and a major variable was the time interval that was required to flash all the dots for a given shape. Recognition declined as the total time for display of the dot inventory was increased. Each shape was shown to a given subject only once and it was either recognized -- named – or not. Although the recorded response was binary, a large number of subjects was tested, which made it possible to derive regression functions and thus specify an intercept and slope for each shape. Shapes differed substantially in their slopes, which is likely due to the amount of redundant information provided by neighboring dots. Indices of shape attributes were also derived, specifically Attneave’s indices of complexity, mean curvature, inflection count, and symmetry. Three of the four shape attributes were significantly related to intercept and slope levels, but none made a substantial contribution. This suggests that these attributes are not essential properties that define shapes and allow for recognition. PMID:23146718
NASA Astrophysics Data System (ADS)
Lee, D. H.; Joannopoulos, J. D.; Negele, J. W.; Landau, D. P.
1984-02-01
Landau-Ginzburg-Wilson symmetry analyses and Monte Carlo calculations for the classical antiferromagnetic planar (XY) model on a triangular lattice reveal a wealth of interesting critical phenomena. From this simple model arise a zero-field transition to a state of long-range order, a new mechanism for spin disordering, and a critical point associated with a possible new universality class.
NASA Technical Reports Server (NTRS)
Gedney, Stephen D.; Lansing, Faiza
1994-01-01
It has been found that the Discrete Integral Equation (DSI)technique is a highly effective technique for the analysis of microwave circuits and devices [1,2]. The DSI is much more robust than the traditional Finite Difference Time Domain (FDTD) method in a number of ways.
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.
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.
Quantum oscillations in a bilayer with broken mirror symmetry: a minimal model for YBa2Cu3O6+δ
NASA Astrophysics Data System (ADS)
Maharaj, Akash; Zhang, Yi; Ramshaw, Brad; Kivelson, Steven
Using an exact numerical solution and semiclassical analysis, we investigate quantum oscillations (QOs) in a model of a bilayer system with an anisotropic (elliptical) electron pocket in each plane. Key features of QO experiments in the high temperature superconducting cuprate YBCO can be reproduced by such a model, in particular the pattern of oscillation frequencies (which reflect ``magnetic breakdown'' between the two pockets) and the polar and azimuthal angular dependence of the oscillation amplitudes. However, the requisite magnetic breakdown is possible only under the assumption that the horizontal mirror plane symmetry is spontaneously broken and that the bilayer tunneling, t⊥, is substantially renormalized from its `bare' value. Under the assumption that t⊥ = Z ~t⊥(0), where Z ~ is a measure of the quasiparticle weight, this suggests that Z ~ <~ 1 / 20 . Detailed comparisons with new YBa2Cu3O6.58 QO data, taken over a very broad range of magnetic field, confirm specific predictions made by the breakdown scenario. Supported in part by the US DOE, Office of Basic Energy Sciences under Contract DE-AC02-76SF00515 (A.V.M.), the US DOE Office of Basic Energy Sciences ``Science at 100 T,'' (B.J.R.) and the National Science Foundation Grant No. DMR 1265593 (S.A.K., YZ).
NASA Astrophysics Data System (ADS)
Abdi, Fatemeh; Siabi-Gerjan, Araz; Savaloni, Hadi
2012-07-01
The use of glancing angle deposition technique provides opportunities for the deposition of sculptured nanostructures of different shape. The optical properties of such nanostructures that are a function of the shape of these nanostructures may be investigated, using the discrete dipole approximation theory which is an appropriate method for solving the light scattering problem from objects of different shape and geometry. In this paper, the extinction spectra of Ag/glass-sculptured nano-flowers with threefold symmetry are modeled and calculated, while the results are compared with similar experimental observations. In modeling the nano-flower-shaped sculptured thin films, it is proposed that the nano-flower is formed as a combination of two chiral thin films with different dimensions. This structure was replaced with 1,405 electrical dipoles, and its extinction spectrum was calculated as a function of incident light angle and azimuthal angle. The extinction spectrum consists of both transverse and longitudinal modes of oscillations. The results showed that by increasing the incident angle, due to increase of amplitude of electrical oscillations, transverse oscillations shift towards longer wavelengths. It was also observed that at azimuthal angles close to nano-flower petals, where sharp points or recesses may exist, the intensity of extinction spectrum for longitudinal mode (long wavelengths in the extinction spectrum) increases.
The symmetry behind extended flavour democracy and large leptonic mixing
NASA Astrophysics Data System (ADS)
Branco, G. C.; Silva-Marcos, J. I.
2002-01-01
We show that there is a minimal discrete symmetry which leads to the extended flavour democracy scenario constraining the Dirac neutrino, the charged lepton and the Majorana neutrino mass term (MR) to be all proportional to the democratic matrix, with all elements equal. In particular, this discreet symmetry forbids other large contributions to MR, such as a term proportional to the unit matrix, which would normally be allowed by a S3L×S3R permutation symmetry. This feature is crucial in order to obtain large leptonic mixing, without violating 't Hooft's naturalness principle.
Hood, Jennifer L.; Morabito, Michael V.; Martinez, Charles R.; Gilbert, James A.; Ferrick, Elizabeth A.; Ayers, Gregory D.; Chappell, James D.; Dermody, Terence S.; Emeson, Ronald B.
2014-01-01
Transcripts encoding ADAR1, a double-stranded, RNA-specific adenosine deaminase involved in the adenosine-to-inosine (A-to-I) editing of mammalian RNAs, can be alternatively spliced to produce an interferon-inducible protein isoform (p150) that is up-regulated in both cell culture and in vivo model systems in response to pathogen or interferon stimulation. In contrast to other tissues, p150 is expressed at extremely low levels in the brain and it is unclear what role, if any, this isoform may play in the innate immune response of the central nervous system (CNS) or whether the extent of editing for RNA substrates critical for CNS function is affected by its induction. To investigate the expression of ADAR1 isoforms in response to viral infection and subsequent alterations in A-to-I editing profiles for endogenous ADAR targets, we used a neuro-tropic strain of reovirus to infect neonatal mice and quantify A-to-I editing in discrete brain regions using a multiplexed, high-throughput sequencing strategy. While intracranial injection of reovirus resulted in a widespread increase in the expression of ADAR1 (p150) in multiple brain regions and peripheral organs, significant changes in site-specific A-to-I conversion were quite limited, suggesting that steady-state levels of p150 expression are not a primary determinant for modulating the extent of editing for numerous ADAR targets in vivo. PMID:24906008
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.
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.
Gravitational waves from domain walls in the next-to-minimal supersymmetric standard model
Kadota, Kenji; Kawasaki, Masahiro; Saikawa, Ken'ichi E-mail: kawasaki@icrr.u-tokyo.ac.jp
2015-10-01
The next-to-minimal supersymmetric standard model predicts the formation of domain walls due to the spontaneous breaking of the discrete Z{sub 3}-symmetry at the electroweak phase transition, and they collapse before the epoch of big bang nucleosynthesis if there exists a small bias term in the potential which explicitly breaks the discrete symmetry. Signatures of gravitational waves produced from these unstable domain walls are estimated and their parameter dependence is investigated. It is shown that the amplitude of gravitational waves becomes generically large in the decoupling limit, and that their frequency is low enough to be probed in future pulsar timing observations.
Unification and Dark Matter in a Minimal Scalar Extension of the Standard Model
Lisanti, Mariangela; Wacker, Jay G.
2007-04-25
The six Higgs doublet model is a minimal extension of the Standard Model (SM) that addresses dark matter and gauge coupling unification. Another Higgs doublet in the 5 representation of a discrete symmetry group, such as S{sub 6}, is added to the SM. The lightest components of the 5-Higgs are neutral, stable and serve as dark matter so long as the discrete symmetry is not broken. Direct and indirect detection signals, as well as collider signatures are discussed. The five-fold multiplicity of the dark matter decreases its mass and typically helps make the dark matter more visible in upcoming experiments.
Gravitational waves from domain walls in the next-to-minimal supersymmetric standard model
Kadota, Kenji; Kawasaki, Masahiro; Saikawa, Ken’ichi
2015-10-16
The next-to-minimal supersymmetric standard model predicts the formation of domain walls due to the spontaneous breaking of the discrete Z{sub 3}-symmetry at the electroweak phase transition, and they collapse before the epoch of big bang nucleosynthesis if there exists a small bias term in the potential which explicitly breaks the discrete symmetry. Signatures of gravitational waves produced from these unstable domain walls are estimated and their parameter dependence is investigated. It is shown that the amplitude of gravitational waves becomes generically large in the decoupling limit, and that their frequency is low enough to be probed in future pulsar timing observations.
NASA Astrophysics Data System (ADS)
Münkler, Hagen; Pollok, Jonas
2015-09-01
Based on an extension of the holographic principle to superspace, we provide a strong-coupling description of smooth super Wilson loops in {N}=4 super Yang-Mills theory in terms of minimal surfaces of the {{AdS}}5× {S}5 superstring. We employ the classical integrability of the Green-Schwarz superstring on {{AdS}}5× {S}5 to derive the superconformal and Yangian Y[{psu}(2,2| 4)] Ward identities for the super Wilson loop, thus extending the strong coupling results obtained for the Maldacena-Wilson loop. In the course of the derivation, we determine the minimal surface solution up to third order in an expansion close to the conformal boundary.
Integrable discrete PT symmetric model.
Ablowitz, Mark J; Musslimani, Ziad H
2014-09-01
An exactly solvable discrete PT invariant nonlinear Schrödinger-like model is introduced. It is an integrable Hamiltonian system that exhibits a nontrivial nonlinear PT symmetry. A discrete one-soliton solution is constructed using a left-right Riemann-Hilbert formulation. It is shown that this pure soliton exhibits unique features such as power oscillations and singularity formation. The proposed model can be viewed as a discretization of a recently obtained integrable nonlocal nonlinear Schrödinger equation.
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.
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.
Discrete symmetries in covariant loop quantum gravity
NASA Astrophysics Data System (ADS)
Rovelli, Carlo; Wilson-Ewing, Edward
2012-09-01
We study time-reversal and parity—on the physical manifold and in internal space—in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform coherently under such transformations. The classical theory is not affected but the quantum theory is slightly different. In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spin foam to occur only across degenerate regions, thus reducing the sources of potential divergences.
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.
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.
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).
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.
Flavored dark matter beyond Minimal Flavor Violation
Agrawal, Prateek; Blanke, Monika; Gemmler, Katrin
2014-10-13
We study the interplay of flavor and dark matter phenomenology for models of flavored dark matter interacting with quarks. We allow an arbitrary flavor structure in the coupling of dark matter with quarks. This coupling is assumed to be the only new source of violation of the Standard Model flavor symmetry extended by a U(3) χ associated with the dark matter. We call this ansatz Dark Minimal Flavor Violation (DMFV) and highlight its various implications, including an unbroken discrete symmetry that can stabilize the dark matter. As an illustration we study a Dirac fermionic dark matter χ which transforms asmore » triplet under U(3) χ , and is a singlet under the Standard Model. The dark matter couples to right-handed down-type quarks via a colored scalar mediator Φ with a coupling λ. We identify a number of “flavor-safe” scenarios for the structure of λ which are beyond Minimal Flavor Violation. Also, for dark matter and collider phenomenology we focus on the well-motivated case of b-flavored dark matter. Furthermore, the combined flavor and dark matter constraints on the parameter space of λ turn out to be interesting intersections of the individual ones. LHC constraints on simplified models of squarks and sbottoms can be adapted to our case, and monojet searches can be relevant if the spectrum is compressed.« less
Flavored dark matter beyond Minimal Flavor Violation
Agrawal, Prateek; Blanke, Monika; Gemmler, Katrin
2014-10-13
We study the interplay of flavor and dark matter phenomenology for models of flavored dark matter interacting with quarks. We allow an arbitrary flavor structure in the coupling of dark matter with quarks. This coupling is assumed to be the only new source of violation of the Standard Model flavor symmetry extended by a U(3) _{χ} associated with the dark matter. We call this ansatz Dark Minimal Flavor Violation (DMFV) and highlight its various implications, including an unbroken discrete symmetry that can stabilize the dark matter. As an illustration we study a Dirac fermionic dark matter χ which transforms as triplet under U(3) _{χ} , and is a singlet under the Standard Model. The dark matter couples to right-handed down-type quarks via a colored scalar mediator Φ with a coupling λ. We identify a number of “flavor-safe” scenarios for the structure of λ which are beyond Minimal Flavor Violation. Also, for dark matter and collider phenomenology we focus on the well-motivated case of b-flavored dark matter. Furthermore, the combined flavor and dark matter constraints on the parameter space of λ turn out to be interesting intersections of the individual ones. LHC constraints on simplified models of squarks and sbottoms can be adapted to our case, and monojet searches can be relevant if the spectrum is compressed.
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
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.
Minimal Pairs: Minimal Importance?
ERIC Educational Resources Information Center
Brown, Adam
1995-01-01
This article argues that minimal pairs do not merit as much attention as they receive in pronunciation instruction. There are other aspects of pronunciation that are of greater importance, and there are other ways of teaching vowel and consonant pronunciation. (13 references) (VWL)
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.
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…
Discrete Variational Optimal Control
NASA Astrophysics Data System (ADS)
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
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
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.
Compatible, energy and symmetry preserving 2D Lagrangian hydrodynamics in rz-cylindrical coordinates
Shashkov, Mikhail; Wendroff, Burton; Burton, Donald; Barlow, A; Hongbin, Guo
2009-01-01
We present a new discretization for 2D Lagrangian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, energy conserving and symmetry preserving. We describe discretization of the basic Lagrangian hydrodynamics equations.
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
Discrete Time Crystals: Rigidity, Criticality, and Realizations.
Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A
2017-01-20
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Discrete Time Crystals: Rigidity, Criticality, and Realizations
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A.
2017-01-01
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
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.
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.
Human Odometry Verifies the Symmetry Perspective on Bipedal Gaits
ERIC Educational Resources Information Center
Turvey, M. T.; Harrison, Steven J.; Frank, Till D.; Carello, Claudia
2012-01-01
Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias "cells") required to model them. Primary gaits are characterized by dihedral symmetry, whereas secondary gaits are characterized by a lower, cyclic symmetry. This fact was used in a test of human…
Optimal Spatial Harvesting Strategy and Symmetry-Breaking
Kurata, Kazuhiro Shi Junping
2008-08-15
A reaction-diffusion model with logistic growth and constant effort harvesting is considered. By minimizing an intrinsic biological energy function, we obtain an optimal spatial harvesting strategy which will benefit the population the most. The symmetry properties of the optimal strategy are also discussed, and related symmetry preserving and symmetry breaking phenomena are shown with several typical examples of habitats.
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
NASA Astrophysics Data System (ADS)
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
Discretization errors in particle tracking
NASA Astrophysics Data System (ADS)
Carmon, G.; Mamman, N.; Feingold, M.
2007-03-01
High precision video tracking of microscopic particles is limited by systematic and random errors. Systematic errors are partly due to the discretization process both in position and in intensity. We study the behavior of such errors in a simple tracking algorithm designed for the case of symmetric particles. This symmetry algorithm uses interpolation to estimate the value of the intensity at arbitrary points in the image plane. We show that the discretization error is composed of two parts: (1) the error due to the discretization of the intensity, bD and (2) that due to interpolation, bI. While bD behaves asymptotically like N-1 where N is the number of intensity gray levels, bI is small when using cubic spline interpolation.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Spontaneous CP Violation in E6 GUT with horizontal symmetry
NASA Astrophysics Data System (ADS)
Maekawa, Nobuhiro
2010-02-01
We consider spontaneous CP violation in E6 grand unified theory (GUT) with horizontal symmetry and anomalous U(1)A gauge symmetry in order to solve the SUSY CP problem. To realize the sufficiently small phases of SUSY Higgs mass μ and mixing parameter B, an additional discrete symmetry is introduced. The discrete symmetry plays multiple roles in explaining various things. By the symmetry, the up-type Yukawa couplings become real, which is important in satisfying the Chromo-EDM constraints to the imaginary part of the off-diagonal elements of squark mass matrices, and the down-type Yukawa couplings become complex, which is important in obtaining the Kobayashi-Maskawa phase. Moreover, this symmetry improves the smallness of up quark mass, and reduces the number of O(1) coefficients. One of the interesting predictions is Vub˜γ4, which is quite good agreement with the measured value. This talk is based on the works in Ref. [1].
Modeling spontaneous breaking of time-translation symmetry
NASA Astrophysics Data System (ADS)
Sacha, Krzysztof
2015-03-01
We show that an ultracold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time-translation symmetry. In many-body simulations, we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time-translation symmetry.
Two-dimensional discrete Coulomb alloy
NASA Astrophysics Data System (ADS)
Xiao, Yuqing; Thorpe, M. F.; Parkinson, J. B.
1999-01-01
We study an A1-xBx alloy on a two-dimensional triangular lattice. The ions A and B have different charges, with a background charge to ensure neutrality, and are constrained to lie at the discrete sites defined by a fixed triangular lattice. We study the various structures formed at different compositions x by doing computer simulations to find the lowest energy, using an energy minimization scheme, together with simulated annealing. Like ions try to avoid each other because of charge repulsion, which leads to structures, which are very different from those in a random alloy. At low concentrations, a triangular Wigner lattice is formed, which evolves continuously up to a concentration of x=1/3. For higher concentrations, 1/3<=x<=1/2 there are long polymer chains, with occasional branches. We show that there is a symmetry about x=1/2, which is the percolation point for nearest neighbors on the triangular lattice. At certain special stoichiometries, regular superlattices are formed, which usually have a slightly lower energy than a disordered configuration. The powder-diffraction patterns are calculated. The magnetic properties of this structure are also studied, and it is shown that the high-temperature susceptibility could be a useful diagnostic tool, in that it is very sensitive to the number of nearest-neighbor magnetic pairs. This work contributes to a better understanding of layered double hydroxides like Ni1-xAlx(OH)2(CO3)x/2.yH2O.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model
Ferreira, P. M.; Haber, Howard E.; Silva, Joao P.
2009-06-01
We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space, which respects either a Z{sub 2} discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs family symmetries, and that this is not possible for the usual CP symmetry. We comment on the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs family symmetries.
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.
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
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.
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap.
Nakayama, Yu; Ohtsuki, Tomoki
2016-09-23
We use the conformal bootstrap program to derive the necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g., Z_{n}) to continuous symmetry [e.g., U(1)] under the renormalization group flow. In three dimensions, in order for Z_{2} symmetry to be enhanced to U(1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy Δ_{1}>1.08. We also obtain the similar necessary conditions for Z_{3} symmetry with Δ_{1}>0.580 and Z_{4} symmetry with Δ_{1}>0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. As applications, we show that our necessary conditions impose severe constraints on the nature of the chiral phase transition in QCD, the deconfinement criticality in Néel valence bond solid transitions, and anisotropic deformations in critical O(n) models. We prove that some fixed points proposed in the literature are unstable under the perturbation that cannot be forbidden by the discrete symmetry. In these situations, the second-order phase transition with enhanced symmetry cannot happen.
NASA Astrophysics Data System (ADS)
Mackay, Alan L.
1985-04-01
A minimal surface is one for which, like a soap film with the same pressure on each side, the mean curvature is zero and, thus, is one where the two principal curvatures are equal and opposite at every point. For every closed circuit in the surface, the area is a minimum. Schwarz1 and Neovius2 showed that elements of such surfaces could be put together to give surfaces periodic in three dimensions. These periodic minimal surfaces are geometrical invariants, as are the regular polyhedra, but the former are curved. Minimal surfaces are appropriate for the description of various structures where internal surfaces are prominent and seek to adopt a minimum area or a zero mean curvature subject to their topology; thus they merit more complete numerical characterization. There seem to be at least 18 such surfaces3, with various symmetries and topologies, related to the crystallographic space groups. Recently, glyceryl mono-oleate (GMO) was shown by Longley and McIntosh4 to take the shape of the F-surface. The structure postulated is shown here to be in good agreement with an analysis of the fundamental geometry of periodic minimal surfaces.
Novel symmetries in N=2 supersymmetric quantum mechanical models
Malik, R.P.; Khare, Avinash
2013-07-15
We demonstrate the existence of a novel set of discrete symmetries in the context of the N=2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic oscillator. We perform the same exercise for the motion of a charged particle in the X–Y plane under the influence of a magnetic field in the Z-direction. We derive the underlying algebra of the existing continuous symmetry transformations (and corresponding conserved charges) and establish its relevance to the algebraic structures of the de Rham cohomological operators of differential geometry. We show that the discrete symmetry transformations of our present general theories correspond to the Hodge duality operation. Ultimately, we conjecture that any arbitrary N=2 SUSY quantum mechanical system can be shown to be a tractable model for the Hodge theory. -- Highlights: •Discrete symmetries of two completely different kinds of N=2 supersymmetric quantum mechanical models have been discussed. •The discrete symmetries provide physical realizations of Hodge duality. •The continuous symmetries provide the physical realizations of de Rham cohomological operators. •Our work sheds a new light on the meaning of the above abstract operators.
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.
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…
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)
Commutation Relations and Discrete Garnier Systems
NASA Astrophysics Data System (ADS)
Ormerod, Christopher M.; Rains, Eric M.
2016-11-01
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
A Few Continuous and Discrete Dynamical Systems
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Rui, Wenjuan
2016-08-01
Starting from a 2-unimodular group, we construct its new Lie algebras for which the positive-order Lax pairs and the negative-order Lax pairs are introduced, respectively. With the help of the resulting structure equation of the group we generate some partial differential equations including the well-known MKdV equation, the sine-Gordon equation, the hyperbolic sine-Gordon equation and other new nonlinear evolution equations. With the aid of the Tu scheme combined with the given Lax pairs, we obtain the isospectral and nonisospectral hierarchies of evolution equations, from which we generate two sets of symmetries of a generalized nonlinear Schrödinger (gNLS) equation. Finally, we discretize the Lax pairs to obtain a set of coupled semi-discrete equations. As their reduction, we produce the semi-discrete MKdV equation and semi-discrete NLS equation.
ERIC Educational Resources Information Center
Kirchner, Jesse Saba
2010-01-01
This dissertation introduces Minimal Reduplication, a new theory and framework within generative grammar for analyzing reduplication in human language. I argue that reduplication is an emergent property in multiple components of the grammar. In particular, reduplication occurs independently in the phonology and syntax components, and in both cases…
Minimal Doubling and Point Splitting
Creutz, M.
2010-06-14
Minimally-doubled chiral fermions have the unusual property of a single local field creating two fermionic species. Spreading the field over hypercubes allows construction of combinations that isolate specific modes. Combining these fields into bilinears produces meson fields of specific quantum numbers. Minimally-doubled fermion actions present the possibility of fast simulations while maintaining one exact chiral symmetry. They do, however, introduce some peculiar aspects. An explicit breaking of hyper-cubic symmetry allows additional counter-terms to appear in the renormalization. While a single field creates two different species, spreading this field over nearby sites allows isolation of specific states and the construction of physical meson operators. Finally, lattice artifacts break isospin and give two of the three pseudoscalar mesons an additional contribution to their mass. Depending on the sign of this mass splitting, one can either have a traditional Goldstone pseudoscalar meson or a parity breaking Aoki-like phase.
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.
Symmetry-preserving difference schemes for some heat transfer equations
NASA Astrophysics Data System (ADS)
Bakirova, M. I.; Dorodnitsyn, V. A.; Kozlov, R. V.
1997-12-01
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modelling helps to retain qualitative properties of the differential equations in their difference counterparts.
NASA Astrophysics Data System (ADS)
Jiang, Shenghan; Ran, Ying
2017-03-01
We present systematic constructions of tensor-network wave functions for bosonic symmetry-protected topological (SPT) phases respecting both onsite and spatial symmetries. From the classification point of view, our results show that in spatial dimensions d =1 ,2 ,3 , the cohomological bosonic SPT phases protected by a general symmetry group SG involving onsite and spatial symmetries are classified by the cohomology group Hd +1[SG,U(1 ) ] , in which both the time-reversal symmetry and mirror-reflection symmetries should be treated as antiunitary operations. In addition, for every SPT phase protected by a discrete symmetry group and some SPT phases protected by continuous symmetry groups, generic tensor-network wave functions can be constructed which would be useful for the purpose of variational numerical simulations. As a by-product, our results demonstrate a generic connection between rather conventional symmetry-enriched topological phases and SPT phases via an anyon condensation mechanism.
Special relativity in a discrete quantum universe
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-10-01
The hypothesis of a discrete fabric of the universe, the "Planck scale," is always on stage since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for the continuum. Here, we show how the clash can be overcome within a discrete quantum theory where the evolution of fields is described by a quantum cellular automaton. The reconciliation is achieved by defining the change of observer as a change of representation of the dynamics, without any reference to space-time. We use the relativity principle, i.e., the invariance of dynamics under change of inertial observer, to identify a change of inertial frame with a symmetry of the dynamics. We consider the full group of such symmetries, and recover the usual Lorentz group in the relativistic regime of low energies, while at the Planck scale the covariance is nonlinearly distorted.
Symmetry protected topological superfluid (3)He-B.
Mizushima, Takeshi; Tsutsumi, Yasumasa; Sato, Masatoshi; Machida, Kazushige
2015-03-25
Owing to the richness of symmetry and well-established knowledge of bulk superfluidity, the superfluid (3)He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of (3)He in a multifaceted manner, including symmetry considerations, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the (3)He-B confined in a slab geometry. The (3)He-B under a magnetic field is separated to two different sub-phases: the symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of the (3)He nucleus. It is also demonstrated that odd-frequency even-parity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt3 and Rashba superconductors as examples.
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.
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.
NASA Astrophysics Data System (ADS)
Babu, K. S.; Khan, S.
2015-10-01
We present a minimal renormalizable nonsupersymmetric S O (10 ) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 5 4H+12 6H+1 0H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings, and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 1035 yr for proton lifetime, which is not too far from the present Super-Kamiokande limit of τp≳1.29 ×1034 yr . With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong C P problem. The intermediate scale, MI≈(1013- 1014) GeV which is also the B -L scale, is of the right order for the right-handed neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p →e+π0 and p →ν ¯π+. Even though the model predicts no new physics within the reach of the LHC, the next-generation proton decay detectors and axion search experiments have the capability to reach a verdict on this minimal scenario.
On the flexibility and symmetry of overconstrained mechanisms
Stachel, Hellmuth
2014-01-01
In kinematics, a framework is called overconstrained if its continuous flexibility is caused by particular dimensions; in the generic case, a framework of this type is rigid. Famous examples of overconstrained structures are the Bricard octahedra, the Bennett isogram, the Grünbaum framework, Bottema's 16-bar mechanism, Chasles’ body–bar framework, Burmester's focal mechanism or flexible quad meshes. The aim of this paper is to present some examples in detail and to focus on their symmetry properties. It turns out that only for a few is a global symmetry a necessary condition for flexibility. Sometimes, there is a hidden symmetry, and in some cases, for example, at the flexible type-3 octahedra or at discrete Voss surfaces, there is only a local symmetry. However, there remain overconstrained frameworks where the underlying algebraic conditions for flexibility have no relation to symmetry at all. PMID:24379430
Wilson loops in minimal surfaces
Drukker, Nadav; Gross, David J.; Ooguri, Hirosi
1999-04-27
The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.
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.
Broken flavor symmetries in high energy particle phenomenology
Antaramian, Aram
1995-02-22
Over the past couple of decades, the Standard Model of high energy particle physics has clearly established itself as an invaluable tool in the analysis of high energy particle phenomenon. However, from a field theorists point of view, there are many dissatisfying aspects to the model. One of these, is the large number of free parameters in the theory arising from the Yukawa couplings of the Higgs doublet. In this thesis, we examine various issues relating to the Yukawa coupeng structure of high energy particle field theories. We begin by examining extensions to the Standard Model of particle physics which contain additional scalar fields. By appealing to the flavor structure observed in the fermion mass and Kobayashi-Maskawa matrices, we propose a reasonable phenomenological parameterization of the new Yukawa couplings based on the concept of approximate flavor symmetries. It is shown that such a parameterization eliminates the need for discrete symmetries which limit the allowed couplings of the new scalars. New scalar particles which can mediate exotic flavor changing reactions can have masses as low as the weak scale. Next, we turn to the issue of neutrino mass matrices, where we examine a particular texture which leads to matter independent neutrino oscillation results for solar neutrinos. We, then, examine the basis for extremely strict limits placed on flavor changing interactions which also break lepton- and/or baryon-number. These limits are derived from cosmological considerations. Finally, we embark on an extended analysis of proton decay in supersymmetric SO(10) grand unified theories. In such theories, the dominant decay diagrams involve the Yukawa couplings of a heavy triplet superfield. We argue that past calculations of proton decay which were based on the minimal supersymmetric SU(5) model require reexamination because the Yukawa couplings of that theory are known to be wrong.
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.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
NASA Astrophysics Data System (ADS)
Piazza, Federico; Schücker, Thomas
2016-04-01
The minimal requirement for cosmography—a non-dynamical description of the universe—is a prescription for calculating null geodesics, and time-like geodesics as a function of their proper time. In this paper, we consider the most general linear connection compatible with homogeneity and isotropy, but not necessarily with a metric. A light-cone structure is assigned by choosing a set of geodesics representing light rays. This defines a "scale factor" and a local notion of distance, as that travelled by light in a given proper time interval. We find that the velocities and relativistic energies of free-falling bodies decrease in time as a consequence of cosmic expansion, but at a rate that can be different than that dictated by the usual metric framework. By extrapolating this behavior to photons' redshift, we find that the latter is in principle independent of the "scale factor". Interestingly, redshift-distance relations and other standard geometric observables are modified in this extended framework, in a way that could be experimentally tested. An extremely tight constraint on the model, however, is represented by the blackbody-ness of the cosmic microwave background. Finally, as a check, we also consider the effects of a non-metric connection in a different set-up, namely, that of a static, spherically symmetric spacetime.
Noncommutative spaces, the quantum of time, and Lorentz symmetry
Romero, Juan M.; Vergara, J. D.; Santiago, J. A.
2007-03-15
We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are not commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.
Mesonic spectroscopy of minimal walking technicolor
Del Debbio, Luigi; Lucini, Biagio; Patella, Agostino; Pica, Claudio; Rago, Antonio
2010-07-01
We investigate the structure and the novel emerging features of the mesonic nonsinglet spectrum of the minimal walking technicolor theory. Precision measurements in the nonsinglet pseudoscalar and vector channels are compared to the expectations for an IR-conformal field theory and a QCD-like theory. Our results favor a scenario in which minimal walking technicolor is (almost) conformal in the infrared, while spontaneous chiral symmetry breaking seems less plausible.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Generalized Legendre transformations and symmetries of the WDVV equations
NASA Astrophysics Data System (ADS)
Strachan, Ian A. B.; Stedman, Richard
2017-03-01
The Witten–Dijkgraaf–Verlinde–Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class—the so-called Legendre transformations—were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations.
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.
Challenging the minimal supersymmetric SU(5) model
Bajc, Borut; Lavignac, Stéphane; Mede, Timon
2014-06-24
We review the main constraints on the parameter space of the minimal renormalizable supersymmetric SU(5) grand unified theory. They consist of the Higgs mass, proton decay, electroweak symmetry breaking and fermion masses. Superpartner masses are constrained both from below and from above, giving hope for confirming or definitely ruling out the theory in the future. This contribution is based on Ref. [1].
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.
Principles of Discrete Time Mechanics
NASA Astrophysics Data System (ADS)
Jaroszkiewicz, George
2014-04-01
1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.
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.
Constraint analysis for variational discrete systems
Dittrich, Bianca; Höhn, Philipp A.
2013-09-15
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves and naturally incorporates both constant and evolving phase spaces, the latter of which is necessary for a time varying discretization. The different roles of constraints in the discrete and the conditions under which they are first or second class and/or symmetry generators are clarified. The (non-) preservation of constraints and the symplectic structure is discussed; on evolving phase spaces the number of constraints at a fixed time step depends on the initial and final time step of evolution. Moreover, the definition of observables and a reduced phase space is provided; again, on evolving phase spaces the notion of an observable as a propagating degree of freedom requires specification of an initial and final step and crucially depends on this choice, in contrast to the continuum. However, upon restriction to translation invariant systems, one regains the usual time step independence of canonical concepts. This analysis applies, e.g., to discrete mechanics, lattice field theory, quantum gravity models, and numerical analysis.
Observation of a discrete time crystal
NASA Astrophysics Data System (ADS)
Zhang, J.; Hess, P. W.; Kyprianidis, A.; Becker, P.; Lee, A.; Smith, J.; Pagano, G.; Potirniche, I.-D.; Potter, A. C.; Vishwanath, A.; Yao, N. Y.; Monroe, C.
2017-03-01
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a ‘time crystal’ was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a ‘discrete time crystal’. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.
Observation of a discrete time crystal.
Zhang, J; Hess, P W; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I-D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C
2017-03-08
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, including cosmology, particle physics and condensed matter. An example is the breaking of spatial translational symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Using the analogy of crystals in space, the breaking of translational symmetry in time and the emergence of a 'time crystal' was recently proposed, but was later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems, which are subject to a periodic drive, can exhibit persistent time correlations at an emergent subharmonic frequency. This new phase of matter has been dubbed a 'discrete time crystal'. Here we present the experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization conditions, and observe a subharmonic temporal response that is robust to external perturbations. The observation of such a time crystal opens the door to the study of systems with long-range spatio-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.
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.
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.
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
NASA Astrophysics Data System (ADS)
Khan, Saki
2016-06-01
We present a minimal renormalizable non-supersymmetric S O(10) grand unified model with a symmetry breaking sector consisting of Higgs fields in the 54H + 126H + 10H representations. This model admits a single intermediate scale associated with Pati-Salam symmetry along with a discrete parity. Spontaneous symmetry breaking, the unification of gauge couplings and proton lifetime estimates are studied in detail in this framework. Including threshold corrections self-consistently, obtained from a full analysis of the Higgs potential, we show that the model is compatible with the current experimental bound on proton lifetime. The model generally predicts an upper bound of few times 1035 yrs for proton lifetime, which is not too far from the present Super-Kamiokande limit of τp ≳ 1.29 × 1034 yrs. With the help of a Pecci-Quinn symmetry and the resulting axion, the model provides a suitable dark matter candidate while also solving the strong CP problem. The intermediate scale, MI ≈ (1013 - 1014) GeV which is also the B - L scale, is of the right order for the right-handed neutrino mass which enables a successful description of light neutrino masses and oscillations. The Yukawa sector of the model consists of only two matrices in family space and leads to a predictive scenario for quark and lepton masses and mixings. The branching ratios for proton decay are calculable with the leading modes being p → e+π0 and p →v ¯π+ . Even though the model predicts no new physics within the reach of LHC, the next generation proton decay detectors and axion search experiments have the capability to pass verdict on this minimal scenario.
Classically conformal radiative neutrino model with gauged B - L symmetry
NASA Astrophysics Data System (ADS)
Okada, Hiroshi; Orikasa, Yuta
2016-09-01
We propose a classically conformal model in a minimal radiative seesaw, in which we employ a gauged B - L symmetry in the standard model that is essential in order to work the Coleman-Weinberg mechanism well that induces the B - L symmetry breaking. As a result, nonzero Majorana mass term and electroweak symmetry breaking simultaneously occur. In this framework, we show a benchmark point to satisfy several theoretical and experimental constraints. Here theoretical constraints represent inert conditions and Coleman-Weinberg condition. Experimental bounds come from lepton flavor violations (especially μ → eγ), the current bound on the Z‧ mass at the CERN Large Hadron Collider, and neutrino oscillations.
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.
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.
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Synchronous Discrete Harmonic Oscillator
NASA Astrophysics Data System (ADS)
Antippa, Adel F.; Dubois, Daniel M.
2008-10-01
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2π in phase space, is an integral multiple N of the discrete time step Δt. It is fully synchronous when N is even. It is pseudo-synchronous when T/Δt is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is "blue shifted" relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval Δt. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Symmetries, Large Leptonic Mixing and a Fourth Generation
NASA Astrophysics Data System (ADS)
Silva-Marcos, Joaquim I.
2002-12-01
We show that large leptonic mixing occurs most naturally in the framework of the Sandard Model just by adding a fourth generation. One can then construct a small Z4 discrete symmetry, instead of the large S4L × S4R, which requires that the neutrino as well as the charged lepton mass matrices be proportional to a 4 × 4 democratic mass matrix, where all entries are equal to unity. Without considering the see-saw mechanism, or other more elaborate extensions of the SM, and contrary to the case with only 3 generations, large leptonic mixing is obtained when the symmetry is broken.
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)
Discrete dislocations in graphene
NASA Astrophysics Data System (ADS)
Ariza, M. P.; Ortiz, M.
2010-05-01
In this work, we present an application of the theory of discrete dislocations of Ariza and Ortiz (2005) to the analysis of dislocations in graphene. Specifically, we discuss the specialization of the theory to graphene and its further specialization to the force-constant model of Aizawa et al. (1990). The ability of the discrete-dislocation theory to predict dislocation core structures and energies is critically assessed for periodic arrangements of dislocation dipoles and quadrupoles. We show that, with the aid of the discrete Fourier transform, those problems are amenable to exact solution within the discrete-dislocation theory, which confers the theory a distinct advantage over conventional atomistic models. The discrete dislocations exhibit 5-7 ring core structures that are consistent with observation and result in dislocation energies that fall within the range of prediction of other models. The asymptotic behavior of dilute distributions of dislocations is characterized analytically in terms of a discrete prelogarithmic energy tensor. Explicit expressions for this discrete prelogarithmic energy tensor are provided up to quadratures.
NASA Astrophysics Data System (ADS)
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
Mechanochemical Symmetry Breaking in Hydra Aggregates
Mercker, Moritz; Köthe, Alexandra; Marciniak-Czochra, Anna
2015-01-01
Tissue morphogenesis comprises the self-organized creation of various patterns and shapes. Although detailed underlying mechanisms are still elusive in many cases, an increasing amount of experimental data suggests that chemical morphogen and mechanical processes are strongly coupled. Here, we develop and test a minimal model of the axis-defining step (i.e., symmetry breaking) in aggregates of the Hydra polyp. Based on previous findings, we combine osmotically driven shape oscillations with tissue mechanics and morphogen dynamics. We show that the model incorporating a simple feedback loop between morphogen patterning and tissue stretch reproduces a wide range of experimental data. Finally, we compare different hypothetical morphogen patterning mechanisms (Turing, tissue-curvature, and self-organized criticality). Our results suggest the experimental investigation of bigger (i.e., multiple head) aggregates as a key step for a deeper understanding of mechanochemical symmetry breaking in Hydra. PMID:25954896
ERIC Educational Resources Information Center
Peters, James V.
2004-01-01
Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.
ERIC Educational Resources Information Center
Crisler, Nancy; Froelich, Gary
1990-01-01
Discussed are summary recommendations concerning the integration of some aspects of discrete mathematics into existing secondary mathematics courses. Outlines of course activities are grouped into the three levels of prealgebra, algebra, and geometry. Some sample problems are included. (JJK)
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…
Entwinement in discretely gauged theories
NASA Astrophysics Data System (ADS)
Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.
2016-12-01
We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
The Minimal Supersymmetric Fat Higgs Model
Harnik, Roni; Kribs, Graham D.; Larson, Daniel T.; Murayama, Hitoshi
2003-11-26
We present a calculable supersymmetric theory of a composite"fat'" Higgs boson. Electroweak symmetry is broken dynamically through a new gauge interaction that becomes strong at an intermediate scale. The Higgs mass can easily be 200-450 GeV along with the superpartner masses, solving the supersymmetric little hierarchy problem. We explicitly verify that the model is consistent with precision electroweak data without fine-tuning. Gauge coupling unification can be maintained despite the inherently strong dynamics involved in electroweak symmetry breaking. Supersymmetrizing the Standard Model therefore does not imply a light Higgs mass, contrary to the lore in the literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum that is distinctly different from the Minimal Supersymmetric Standard Model.
Esophagectomy - minimally invasive
Minimally invasive esophagectomy; Robotic esophagectomy; Removal of the esophagus - minimally invasive; Achalasia - esophagectomy; Barrett esophagus - esophagectomy; Esophageal cancer - esophagectomy - laparoscopic; Cancer of the ...
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.
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
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.
Mu-tau reflection symmetry with a texture-zero
NASA Astrophysics Data System (ADS)
Nishi, C. C.; Sánchez-Vega, B. L.
2017-01-01
The μτ-reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering. We show that by combining it with a discrete abelian symmetry in a nontrivial way we can additionally enforce a texture-zero and obtain a highly predictive scenario where the lightest neutrino mass is fixed to be in the few meV range for two normal ordering (NO) solutions or in the tens of meV in one inverted ordering (IO) solution. The rate for neutrinoless double beta decay is predicted to be negligible for NO or have effective mass m ββ ≈ 14-29 meV for IO, right in the region to be probed in future experiments.
Strongly broken Peccei-Quinn symmetry in the early Universe
Takahashi, Fuminobu; Yamada, Masaki E-mail: yamadam@icrr.u-tokyo.ac.jp
2015-10-01
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3){sub c} strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Strongly broken Peccei-Quinn symmetry in the early Universe
Takahashi, Fuminobu; Yamada, Masaki
2015-10-06
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3){sub c} strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Strongly broken Peccei-Quinn symmetry in the early Universe
NASA Astrophysics Data System (ADS)
Takahashi, Fuminobu; Yamada, Masaki
2015-10-01
We consider QCD axion models where the Peccei-Quinn symmetry is badly broken by a larger amount in the past than in the present, in order to avoid the axion isocurvature problem. Specifically we study supersymmetric axion models where the Peccei-Quinn symmetry is dynamically broken by either hidden gauge interactions or the SU(3)c strong interactions whose dynamical scales are temporarily enhanced by the dynamics of flat directions. The former scenario predicts a large amount of self-interacting dark radiation as the hidden gauge symmetry is weakly coupled in the present Universe. We also show that the observed amount of baryon asymmetry can be generated by the QCD axion dynamics via spontaneous baryogenesis. We briefly comment on the case in which the PQ symmetry is broken by a non-minimal coupling to gravity.
Supersymmetry, grand unification and flavor symmetry
NASA Astrophysics Data System (ADS)
Enkhbat, Tsedenbaljir
In this thesis I have presented the findings of my research pursued during my Ph.D. study. The purpose of this thesis was to study different theoretical ideas in high energy physics model building addressed primarily towards understanding the fermion mass problem and the gauge hierarchy problem. These include: Anomalous flavor U(1) symmetry and its experimental implications, finite GUT models with discrete family symmetry, and a product GUT model in a 2D deconstructed theory space. The second and third chapters of the thesis describe our study of lepton flavor violation (LFV) and electric dipole moments (EDM) induced by a flavor-dependent anomalous U(1) gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U(1) breaking scale. The fourth chapter of the thesis contains our work on a concrete realization of SUSY breaking using interference between the anomalous U(1) flavor gauge symmetry and a strongly coupled SU(N c), leading to the so called Split SUSY spectrum where the sfermions and the gravitino acquire masses of order 105 ÷ 108 GeV while the gauginos and the Higgsinos have masses of order 102 ÷ 103 GeV. We have calculated the leading order supergravity corrections and have presented a class of explicit models of Split SUSY which are phenomenologically consistent. In the fifth chapter I have presented models for realistic quark masses and mixings in the context of finite SU(5) GUT wherein the beta functions for the gauge and the Yukawa couplings vanish to all orders in perturbation theory. The models presented are based on non-Abelian discrete symmetries. In the case of (Z4)3 x P and A4 symmetries we have found models finite to all order of perturbation theory
PREFACE: Symmetries and Integrability of Difference Equations
NASA Astrophysics Data System (ADS)
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of
NASA Astrophysics Data System (ADS)
Klette, Reinhard; Jiang, Ruyi; Morales, Sandino; Vaudrey, Tobi
Applying computer technology, such as computer vision in driver assistance, implies that processes and data are modeled as being discretized rather than being continuous. The area of stereo vision provides various examples how concepts known in discrete mathematics (e.g., pixel adjacency graphs, belief propagation, dynamic programming, max-flow/min-cut, or digital straight lines) are applied when aiming for efficient and accurate pixel correspondence solutions. The paper reviews such developments for a reader in discrete mathematics who is interested in applied research (in particular, in vision-based driver assistance). As a second subject, the paper also discusses lane detection and tracking, which is a particular task in driver assistance; recently the Euclidean distance transform proved to be a very appropriate tool for obtaining a fairly robust solution.
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.
NASA Astrophysics Data System (ADS)
Allanach, B. C.; Athron, P.; Tunstall, Lewis C.; Voigt, A.; Williams, A. G.
2014-09-01
We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a Z3 symmetry is imposed upon the model. SOFTSUSY can calculate the spectrum in this case as well as the case where general Z3 violating (denoted as =) terms are added to the soft supersymmetry breaking terms and the superpotential. The user provides a theoretical boundary condition for the couplings and mass terms of the singlet. Radiative electroweak symmetry breaking data along with electroweak and CKM matrix data are used as weak-scale boundary conditions. The renormalisation group equations are solved numerically between the weak scale and a high energy scale using a nested iterative algorithm. This paper serves as a manual to the NMSSM mode of the program, detailing the approximations and conventions used. Catalogue identifier: ADPM_v4_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPM_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 154886 No. of bytes in distributed program, including test data, etc.: 1870890 Distribution format: tar.gz Programming language: C++, fortran. Computer: Personal computer. Operating system: Tested on Linux 3.x. Word size: 64 bits Classification: 11.1, 11.6. Does the new version supersede the previous version?: Yes Catalogue identifier of previous version: ADPM_v3_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 785 Nature of problem: Calculating supersymmetric particle spectrum and mixing parameters in the next-to-minimal supersymmetric standard model. The solution to the
Discrete breathers in crystals
NASA Astrophysics Data System (ADS)
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
Minimal covering problem and PLA minimization
Young, M.H.; Muroga, S.
1985-12-01
Solving the minimal covering problem by an implicit enumeration method is discussed. The implicit enumeration method in this paper is a modification of the Quine-McCluskey method tailored to computer processing and also its extension, utilizing some new properties of the minimal covering problem for speedup. A heuristic algorithm is also presented to solve large-scale problems. Its application to the minimization of programmable logic arrays (i.e., PLAs) is shown as an example. Computational experiences are presented to confirm the improvements by the implicit enumeration method discussed.
Discrete gap solitons in nonlinear binary plasmonic waveguide arrays
NASA Astrophysics Data System (ADS)
Yan, Jie-Yun
2015-03-01
We investigate plasmonic mode propagation in nonlinear binary plasmonic waveguide arrays composed of two kinds of metal slabs alternately embedded in nonlinear dielectric materials, and numerically obtain soliton solutions with different symmetries. In particular, we find discrete gap solitons with strong transverse confinements reaching the scale of 10 nm. The equations to describe the mode propagations indicate that the system also provides a plasmonic platform to simulate aspects of quantum dynamics.
Unification mechanism for gauge and spacetime symmetries
NASA Astrophysics Data System (ADS)
László, András
2017-03-01
A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so called Levi factor of the gauge group needs to be compact semisimple, not the entire gauge group. This allows a non-conventional supersymmetry-like extension of the gauge group, glueing together the gauge and spacetime symmetries, but not needing any new exotic gauge particles. It is shown that this new relaxed requirement on the gauge group is nothing but the minimal condition for energy positivity. The mechanism is demonstrated to be mathematically possible and physically plausible on a \\text{U}(1) based gauge theory setting. The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman–Mandula no-go theorems in a non-supersymmetric way.
Radiatively broken symmetries of nonhierarchical neutrinos
NASA Astrophysics Data System (ADS)
Dighe, Amol; Goswami, Srubabati; Roy, Probir
2007-11-01
Symmetry-based ideas, such as the quark-lepton complementarity principle and the tribimaximal mixing scheme, have been proposed to explain the observed mixing pattern of neutrinos. We argue that such symmetry relations need to be imposed at a high scale Λ˜1012GeV characterizing the large masses of right-handed neutrinos required to implement the seesaw mechanism. For nonhierarchical neutrinos, renormalization group evolution down to a laboratory energy scale λ˜103GeV tends to radiatively break these symmetries at a significant level and spoil the mixing pattern predicted by them. However, for Majorana neutrinos, suitable constraints on the extra phases α2,3 enable the retention of those high scale mixing patterns at laboratory energies. We examine this issue within the minimal supersymmetric standard model and demonstrate the fact posited above for two versions of quark-lepton complementarity and two versions of tribimaximal mixing. The appropriate constraints are worked out for all these four cases. Specifically, a preference for α2≈π (i.e., m1≈-m2) emerges in each case. We also show how a future accurate measurement of θ13 may enable some discrimination among these four cases in spite of renormalization group evolution.
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
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.
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.
NASA Astrophysics Data System (ADS)
Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel
2009-11-01
The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first
Makris, Konstantinos G; Suntsov, Sergiy; Christodoulides, Demetrios N; Stegeman, George I; Hache, Alain
2005-09-15
It is theoretically shown that discrete nonlinear surface waves are possible in waveguide lattices. These self-trapped states are located at the edge of the array and can exist only above a certain power threshold. The excitation characteristics and stability properties of these surface waves are systematically investigated.
[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.
3D toroidal physics: Testing the boundaries of symmetry breaking
Spong, Donald A.
2015-05-15
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
3D toroidal physics: Testing the boundaries of symmetry breakinga)
NASA Astrophysics Data System (ADS)
Spong, Donald A.
2015-05-01
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to provide the plasma control needed for a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D edge localized mode suppression fields to stellarators with more dominant 3D field structures. This motivates the development of physics models that are applicable across the full range of 3D devices. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with the requirements of future fusion reactors.
Observable T{sub 7} Lepton Flavor Symmetry at the Large Hadron Collider
Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-04-01
More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T{sub 7} and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.
Symmetry Protection of Critical Phases and a Global Anomaly in 1 +1 Dimensions
NASA Astrophysics Data System (ADS)
Furuya, Shunsuke C.; Oshikawa, Masaki
2017-01-01
We derive a selection rule among the (1 +1 )-dimensional SU(2) Wess-Zumino-Witten theories, based on the global anomaly of the discrete Z2 symmetry found by Gepner and Witten. In the presence of both the SU(2) and Z2 symmetries, a renormalization-group flow is possible between level-k and level-k' Wess-Zumino-Witten theories only if k ≡k' mod 2 . This classifies the Lorentz-invariant, SU(2)-symmetric critical behavior into two "symmetry-protected" categories corresponding to even and odd levels, restricting possible gapless critical behavior of translation-invariant quantum spin chains.
Quantum Algorithms, Symmetry, and Fourier Analysis
NASA Astrophysics Data System (ADS)
Denney, Aaron
I describe the role of symmetry in two quantum algorithms, with a focus on how that symmetry is made manifest by the Fourier transform. The Fourier transform can be considered in a wider context than the familiar one of functions on
... seen under a very powerful microscope called an electron microscope. Minimal change disease is the most common ... biopsy and examination of the tissue with an electron microscope can show signs of minimal change disease.
NASA Astrophysics Data System (ADS)
Maletti, Andreas
Hyper-minimization aims to compute a minimal deterministic finite automaton (dfa) that recognizes the same language as a given dfa up to a finite number of errors. Algorithms for hyper-minimization that run in time O(n logn), where n is the number of states of the given dfa, have been reported recently in [Gawrychowski and Jeż: Hyper-minimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n logn algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. These algorithms are improved to return a hyper-minimal dfa that commits the least number of errors. This closes another open problem of [Badr, Geffert, and Shipman: Hyper-minimizing minimized deterministic finite state automata. Rairo Theor. Inf. Appl. 43, 2009]. Unfortunately, the time complexity for the obtained algorithm increases to O(n 2).
Epitaxy on Substrates with Hexagonal Lattice Symmetry.
NASA Astrophysics Data System (ADS)
Braun, Max Willi Hermann
A general description of epitaxy between thin films and substrates of general symmetry was developed from a model with rigid substrate and overgrowth and extended to include strain of the overgrowth. The overgrowth-substrate interaction was described by Fourier series, usually truncated, defined on the reciprocal lattice of the interface surfaces of the crystals. Energy considerations lead directly to a criterion that epitaxial configurations occur when a pair of surface reciprocal lattice vectors of the substrate and overgrowth coincide, equivalent to atomic row matching. This is analogous to the von Laue criterion and Bragg equations of diffraction theory, with a geometrical realization related to the Ewald construction. When generalized, misfit strain, the spacing, line sense and Burgers vectors of misfit dislocations and misfit verniers are obtained from the reciprocal lattices of crystals with any symmetry and misfit. The most general structures can be described with convenient unit cells by using structure factors. Homogeneous misfit strain, the interfacial atom positions after local relaxation and misfit and elastic (harmonic approximation) strain energies were obtained by direct minimization of the total interfacial energy of a large (1105 atoms), but finite, system. The local relaxation was calculated with a Finite Element formulation. Systems with fcc {111 } or bcc{ 110} overgrowths on fcc {111} or hcp{0001} substrates were studied with respect to substrate symmetry, overgrowth size and anisotropy of the overgrowth elastic constants. Configurations such as Kurdjumov-Sachs (KS), Nishiyama-Wassermann (NW) and a pseudomorphic phase (2DC) were explained, while several other higher order configurations were predicted. The inherent difference in nature between the KS and NW and their relationship to the 2DC were emphasized. Deviations from the ideal orientation of KS linked to anisotropy for systems undergoing misfit strain were discovered. Deviations were also
Increasingly minimal bias routing
Bataineh, Abdulla; Court, Thomas; Roweth, Duncan
2017-02-21
A system and algorithm configured to generate diversity at the traffic source so that packets are uniformly distributed over all of the available paths, but to increase the likelihood of taking a minimal path with each hop the packet takes. This is achieved by configuring routing biases so as to prefer non-minimal paths at the injection point, but increasingly prefer minimal paths as the packet proceeds, referred to herein as Increasing Minimal Bias (IMB).
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)
Discrete canonical analysis of three-dimensional gravity with cosmological constant
NASA Astrophysics Data System (ADS)
Berra-Montiel, J.; E. Rosales-Quintero, J.
2015-05-01
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, correspond to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.
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.
Discretized Abelian Chern-Simons gauge theory on arbitrary graphs
NASA Astrophysics Data System (ADS)
Sun, Kai; Kumar, Krishna; Fradkin, Eduardo
2015-09-01
In this paper, we show how to discretize the Abelian Chern-Simons gauge theory on generic planar lattices/graphs (with or without translational symmetries) embedded in arbitrary two-dimensional closed orientable manifolds. We find that, as long as a one-to-one correspondence between vertices and faces can be defined on the graph such that each face is paired up with a neighboring vertex (and vice versa), a discretized Abelian Chern-Simons theory can be constructed consistently. We further verify that all the essential properties of the Chern-Simons gauge theory are preserved in the discretized setup. In addition, we find that the existence of such a one-to-one correspondence is not only a sufficient condition for discretizing a Chern-Simons gauge theory but, for the discretized theory to be nonsingular and to preserve some key properties of the topological field theory, this correspondence is also a necessary one. A specific example will then be provided, in which we discretize the Abelian Chern-Simons gauge theory on a tetrahedron.
Higher-order discrete variational problems with constraints
NASA Astrophysics Data System (ADS)
Colombo, Leonardo; Martín de Diego, David; Zuccalli, Marcela
2013-09-01
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this paper, we derive new variational integrators for higher-order Lagrangian mechanical system subjected to higher-order constraints. From the discretization of the variational principles, we show that our methods are automatically symplectic and, in consequence, with a very good energy behavior. Additionally, the symmetries of the discrete Lagrangian imply that momentum is conserved by the integrator. Moreover, we extend our construction to variational integrators where the Lagrangian is explicitly time-dependent. Finally, some motivating applications of higher-order problems are considered; in particular, optimal control problems for explicitly time-dependent underactuated systems and an interpolation problem on Riemannian manifolds.
Applications of flavor symmetry to the phenomenology of elementary particles
Kaeding, Thomas A.
1995-05-01
Some applications of flavor symmetry are examined. Approximate flavor symmetries and their consequences in the MSSM (Minimal Supersymmetric Standard Model) are considered, and found to give natural values for the possible B- and L-violating couplings that are empirically acceptable, except for the case of proton decay. The coupling constants of SU(3) are calculated and used to parameterize the decays of the D mesons in broken flavor SU(3). The resulting couplings are used to estimate the long-distance contributions to D-meson mixing.
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.)
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…
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.
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.
Steerable Discrete Fourier Transform
NASA Astrophysics Data System (ADS)
Fracastoro, Giulia; Magli, Enrico
2017-03-01
Directional transforms have recently raised a lot of interest thanks to their numerous applications in signal compression and analysis. In this letter, we introduce a generalization of the discrete Fourier transform, called steerable DFT (SDFT). Since the DFT is used in numerous fields, it may be of interest in a wide range of applications. Moreover, we also show that the SDFT is highly related to other well-known transforms, such as the Fourier sine and cosine transforms and the Hilbert transforms.
The Discrete Wavelet Transform
1991-06-01
Split- Band Coding," Proc. ICASSP, May 1977, pp 191-195. 12. Vetterli, M. "A Theory of Multirate Filter Banks ," IEEE Trans. ASSP, 35, March 1987, pp 356...both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one’s choice of filters . In...B-1 ,.iii FIGURES 1.1 A wavelet filter bank structure ..................................... 2 2.1 Diagram illustrating the dialation and
A paradigm for discrete physics
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
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.
Samoylovich, Mikhail; Talis, Alexander
2014-03-01
The chain of algebraic geometry and topology constructions is mapped on a structural level that allows one to single out a special class of discrete helicoidal structures. A structure that belongs to this class is locally periodic, topologically stable in three-dimensional Euclidean space and corresponds to the bifurcation domain. Singular points of its bounding minimal surface are related by transformations determined by symmetries of the second coordination sphere of the eight-dimensional crystallographic lattice E8. These points represent cluster vertices, whose helicoid joining determines the topology and structural parameters of linear biopolymers. In particular, structural parameters of the α-helix are determined by the seven-vertex face-to-face joining of tetrahedra with the E8 non-integer helical axis 40/11 having a rotation angle of 99°, and the development of its surface coincides with the cylindrical development of the α-helix. Also, packing models have been created which determine the topology of the A, B and Z forms of DNA.
Near minimally normed spline quasi-interpolants on uniform partitions
NASA Astrophysics Data System (ADS)
Barrera, D.; Ibanez, M. J.; Sablonniere, P.; Sbibih, D.
2005-09-01
Spline quasi-interpolants (QIs) are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline QIs on uniform partitions of the real line having small infinity norms. We call them near minimally normed QIs: they are exact on polynomial spaces and minimize a simple upper bound of their infinity norms. We give precise results for cubic and quintic QIs. Also the QI error is considered, as well as the advantage that these QIs present when approximating functions with isolated discontinuities.
Symmetries and vanishing couplings in string-derived low energy effective field theory
Kobayashi, Tatsuo
2012-07-27
We study 4D low-energy effective field theory, derived from heterotic string theory on the orbifolds. In particular, we study Abelian and non-Abelian discrete symmetries and their anomalies. Furthermore, stringy computations also provide with stringy coupling selection rules.
Symmetry of the d-vector hedgehogs in superfluid 3HeA
NASA Astrophysics Data System (ADS)
Salomaa, M. M.
1990-08-01
Core structures of axisymmetric ď-vector monopole states in superfluid 3HeA are classified in terms of discrete symmetries. The pointlike order-parameter singularity may be resolved via the formation of a topologically stable half-integer disclination ring; phase transitions may occur between these ď-hedgehogs.
Discretization of the Schwarzian derivative
NASA Astrophysics Data System (ADS)
Itoh, Toshiaki
2016-10-01
Numerical treatment of the Schwarzian derivatives from the exact discretization point is useful for many applications. Since we found the discrete counterpart of Schwarzian derivative is the Cross-ratio, we can regard the Cross-ratio to the discrete conformal mapping function instead of the Schwarzian derivative. By this approach we found some integrable system of special functions are derived by the classical treatment of 2nd order ODE and difference equations. Such discrete integrable system is composed of simultameous equation of the two Möbius transformations or discrete Riccati's eqautions.
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
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.
Optimization of Operations Resources via Discrete Event Simulation Modeling
NASA Technical Reports Server (NTRS)
Joshi, B.; Morris, D.; White, N.; Unal, R.
1996-01-01
The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.
Minimizing Classroom Interruptions.
ERIC Educational Resources Information Center
Partin, Ronald L.
1987-01-01
Offers suggestions for minimizing classroom interruptions, such as suggesting to the principal that announcements not be read over the intercom during class time and arranging desks and chairs so as to minimize visual distractions. Contains a school interruption survey form. (JC)
E6 inspired supersymmetric models with exact custodial symmetry
NASA Astrophysics Data System (ADS)
Nevzorov, Roman
2013-01-01
The breakdown of E6 gauge symmetry at high energies may lead to supersymmetric models based on the standard model gauge group together with extra U(1)ψ and U(1)χ gauge symmetries. To ensure anomaly cancellation the particle content of these E6 inspired models involves extra exotic states that generically give rise to nondiagonal flavor transitions and rapid proton decay. We argue that a single discrete Z˜2H symmetry can be used to forbid tree-level flavor changing transitions, as well as the most dangerous baryon and lepton number violating operators. We present 5D and 6D orbifold grand unified theory constructions that lead to the E6 inspired supersymmetric models of this type. The breakdown of U(1)ψ and U(1)χ gauge symmetries that preserves E6 matter parity assignment guarantees that ordinary quarks and leptons and their superpartners, as well as the exotic states which originate from 27 representations of E6, survive to low energies. These E6 inspired models contain two dark matter candidates and must also include additional TeV scale vectorlike lepton or vectorlike down-type quark states to render the lightest exotic quark unstable. We examine gauge coupling unification in these models and discuss their implications for collider phenomenology and cosmology.
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.
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.
Casimir effect at finite temperature for pure-photon sector of the minimal Standard Model Extension
NASA Astrophysics Data System (ADS)
Santos, A. F.; Khanna, Faqir C.
2016-12-01
Dynamics between particles is governed by Lorentz and CPT symmetry. There is a violation of Parity (P) and CP symmetry at low levels. The unified theory, that includes particle physics and quantum gravity, may be expected to be covariant with Lorentz and CPT symmetry. At high enough energies, will the unified theory display violation of any symmetry? The Standard Model Extension (SME), with Lorentz and CPT violating terms, has been suggested to include particle dynamics. The minimal SME in the pure photon sector is considered in order to calculate the Casimir effect at finite temperature.
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.
Error minimizing algorithms for nearest eighbor classifiers
Porter, Reid B; Hush, Don; Zimmer, G. Beate
2011-01-03
Stack Filters define a large class of discrete nonlinear filter first introd uced in image and signal processing for noise removal. In recent years we have suggested their application to classification problems, and investigated their relationship to other types of discrete classifiers such as Decision Trees. In this paper we focus on a continuous domain version of Stack Filter Classifiers which we call Ordered Hypothesis Machines (OHM), and investigate their relationship to Nearest Neighbor classifiers. We show that OHM classifiers provide a novel framework in which to train Nearest Neighbor type classifiers by minimizing empirical error based loss functions. We use the framework to investigate a new cost sensitive loss function that allows us to train a Nearest Neighbor type classifier for low false alarm rate applications. We report results on both synthetic data and real-world image data.
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; Tartakovsky, Daniel M.
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
Supersymmetric parameter space of family symmetries
Velasco-Sevilla, L.
2008-11-23
In this talk I have emphasized the effects of considering departures from the minimal flavour violation conditions, in the context of CMSSM-like theories, introduced by boundary conditions at GUT scale from Family Symmetries. In [1] we have shown the results of running these conditions down to EW, where constraints from fermion masses and CKM matrix elements have been used. Only when the expansion parameter in the sdown-squark sector is relatively large it is possible to relax the lower limit from b{yields}s{gamma} on the universal gaugino mass. The expansion parameter associated with the slepton sector needs to be smaller than the analogous in the sdown-squark sector in order to satisfy the bound imposed by the decay of {tau}{yields}{mu}{mu}.
Symmetries in Three-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
Bashkirov, Denis
Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].
Evidence for a Phase with Broken Translational Symmetry
Emelyanov, S. A.; Ivanov, S. V.
2011-12-23
We report on the discovering of a quantum phase which possesses neither continuous nor discrete translational symmetry. The phase emerges from the Quantum Hall state of matter and is induced by a toroidal moment which is a cross product of 'built-in' transverse electric field and tilted quantizing magnetic field. The phase is detected by the method of terahertz photo-voltaic spectroscopy which is insensitive to the vast majority of electrons remaining in conventional Quantum Hall states. The electrons in the new phase are demonstrated to have spatially-separated macroscopic-scale orbitlike wavefunctions distributed over a macroscopic sample with no spatial periodicity.
Minimal Left-Right Symmetric Dark Matter.
Heeck, Julian; Patra, Sudhanwa
2015-09-18
We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z_{2} subgroup of B-L. Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for SU(2)×SU(2)×U(1) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV.
Minimal flavor violation in the minimal U(1)B-L model and resonant leptogenesis
NASA Astrophysics Data System (ADS)
Okada, Nobuchika; Orikasa, Yuta; Yamada, Toshifumi
2012-10-01
We investigate the resonant leptogenesis scenario in the minimally U(1)B-L extended standard model with minimal flavor violation. In our model, the U(1)B-L gauge symmetry is broken at the TeV scale and standard model singlet neutrinos gain Majorana masses of order TeV. In addition, we introduce a flavor symmetry on the singlet neutrinos at a scale higher than TeV. The flavor symmetry is explicitly broken by the neutrino Dirac Yukawa coupling, which induces splittings in the singlet neutrino Majorana masses at lower scales through renormalization group evolutions. We call this setup minimal flavor violation. The mass splittings are proportional to the tiny Dirac Yukawa coupling, and hence they automatically enhance the CP asymmetry parameter necessary for the resonant leptogenesis mechanism. In this paper, we calculate the baryon number yield by solving the Boltzmann equations, including the effects of U(1)B-L gauge boson that also has TeV scale mass and causes washing-out of the singlet neutrinos in the course of thermal leptogenesis. The Dirac Yukawa coupling for neutrinos is fixed in terms of neutrino oscillation data and an arbitrary 3×3 complex-valued orthogonal matrix. We show that the right amount of baryon number asymmetry can be achieved through thermal leptogenesis in the context of the minimal flavor violation with singlet neutrinos and U(1)B-L gauge boson at the TeV scale. These particles can be discovered at the LHC in the near future.
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
Manpower Analysis Using Discrete Simulation
2015-12-01
building using Discrete Event Simulation (DES) and experimentation using Design of Experiments (DOE). We derived five metamodels to identify the most...objectives were met. 14. SUBJECT TERMS manpower policy analysis, discrete event simulation, Simkit 15. NUMBER OF PAGES 85 16. PRICE CODE 17. SECURITY...using Discrete Event Simulation (DES) and experimentation using Design of Experiments (DOE). We derived five metamodels to identify the most
Houbraken, Maarten; Demeyer, Sofie; Michoel, Tom; Audenaert, Pieter; Colle, Didier; Pickavet, Mario
2014-01-01
Subgraph matching algorithms are used to find and enumerate specific interconnection structures in networks. By enumerating these specific structures/subgraphs, the fundamental properties of the network can be derived. More specifically in biological networks, subgraph matching algorithms are used to discover network motifs, specific patterns occurring more often than expected by chance. Finding these network motifs yields information on the underlying biological relations modelled by the network. In this work, we present the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS), an improved version of the Index-based Subgraph Matching Algorithm (ISMA). ISMA quickly finds all instances of a predefined motif in a network by intelligently exploring the search space and taking into account easily identifiable symmetric structures. However, more complex symmetries (possibly involving switching multiple nodes) are not taken into account, resulting in superfluous output. ISMAGS overcomes this problem by using a customised symmetry analysis phase to detect all symmetric structures in the network motif subgraphs. These structures are then converted to symmetry-breaking constraints used to prune the search space and speed up calculations. The performance of the algorithm was tested on several types of networks (biological, social and computer networks) for various subgraphs with a varying degree of symmetry. For subgraphs with complex (multi-node) symmetric structures, high speed-up factors are obtained as the search space is pruned by the symmetry-breaking constraints. For subgraphs with no or simple symmetric structures, ISMAGS still reduces computation times by optimising set operations. Moreover, the calculated list of subgraph instances is minimal as it contains no instances that differ by only a subgraph symmetry. An implementation of the algorithm is freely available at https://github.com/mhoubraken/ISMAGS. PMID:24879305
Thermodynamics of discrete quantum processes
NASA Astrophysics Data System (ADS)
Anders, Janet; Giovannetti, Vittorio
2013-03-01
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Discrete Pearson distributions
Bowman, K.O.; Shenton, L.R.; Kastenbaum, M.A.
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Discrete bisoliton fiber laser
Liu, X. M.; Han, X. X.; Yao, X. K.
2016-01-01
Dissipative solitons, which result from the intricate balance between dispersion and nonlinearity as well as gain and loss, are of the fundamental scientific interest and numerous important applications. Here, we report a fiber laser that generates bisoliton – two consecutive dissipative solitons that preserve a fixed separation between them. Deviations from this separation result in its restoration. It is also found that these bisolitons have multiple discrete equilibrium distances with the quantized separations, as is confirmed by the theoretical analysis and the experimental observations. The main feature of our laser is the anomalous dispersion that is increased by an order of magnitude in comparison to previous studies. Then the spectral filtering effect plays a significant role in pulse-shaping. The proposed laser has the potential applications in optical communications and high-resolution optics for coding and transmission of information in higher-level modulation formats. PMID:27767075
Discrete Reliability Projection
2014-12-01
Defense, Handbook MIL - HDBK -189C, 2011 Hall, J. B., Methodology for Evaluating Reliability Growth Programs of Discrete Systems, Ph.D. thesis, University...pk,i ] · [ 1− (1− θ̆k) · ( N k · T )]k−m , (2.13) 5 2 Hall’s Model where m is the number of observed failure modes and d∗i estimates di (either based...Mode Failures FEF Ni d ∗ i 1 1 0.95 2 1 0.70 3 1 0.90 4 1 0.90 5 4 0.95 6 2 0.70 7 1 0.80 Using equations 2.1 and 2.2 we can calculate the failure
Noyes, H.P. ); Starson, S. )
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
NASA Astrophysics Data System (ADS)
Noyes, H. Pierre; Starson, Scott
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields with the relativistic Wheeler-Feynman action at a distance, allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound.
Discrete bisoliton fiber laser
NASA Astrophysics Data System (ADS)
Liu, X. M.; Han, X. X.; Yao, X. K.
2016-10-01
Dissipative solitons, which result from the intricate balance between dispersion and nonlinearity as well as gain and loss, are of the fundamental scientific interest and numerous important applications. Here, we report a fiber laser that generates bisoliton – two consecutive dissipative solitons that preserve a fixed separation between them. Deviations from this separation result in its restoration. It is also found that these bisolitons have multiple discrete equilibrium distances with the quantized separations, as is confirmed by the theoretical analysis and the experimental observations. The main feature of our laser is the anomalous dispersion that is increased by an order of magnitude in comparison to previous studies. Then the spectral filtering effect plays a significant role in pulse-shaping. The proposed laser has the potential applications in optical communications and high-resolution optics for coding and transmission of information in higher-level modulation formats.
Immigration and Prosecutorial Discretion.
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration.
Steerable Discrete Cosine Transform
NASA Astrophysics Data System (ADS)
Fracastoro, Giulia; Fosson, Sophie M.; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.
Steerable Discrete Cosine Transform.
Fracastoro, Giulia; Fosson, Sophie M; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely, a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.
Nonintegrable Schrodinger discrete breathers.
Gómez-Gardeñes, J; Floría, L M; Peyrard, M; Bishop, A R
2004-12-01
In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrödinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.
Immigration and Prosecutorial Discretion
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
2015-01-01
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration. PMID:26146530
Minimizing Input-to-Output Latency in Virtual Environment
NASA Technical Reports Server (NTRS)
Adelstein, Bernard D.; Ellis, Stephen R.; Hill, Michael I.
2009-01-01
A method and apparatus were developed to minimize latency (time delay ) in virtual environment (VE) and other discrete- time computer-base d systems that require real-time display in response to sensor input s. Latency in such systems is due to the sum of the finite time requi red for information processing and communication within and between sensors, software, and displays.
Peyton, B.W.
1999-07-01
When minimum orderings proved too difficult to deal with, Rose, Tarjan, and Leuker instead studied minimal orderings and how to compute them (Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5:266-283, 1976). This paper introduces an algorithm that is capable of computing much better minimal orderings much more efficiently than the algorithm in Rose et al. The new insight is a way to use certain structures and concepts from modern sparse Cholesky solvers to re-express one of the basic results in Rose et al. The new algorithm begins with any initial ordering and then refines it until a minimal ordering is obtained. it is simple to obtain high-quality low-cost minimal orderings by using fill-reducing heuristic orderings as initial orderings for the algorithm. We examine several such initial orderings in some detail.
Hellinger, Michael D; Al Haddad, Abdullah
2008-02-01
Traditionally, stoma creation and end stoma reversal have been performed via a laparotomy incision. However, in many situations, stoma construction may be safely performed in a minimally invasive nature. This may include a trephine, laparoscopic, or combined approach. Furthermore, Hartmann's colostomy reversal, a procedure traditionally associated with substantial morbidity, may also be performed laparoscopically. The authors briefly review patient selection, preparation, and indications, and focus primarily on surgical techniques and results of minimally invasive stoma creation and Hartmann's reversal.
Minimally invasive lumbar foraminotomy.
Deutsch, Harel
2013-07-01
Lumbar radiculopathy is a common problem. Nerve root compression can occur at different places along a nerve root's course including in the foramina. Minimal invasive approaches allow easier exposure of the lateral foramina and decompression of the nerve root in the foramina. This video demonstrates a minimally invasive approach to decompress the lumbar nerve root in the foramina with a lateral to medial decompression. The video can be found here: http://youtu.be/jqa61HSpzIA.
On global minimizers of repulsive–attractive power-law interaction energies
Carrillo, José Antonio; Chipot, Michel; Huang, Yanghong
2014-01-01
We consider the minimization of the repulsive–attractive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations. PMID:25288810
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 .
Non-thermal leptogenesis with distinct CP violation and minimal dark matter
NASA Astrophysics Data System (ADS)
Zhou, Hang; Gu, Pei-Hong
2017-01-01
We demonstrate a unified scenario for neutrino mass, baryon asymmetry, dark matter and inflation. In addition to a fermion triplet for the so-called minimal dark matter, we extend the standard model by three heavy fields including a scalar singlet, a fermion triplet and a fermion singlet/Higgs triplet. The heavy scalar singlet, which is expected to drive an inflation, and the dark matter fermion triplet are odd under an unbroken Z2 discrete symmetry, while the other fields are all even. The heavy fermion triplet offers a tree-level type-III seesaw and then mediates a three-body decay of the inflaton into the standard model lepton and Higgs doublets with the dark matter fermion triplet. The heavy fermion singlet/Higgs triplet not only results in a type-I/II seesaw at tree level but also contributes to the inflaton decay at one-loop level. In this scenario, the type-I/II seesaw contains all of the physical CP phases in the lepton sector and hence the CP violation for the non-thermal leptogenesis by the inflaton decay exactly comes from the imaginary part of the neutrino mass matrix.
Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, A.; Karpathopoulos, L.; Wojnar, A.; Capozziello, S.
2016-04-01
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
Discrete Mathematics and Its Applications
ERIC Educational Resources Information Center
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Infinitesimal Legendre symmetry in the Geometrothermodynamics programme
García-Peláez, D.; López-Monsalvo, C. S.
2014-08-15
The work within the Geometrothermodynamics programme rests upon the metric structure for the thermodynamic phase-space. Such structure exhibits discrete Legendre symmetry. In this work, we study the class of metrics which are invariant along the infinitesimal generators of Legendre transformations. We solve the Legendre-Killing equation for a K-contact general metric. We consider the case with two thermodynamic degrees of freedom, i.e., when the dimension of the thermodynamic phase-space is five. For the generic form of contact metrics, the solution of the Legendre-Killing system is unique, with the sole restriction that the only independent metric function – Ω – should be dragged along the orbits of the Legendre generator. We revisit the ideal gas in the light of this class of metrics. Imposing the vanishing of the scalar curvature for this system results in a further differential equation for the metric function Ω which is not compatible with the Legendre invariance constraint. This result does not allow us to use Quevedo's interpretation of the curvature scalar as a measure of thermodynamic interaction for this particular class.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.
2014-11-01
We consider 3D Euler fluids endowed with a discrete symmetry whereby the velocity field is invariant under mirror reflections about a 2D surface known as the ``symmetry plane.'' This type of flow is widely used in numerical simulations of classical/magnetic/quantum turbulence and vortex reconnection. On the 2D symmetry plane, the governing equations are best written in terms of two scalars: vorticity and stretching rate of vorticity. These determine the velocity field on the symmetry plane. However, the governing equations are not closed, because of the contribution of a single pressure term that depends on the full 3D velocity profile. By modelling this pressure term we propose a one-parameter family of sensible models for the flow along the 2D symmetry plane. We apply the method of infinitesimal Lie symmetries and solve the governing equations analytically for the two scalars as functions of time. We show how the value of the model's parameter determines if the analytical solution has a finite-time blowup and obtain explicit formulae for the blowup time. We validate the models by showing that a particular choice of the model's parameter corresponds to a well-known exact solution of 3D Euler equations [Gibbon et al., Physica D 132, 497 (1999)]. We discuss practical applications. Supported by Science Foundation Ireland (SFI) under Grant Number 12/IP/1491.
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.
Dual-BRST symmetry: 6D Abelian 3-form gauge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2012-04-01
Within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5+1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.
Novel symmetries in the modified version of two dimensional Proca theory
NASA Astrophysics Data System (ADS)
Bhanja, T.; Shukla, D.; Malik, R. P.
2013-08-01
By exploiting Stueckelberg's approach, we obtain a gauge theory for the two-dimensional, that is, (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.
Baltayiannis, Nikolaos; Michail, Chandrinos; Lazaridis, George; Anagnostopoulos, Dimitrios; Baka, Sofia; Mpoukovinas, Ioannis; Karavasilis, Vasilis; Lampaki, Sofia; Papaiwannou, Antonis; Karavergou, Anastasia; Kioumis, Ioannis; Pitsiou, Georgia; Katsikogiannis, Nikolaos; Tsakiridis, Kosmas; Rapti, Aggeliki; Trakada, Georgia; Zissimopoulos, Athanasios; Zarogoulidis, Konstantinos
2015-01-01
Minimally invasive procedures, which include laparoscopic surgery, use state-of-the-art technology to reduce the damage to human tissue when performing surgery. Minimally invasive procedures require small “ports” from which the surgeon inserts thin tubes called trocars. Carbon dioxide gas may be used to inflate the area, creating a space between the internal organs and the skin. Then a miniature camera (usually a laparoscope or endoscope) is placed through one of the trocars so the surgical team can view the procedure as a magnified image on video monitors in the operating room. Specialized equipment is inserted through the trocars based on the type of surgery. There are some advanced minimally invasive surgical procedures that can be performed almost exclusively through a single point of entry—meaning only one small incision, like the “uniport” video-assisted thoracoscopic surgery (VATS). Not only do these procedures usually provide equivalent outcomes to traditional “open” surgery (which sometimes require a large incision), but minimally invasive procedures (using small incisions) may offer significant benefits as well: (I) faster recovery; (II) the patient remains for less days hospitalized; (III) less scarring and (IV) less pain. In our current mini review we will present the minimally invasive procedures for thoracic surgery. PMID:25861610
Spin flip of multiqubit states in discrete phase space
NASA Astrophysics Data System (ADS)
Srinivasan, K.; Raghavan, G.
2017-02-01
Time reversal and spin flip are discrete symmetry operations of substantial importance to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of universal NOT gates. The present work investigates the relationship between the quantum state of a multiqubit system represented by the discrete Wigner function (DWFs) and its spin-flipped counterpart. The two are shown to be related through a Hadamard matrix that is independent of the choice of the quantum net used for the tomographic reconstruction of the DWF. These results are of interest to cases involving the direct tomographic reconstruction of the DWF from experimental data, and in the analysis of entanglement related properties purely in terms of the DWF.
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).
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.
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.
NASA Technical Reports Server (NTRS)
1986-01-01
This false-color Voyager picture of Uranus shows a discrete cloud seen as a bright streak near the planet's limb. The picture is a highly processed composite of three images obtained Jan. 14, 1986, when the spacecraft was 12.9 million kilometers (8.0 million miles) from the planet. The cloud visible here is the most prominent feature seen in a series of Voyager images designed to track atmospheric motions. (The occasional donut-shaped features, including one at the bottom, are shadows cast by dust in the camera optics; the processing necessary to bring out the faint features on the planet also brings out these camera blemishes.) Three separate images were shuttered through violet, blue and orange filters. Each color image showed the cloud to a different degree; because they were not exposed at exactly the same time, the images were processed to provide a correction for a good spatial match. In a true-color image, the cloud would be barely discernible; the false color helps bring out additional details. The different colors imply variations in vertical structure, but as yet is not possible to be specific about such differences. One possibility is that the Uranian atmosphere contains smog-like constituents, in which case some color differences may represent differences in how these molecules are distributed. The Voyager project is managed for NASA by the Jet Propulsion Laboratory.
Discreteness inducing coexistence
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira
2013-12-01
Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.
Supersolid formation in a quantum gas breaking a continuous translational symmetry
NASA Astrophysics Data System (ADS)
Léonard, Julian; Morales, Andrea; Zupancic, Philip; Esslinger, Tilman; Donner, Tobias
2017-03-01
The concept of a supersolid state combines the crystallization of a many-body system with dissipationless flow of the atoms from which it is built. This quantum phase requires the breaking of two continuous symmetries: the phase invariance of a superfluid and the continuous translational invariance to form the crystal. Despite having been proposed for helium almost 50 years ago, experimental verification of supersolidity remains elusive. A variant with only discrete translational symmetry breaking on a preimposed lattice structure—the ‘lattice supersolid’—has been realized, based on self-organization of a Bose–Einstein condensate. However, lattice supersolids do not feature the continuous ground-state degeneracy that characterizes the supersolid state as originally proposed. Here we report the realization of a supersolid with continuous translational symmetry breaking along one direction in a quantum gas. The continuous symmetry that is broken emerges from two discrete spatial symmetries by symmetrically coupling a Bose–Einstein condensate to the modes of two optical cavities. We establish the phase coherence of the supersolid and find a high ground-state degeneracy by measuring the crystal position over many realizations through the light fields that leak from the cavities. These light fields are also used to monitor the position fluctuations in real time. Our concept provides a route to creating and studying glassy many-body systems with controllably lifted ground-state degeneracies, such as supersolids in the presence of disorder.
NASA Astrophysics Data System (ADS)
Miehe, Christian; Mauthe, Steffen; Teichtmeister, Stephan
2015-09-01
This work develops new minimization and saddle point principles for the coupled problem of Darcy-Biot-type fluid transport in porous media at fracture. It shows that the quasi-static problem of elastically deforming, fluid-saturated porous media is related to a minimization principle for the evolution problem. This two-field principle determines the rate of deformation and the fluid mass flux vector. It provides a canonically compact model structure, where the stress equilibrium and the inverse Darcy's law appear as the Euler equations of a variational statement. A Legendre transformation of the dissipation potential relates the minimization principle to a characteristic three field saddle point principle, whose Euler equations determine the evolutions of deformation and fluid content as well as Darcy's law. A further geometric assumption results in modified variational principles for a simplified theory, where the fluid content is linked to the volumetric deformation. The existence of these variational principles underlines inherent symmetries of Darcy-Biot theories of porous media. This can be exploited in the numerical implementation by the construction of time- and space-discrete variational principles, which fully determine the update problems of typical time stepping schemes. Here, the proposed minimization principle for the coupled problem is advantageous with regard to a new unconstrained stable finite element design, while space discretizations of the saddle point principles are constrained by the LBB condition. The variational principles developed provide the most fundamental approach to the discretization of nonlinear fluid-structure interactions, showing symmetric systems in algebraic update procedures. They also provide an excellent starting point for extensions towards more complex problems. This is demonstrated by developing a minimization principle for a phase field description of fracture in fluid-saturated porous media. It is designed for an
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.
What is integrability of discrete variational systems?
Boll, Raphael; Petrera, Matteo; Suris, Yuri B
2014-02-08
We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form [Formula: see text] on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals [Formula: see text] for anyd-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler-Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations.
What is integrability of discrete variational systems?
Boll, Raphael; Petrera, Matteo; Suris, Yuri B.
2014-01-01
We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. PMID:24511254
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.
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.
Minimally invasive valve surgery.
Woo, Y Joseph
2009-08-01
Traditional cardiac valve replacement surgery is being rapidly supplanted by innovative, minimally invasive approaches toward the repair of these valves. Patients are experiencing benefits ranging from less bleeding and pain to faster recovery and greater satisfaction. These operations are proving to be safe, highly effective, and durable, and their use will likely continue to increase and become even more widely applicable.
CONMIN- CONSTRAINED FUNCTION MINIMIZATION
NASA Technical Reports Server (NTRS)
Vanderplaats, G. N.
1994-01-01
In many mathematical problems, it is necessary to determine the minimum and maximum of a function of several variables, limited by various linear and nonlinear inequality constraints. It is seldom possible, in practical applications, to solve these problems directly. In most cases, an iterative method must be used to numerically obtain a solution. The CONMIN program was developed to numerically perform the minimization of a multi-variable function subject to a set of inequality constraints. The function need not be a simple analytical equation; it may be any function which can be numerically evaluated. The basic analytic technique used by CONMIN is to minimize the function until one or more of the constraints become active. The minimization process then continues by following the constraint boundaries in a direction such that the value of the function continues to decrease. When a point is reached where no further decrease in the function can be obtained, the process is terminated. Function maximization may be achieved by minimizing the negative of the function. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 43K (octal) of 60 bit words. The CONMIN program was originally developed in 1973 and last updated in 1978.
Landau-Ginzburg orbifolds and symmetries of K3 CFTs
Cheng, Miranda C. N.; Ferrari, Francesca; Harrison, Sarah M.; ...
2017-01-11
Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K3 string theory. To test and clarify these proposed K3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K3 sigma models. We compute K3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observedmore » in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from M11 c 2.M12 moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Finally, our results provide strong evidence for the relevance of umbral moonshine for K3 symmetries, as well as new hints for its eventual explanation.« less
Symmetry breaking and singularity structure in Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Commeford, K. A.; Garcia-March, M. A.; Ferrando, A.; Carr, Lincoln D.
2012-08-01
We determine the trajectories of vortex singularities that arise after a single vortex is broken by a discretely symmetric impulse in the context of Bose-Einstein condensates in a harmonic trap. The dynamics of these singularities are analyzed to determine the form of the imprinted motion. We find that the symmetry-breaking process introduces two effective forces: a repulsive harmonic force that causes the daughter trajectories to be ejected from the parent singularity and a Magnus force that introduces a torque about the axis of symmetry. For the analytical noninteracting case we find that the parent singularity is reconstructed from the daughter singularities after one period of the trapping frequency. The interactions between singularities in the weakly interacting system do not allow the parent vortex to be reconstructed. Analytic trajectories were compared to the actual minima of the wave function, showing less than 0.5% error for an impulse strength of v=0.00005. We show that these solutions are valid within the impulse regime for various impulse strengths using numerical integration of the Gross-Pitaevskii equation. We also show that the actual duration of the symmetry-breaking potential does not significantly change the dynamics of the system as long as the strength is below v=0.0005.
Single-Image Vignetting Correction from Gradient Distribution Symmetries
Zheng, Yuanjie; Lin, Stephen; Kang, Sing Bing; Xiao, Rui; Gee, James C.; Kambhamettu, Chandra
2014-01-01
We present novel techniques for single-image vignetting correction based on symmetries of two forms of image gradients: semicircular tangential gradients (SCTG) and radial gradients (RG). For a given image pixel, an SCTG is an image gradient along the tangential direction of a circle centered at the presumed optical center and passing through the pixel. An RG is an image gradient along the radial direction with respect to the optical center. We observe that the symmetry properties of SCTG and RG distributions are closely related to the vignetting in the image. Based on these symmetry properties we develop an automatic optical center estimation algorithm by minimizing the asymmetry of SCTG distributions, and also present two methods for vignetting estimation based on minimizing the asymmetry of RG distributions. In comparison to prior approaches to single-image vignetting correction, our methods do not rely on image segmentation and they produce more accurate results. Experiments show our techniques to work well for a wide range of images while achieving a speed-up of 3-5 times compared to a state-of-the-art method. PMID:23599060
Single-image vignetting correction from gradient distribution symmetries.
Zheng, Yuanjie; Lin, Stephen; Kang, Sing Bing; Xiao, Rui; Gee, James C; Kambhamettu, Chandra
2013-06-01
We present novel techniques for single-image vignetting correction based on symmetries of two forms of image gradients: semicircular tangential gradients (SCTG) and radial gradients (RG). For a given image pixel, an SCTG is an image gradient along the tangential direction of a circle centered at the presumed optical center and passing through the pixel. An RG is an image gradient along the radial direction with respect to the optical center. We observe that the symmetry properties of SCTG and RG distributions are closely related to the vignetting in the image. Based on these symmetry properties, we develop an automatic optical center estimation algorithm by minimizing the asymmetry of SCTG distributions, and also present two methods for vignetting estimation based on minimizing the asymmetry of RG distributions. In comparison to prior approaches to single-image vignetting correction, our methods do not rely on image segmentation and they produce more accurate results. Experiments show our techniques to work well for a wide range of images while achieving a speed-up of 3-5 times compared to a state-of-the-art method.
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
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)
Chaos in Periodic Discrete Systems
NASA Astrophysics Data System (ADS)
Shi, Yuming; Zhang, Lijuan; Yu, Panpan; Huang, Qiuling
This paper focuses on chaos in periodic discrete systems, whose state space may vary with time. Some close relationships between some chaotic dynamical behaviors of a periodic discrete system and its autonomous induced system are given. Based on these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for periodic discrete systems. Further, it is shown that a finite-dimensional linear periodic discrete system is not chaotic in the sense of Li-Yorke or Wiggins. In particular, an interesting problem of whether nonchaotic rules may generate a chaotic system is studied, with some examples provided, one of which surprisingly shows that a composition of globally asymptotically stable maps can be chaotic. In addition, some properties of sign pattern matrices of non-negative square matrices are given for convenience of the study.
Microscopic derivation of discrete hydrodynamics.
Español, Pep; Anero, Jesús G; Zúñiga, Ignacio
2009-12-28
By using the standard theory of coarse graining based on Zwanzig's projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations.
Variational discretizations for the dynamics of fluid-conveying flexible tubes
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Putkaradze, Vakhtang
2016-11-01
We derive a variational approach for discretizing fluid-structure interactions, with a particular focus on the dynamics of fluid-conveying elastic tubes. Our method is based on a discretization of the fluid's back-to-labels map and a Lie group discretization of the tube's variables, coupled with an appropriately formulated discrete version of the fluid conservation law. This approach allows the development of geometric numerical schemes for the dynamics of fluid-conveying collapsible tubes, which preserve several intrinsic geometric properties of the continuous system, such as symmetries and symplecticity. In addition, our approach can also be used to derive simplified, but geometrically consistent, low-component models for further analytical and numerical analysis of the system. xml:lang="fr"
Time Discretization Approach to Dynamic Localization Conditions
NASA Astrophysics Data System (ADS)
Papp, E.
An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J0(z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.
Discrete solitons in graphene metamaterials
NASA Astrophysics Data System (ADS)
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
Concurrency and discrete event control
NASA Technical Reports Server (NTRS)
Heymann, Michael
1990-01-01
Much of discrete event control theory has been developed within the framework of automata and formal languages. An alternative approach inspired by the theories of process-algebra as developed in the computer science literature is presented. The framework, which rests on a new formalism of concurrency, can adequately handle nondeterminism and can be used for analysis of a wide range of discrete event phenomena.
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.
Minimal hepatic encephalopathy.
Zamora Nava, Luis Eduardo; Torre Delgadillo, Aldo
2011-06-01
The term minimal hepatic encephalopathy (MHE) refers to the subtle changes in cognitive function, electrophysiological parameters, cerebral neurochemical/neurotransmitter homeostasis, cerebral blood flow, metabolism, and fluid homeostasis that can be observed in patients with cirrhosis who have no clinical evidence of hepatic encephalopathy; the prevalence is as high as 84% in patients with hepatic cirrhosis. Physician does generally not perceive cirrhosis complications, and neuropsychological tests and another especial measurement like evoked potentials and image studies like positron emission tomography can only make diagnosis. Diagnosis of minimal hepatic encephalopathy may have prognostic and therapeutic implications in cirrhotic patients. The present review pretends to explore the clinic, therapeutic, diagnosis and prognostic aspects of this complication.
Charged Boundary States in a Z3 Extended Minimal String
NASA Astrophysics Data System (ADS)
Kawamoto, Shoichi; Wheater, John F.; Wilshin, Simon
In this poster, we study the boundary states of the three-state Potts model coupled to two dimensional gravity, which we call Z3 extended minimal string. We find that two different boundary states of this model can be identified with a shift of the boundary cosmological constant. We also point out that the boundary states are classified with respect to the symmetry of the theory. This presentation is based on Ref. 1 to appear soon.
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.
Symmetry-adapted Wannier functions in the maximal localization procedure
NASA Astrophysics Data System (ADS)
Sakuma, R.
2013-06-01
A procedure to construct symmetry-adapted Wannier functions in the framework of the maximally localized Wannier function approach [Marzari and Vanderbilt, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.56.12847 56, 12847 (1997); Souza, Marzari, and Vanderbilt, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.65.035109 65, 035109 (2001)] is presented. In this scheme, the minimization of the spread functional of the Wannier functions is performed with constraints that are derived from symmetry properties of the specified set of the Wannier functions and the Bloch functions used to construct them, therefore one can obtain a solution that does not necessarily yield the global minimum of the spread functional. As a test of this approach, results of atom-centered Wannier functions for GaAs and Cu are presented.
R-symmetry violation in an era of precision cosmology
NASA Astrophysics Data System (ADS)
Sabo, Eric
We consider well-motivated particle physics corrections to the standard supersymmetric hybrid inflation scenario. By allowing certain higher order, Planck scale suppressed, R-symmetry violating operators in the superpotential, we are able to give masses to right-handed neutrinos without negatively affecting the down-type quarks. We provide an example with minimal Kahler potential, with the R-symmetry breaking term relevant during inflation being alphaS4, where S denotes the well-known gauge singlet inflaton superfield. The inflationary potential takes into account the radiative and supergravity corrections, as well as the soft supersymmetry breaking terms. For successful inflation, with the scalar spectral index in the currently preferred range, n s ≈ 0.9603 we find |alpha| < 10-7. The tensor to scalar ratio r < 10-4, while |d n s/d ln k| ~ O(10-3 ) -- O(10-4).
A scalar field dark energy model: Noether symmetry approach
NASA Astrophysics Data System (ADS)
Dutta, Sourav; Panja, Madan Mohan; Chakraborty, Subenoy
2016-04-01
Scalar field dark energy cosmology has been investigated in the present paper in the frame work of Einstein gravity. In the context of Friedmann-Lemaitre-Robertson-Walker space time minimally coupled scalar field with self interacting potential and non-interacting perfect fluid with barotropic equation of state (dark matter) is chosen as the matter context. By imposing Noether symmetry on the Lagrangian of the system the symmetry vector is obtained and the self interacting potential for the scalar field is determined. Then we choose a point transformation (a, φ )→ (u, v) such that one of the transformation variable (say u) is cyclic for the Lagrangian. Subsequently, using conserved charge (corresponding to the cyclic co-ordinate) and the constant of motion, solutions are obtained. Finally, the cosmological implication of the solutions in the perspective of recent observation has been examined.
Yukawa textures with an anomalous horizontal abelian symmetry
Binetruy, P.; Lavignac, S.; Ramond, P.
1996-01-01
The observed hierarchy of quark and lepton masses and mixings may be obtained by adding an abelian family symmetry to the Minimal Supersymmetric Model and coupling quarks and leptons to an electroweak singlet scalar field. In a large class of such models, this symmetry suffers from anomalies which must be compensated by the Green-Schwarz mechanism; this in turn fixes the electroweak mixing angle to be sin{sup 2}{theta}{sub W} = 3/8 at the string scale, without any assumed GUT structure. The analysis is extended to two distinct generalizations of the Standard Model: neutrino masses and mixings and R-parity violating interactions. (author). 31 refs., 2 tabs.
Discrete breathers in alpha-uranium
NASA Astrophysics Data System (ADS)
Murzaev, Ramil T.; Babicheva, Rita I.; Zhou, Kun; Korznikova, Elena A.; Fomin, Sergey Yu.; Dubinko, Vladimir I.; Dmitriev, Sergey V.
2016-07-01
Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.
[Minimally invasive thymus surgery].
Rückert, J C; Ismail, M; Swierzy, M; Braumann, C; Badakhshi, H; Rogalla, P; Meisel, A; Rückert, R I; Müller, J M
2008-01-01
There are absolute and relative indications for complete removal of the thymus gland. In the complex therapy of autoimmune-related myasthenia gravis, thymectomy plays a central role and is performed with relative indication. In case of thymoma with or without myasthenia, thymectomy is absolutely indicated. Thymus resection is further necessary for cases of hyperparathyroidism with ectopic intrathymic parathyroids or with certain forms of multiple endocrine neoplasia. The transcervical operation technique traditionally reflected the well-founded desire for minimal invasiveness for thymectomy. Due to the requirement of radicality however, most of these operations were performed using sternotomy. With the evolution of therapeutic thoracoscopy in thoracic surgery, several pure or extended minimally invasive operation techniques for thymectomy have been developed. At present uni- or bilateral, subxiphoid, and modified transcervical single or combination thoracoscopic techniques are in use. Recently a very precise new level of thoracoscopic operation technique was developed using robotic-assisted surgery. There are special advantages of this technique for thymectomy. An overview of the development and experiences with minimally invasive thymectomy is presented, including data from the largest series published so far.
Waste Minimization Crosscut Plan
Not Available
1992-05-13
On November 27, 1991, the Secretary of Energy directed that a Department of Energy (DOE) crosscut plan for waste minimization (WMin) be prepared and submitted by March 1, 1992. This Waste Minimization Crosscut Plan responds to the Secretary's direction and supports the National Energy Strategy (NES) goals of achieving greater energy security, increasing energy and economic efficiency, and enhancing environmental quality. It provides a DOE-wide planning framework for effective coordination of all DOE WMin activities. This Plan was jointly prepared by the following Program Secretarial Officer (PSO) organizations: Civilian Radioactive Waste Management (RW); Conservation and Renewable Energy (CE); Defense Programs (DP); Environmental Restoration and Waste Management (EM), lead; Energy Research (ER); Fossil Energy (FE); Nuclear Energy (NE); and New Production Reactors (NP). Assistance and guidance was provided by the offices of Policy, Planning, and Analysis (PE) and Environment, Safety and Health (EH). Comprehensive application of waste minimization within the Department and in both the public and private sectors will provide significant benefits and support National Energy Strategy goals. These benefits include conservation of a substantial proportion of the energy now used by industry and Government, improved environmental quality, reduced health risks, improved production efficiencies, and longer useful life of disposal capacity. Taken together, these benefits will mean improved US global competitiveness, expanded job opportunities, and a better quality of life for all citizens.
Waste Minimization Crosscut Plan
Not Available
1992-05-13
On November 27, 1991, the Secretary of Energy directed that a Department of Energy (DOE) crosscut plan for waste minimization (WMin) be prepared and submitted by March 1, 1992. This Waste Minimization Crosscut Plan responds to the Secretary`s direction and supports the National Energy Strategy (NES) goals of achieving greater energy security, increasing energy and economic efficiency, and enhancing environmental quality. It provides a DOE-wide planning framework for effective coordination of all DOE WMin activities. This Plan was jointly prepared by the following Program Secretarial Officer (PSO) organizations: Civilian Radioactive Waste Management (RW); Conservation and Renewable Energy (CE); Defense Programs (DP); Environmental Restoration and Waste Management (EM), lead; Energy Research (ER); Fossil Energy (FE); Nuclear Energy (NE); and New Production Reactors (NP). Assistance and guidance was provided by the offices of Policy, Planning, and Analysis (PE) and Environment, Safety and Health (EH). Comprehensive application of waste minimization within the Department and in both the public and private sectors will provide significant benefits and support National Energy Strategy goals. These benefits include conservation of a substantial proportion of the energy now used by industry and Government, improved environmental quality, reduced health risks, improved production efficiencies, and longer useful life of disposal capacity. Taken together, these benefits will mean improved US global competitiveness, expanded job opportunities, and a better quality of life for all citizens.
Two-Higgs-doublet models with Minimal Flavour Violation
Carlucci, Maria Valentina
2010-12-22
The tree-level flavour-changing neutral currents in the two-Higgs-doublet models can be suppressed by protecting the breaking of either flavour or flavour-blind symmetries, but only the first choice, implemented by the application of the Minimal Flavour Violation hypothesis, is stable under quantum corrections. Moreover, a two-Higgs-doublet model with Minimal Flavour Violation enriched with flavour-blind phases can explain the anomalies recently found in the {Delta}F = 2 transitions, namely the large CP-violating phase in B{sub s} mixing and the tension between {epsilon}{sub K} and S{sub {psi}KS}.
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.
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
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.
Beyond minimal lepton-flavored Dark Matter
Chen, Mu-Chun; Huang, Jinrui; Takhistov, Volodymyr
2016-02-09
In this paper ,we consider a class of flavored dark matter (DM) theories where dark matter interacts with the Standard Model lepton fields at the renormalizable level. We allow for a general coupling matrix between the dark matter and leptons whose structure is beyond the one permitted by the minimal flavor violation (MFV) assumption. It is assumed that this is the only new source of flavor violation in addition to the Standard Model (SM) Yukawa interactions. The setup can be described by augmenting the SM flavor symmetry by an additional SU(3)_{χ}, under which the dark matter χ transforms. This framework is especially phenomenologically rich, due to possible novel flavor-changing interactions which are not present within the more restrictive MFV framework. As a representative case study of this setting, which we call “beyond MFV” (BMFV), we consider Dirac fermion dark matter which transforms as a singlet under the SM gauge group and a triplet under SU(3)_{χ}. The DM fermion couples to the SM lepton sector through a scalar mediator Φ. Unlike the case of quark-flavored DM, we show that there is no Z_{3} symmetry within either the MFV or BMFV settings which automatically stabilizes the lepton-flavored DM. We discuss constraints on this setup from flavor-changing processes, DM relic abundance as well as direct and indirect detections. We find that relatively large flavor-changing couplings are possible, while the dark matter mass is still within the phenomenologically interesting region below the TeV scale. Collider signatures which can be potentially searched for at the lepton and hadron colliders are discussed. Finally, we discuss the implications for decaying dark matter, which can appear if an additional stabilizing symmetry is not imposed.
Beyond minimal lepton-flavored Dark Matter
Chen, Mu-Chun; Huang, Jinrui; Takhistov, Volodymyr
2016-02-09
In this paper ,we consider a class of flavored dark matter (DM) theories where dark matter interacts with the Standard Model lepton fields at the renormalizable level. We allow for a general coupling matrix between the dark matter and leptons whose structure is beyond the one permitted by the minimal flavor violation (MFV) assumption. It is assumed that this is the only new source of flavor violation in addition to the Standard Model (SM) Yukawa interactions. The setup can be described by augmenting the SM flavor symmetry by an additional SU(3)χ, under which the dark matter χ transforms. This frameworkmore » is especially phenomenologically rich, due to possible novel flavor-changing interactions which are not present within the more restrictive MFV framework. As a representative case study of this setting, which we call “beyond MFV” (BMFV), we consider Dirac fermion dark matter which transforms as a singlet under the SM gauge group and a triplet under SU(3)χ. The DM fermion couples to the SM lepton sector through a scalar mediator Φ. Unlike the case of quark-flavored DM, we show that there is no Z3 symmetry within either the MFV or BMFV settings which automatically stabilizes the lepton-flavored DM. We discuss constraints on this setup from flavor-changing processes, DM relic abundance as well as direct and indirect detections. We find that relatively large flavor-changing couplings are possible, while the dark matter mass is still within the phenomenologically interesting region below the TeV scale. Collider signatures which can be potentially searched for at the lepton and hadron colliders are discussed. Finally, we discuss the implications for decaying dark matter, which can appear if an additional stabilizing symmetry is not imposed.« less
Characterizing Floral Symmetry in the Core Goodeniaceae with Geometric Morphometrics
Gardner, Andrew G.; Fitz Gerald, Jonathan N.; Menz, John; Shepherd, Kelly A.; Howarth, Dianella G.; Jabaily, Rachel S.
2016-01-01
Core Goodeniaceae is a clade of ~330 species primarily distributed in Australia. Considerable variation in flower morphology exists within this group and we aim to use geometric morphometrics to characterize this variation across the two major subclades: Scaevola sensu lato (s.l.) and Goodenia s.l., the latter of which was hypothesized to exhibit greater variability in floral symmetry form. We test the hypothesis that floral morphological variation can be adequately characterized by our morphometric approach, and that discrete groups of floral symmetry morphologies exist, which broadly correlate with subjectively determined groups. From 335 images of 44 species in the Core Goodeniaceae, two principal components were computed that describe >98% of variation in all datasets. Increasing values of PC1 ventralize the dorsal petals (increasing the angle between them), whereas increasing values of PC2 primarily ventralize the lateral petals (decreasing the angle between them). Manipulation of these two morphological “axes” alone was sufficient to recreate any of the general floral symmetry patterns in the Core Goodeniaceae. Goodenia s.l. exhibits greater variance than Scaevola s.l. in PC1 and PC2, and has a significantly lower mean value for PC1. Clustering clearly separates fan-flowers (with dorsal petals at least 120° separated) from the others, whereas the distinction between pseudo-radial and bilabiate clusters is less clear and may form a continuum rather than two distinct groups. Transitioning from the average fan-flower to the average non-fan-flower is described almost exclusively by PC1, whereas PC2 partially describes the transition between bilabiate and pseudo-radial morphologies. Our geometric morphometric method accurately models Core Goodeniaceae floral symmetry diversity. PMID:27148960
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
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
Minimally invasive mediastinal surgery
Melfi, Franca M. A.; Mussi, Alfredo
2016-01-01
In the past, mediastinal surgery was associated with the necessity of a maximum exposure, which was accomplished through various approaches. In the early 1990s, many surgical fields, including thoracic surgery, observed the development of minimally invasive techniques. These included video-assisted thoracic surgery (VATS), which confers clear advantages over an open approach, such as less trauma, short hospital stay, increased cosmetic results and preservation of lung function. However, VATS is associated with several disadvantages. For this reason, it is not routinely performed for resection of mediastinal mass lesions, especially those located in the anterior mediastinum, a tiny and remote space that contains vital structures at risk of injury. Robotic systems can overcome the limits of VATS, offering three-dimensional (3D) vision and wristed instrumentations, and are being increasingly used. With regards to thymectomy for myasthenia gravis (MG), unilateral and bilateral VATS approaches have demonstrated good long-term neurologic results with low complication rates. Nevertheless, some authors still advocate the necessity of maximum exposure, especially when considering the distribution of normal and ectopic thymic tissue. In recent studies, the robotic approach has shown to provide similar neurological outcomes when compared to transsternal and VATS approaches, and is associated with a low morbidity. Importantly, through a unilateral robotic technique, it is possible to dissect and remove at least the same amount of mediastinal fat tissue. Preliminary results on early-stage thymomatous disease indicated that minimally invasive approaches are safe and feasible, with a low rate of pleural recurrence, underlining the necessity of a “no-touch” technique. However, especially for thymomatous disease characterized by an indolent nature, further studies with long follow-up period are necessary in order to assess oncologic and neurologic results through minimally
Simulating granular materials by energy minimization
NASA Astrophysics Data System (ADS)
Krijgsman, D.; Luding, S.
2016-11-01
Discrete element methods are extremely helpful in understanding the complex behaviors of granular media, as they give valuable insight into all internal variables of the system. In this paper, a novel discrete element method for performing simulations of granular media is presented, based on the minimization of the potential energy in the system. Contrary to most discrete element methods (i.e., soft-particle method, event-driven method, and non-smooth contact dynamics), the system does not evolve by (approximately) integrating Newtons equations of motion in time, but rather by searching for mechanical equilibrium solutions for the positions of all particles in the system, which is mathematically equivalent to locally minimizing the potential energy. The new method allows for the rapid creation of jammed initial conditions (to be used for further studies) and for the simulation of quasi-static deformation problems. The major advantage of the new method is that it allows for truly static deformations. The system does not evolve with time, but rather with the externally applied strain or load, so that there is no kinetic energy in the system, in contrast to other quasi-static methods. The performance of the algorithm for both types of applications of the method is tested. Therefore we look at the required number of iterations, for the system to converge to a stable solution. For each single iteration, the required computational effort scales linearly with the number of particles. During the process of creating initial conditions, the required number of iterations for two-dimensional systems scales with the square root of the number of particles in the system. The required number of iterations increases for systems closer to the jamming packing fraction. For a quasi-static pure shear deformation simulation, the results of the new method are validated by regular soft-particle dynamics simulations. The energy minimization algorithm is able to capture the evolution of the
Fischler, Mark S.; Sachs, D.; /Fermilab
2004-11-01
A new object-oriented Minimization package is available for distribution in the same manner as CLHEP. This package, designed for use in HEP applications, has all the capabilities of Minuit, but is a re-write from scratch, adhering to modern C++ design principles. A primary goal of this package is extensibility in several directions, so that its capabilities can be kept fresh with as little maintenance effort as possible. This package is distinguished by the priority that was assigned to C++ design issues, and the focus on producing an extensible system that will resist becoming obsolete.
NASA Technical Reports Server (NTRS)
1977-01-01
A status report is presented on research directed at reducing the vortex disturbances of aircraft wakes. The objective of such a reduction is to minimize the hazard to smaller aircraft that might encounter these wakes. Inviscid modeling was used to study trailing vortices and viscous effects were investigated. Laser velocimeters were utilized in the measurement of aircraft wakes. Flight and wind tunnel tests were performed on scale and full model scale aircraft of various design. Parameters investigated included the effect of wing span, wing flaps, spoilers, splines and engine thrust on vortex attenuation. Results indicate that vortives may be alleviated through aerodynamic means.
Minimally refined biomass fuel
Pearson, Richard K.; Hirschfeld, Tomas B.
1984-01-01
A minimally refined fluid composition, suitable as a fuel mixture and derived from biomass material, is comprised of one or more water-soluble carbohydrates such as sucrose, one or more alcohols having less than four carbons, and water. The carbohydrate provides the fuel source; water solubilizes the carbohydrates; and the alcohol aids in the combustion of the carbohydrate and reduces the vicosity of the carbohydrate/water solution. Because less energy is required to obtain the carbohydrate from the raw biomass than alcohol, an overall energy savings is realized compared to fuels employing alcohol as the primary fuel.
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.
Wave functions of symmetry-protected topological phases from conformal field theories
NASA Astrophysics Data System (ADS)
Scaffidi, Thomas; Ringel, Zohar
2016-03-01
We propose a method for analyzing two-dimensional symmetry-protected topological (SPT) wave functions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the fractional quantum Hall effect wherein the wave-function amplitude is written as a many-operator correlator in the CFT. Adopting a bottom-up approach, we start from various known microscopic wave functions of SPTs with discrete symmetries and show how the CFT description emerges at large scale, thereby revealing a deep connection between group cocycles and critical, sometimes integrable, models. We show that the CFT describing the bulk wave function is often also the one describing the entanglement spectrum, but not always. Using a plasma analogy, we also prove the existence of hidden quasi-long-range order for a large class of SPTs. Finally, we show how response to symmetry fluxes is easily described in terms of the CFT.
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
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.
Neutrino sector with Majorana mass terms and Friedberg-Lee symmetry
NASA Astrophysics Data System (ADS)
Jarlskog, C.
2008-04-01
We examine a recently proposed symmetry/condition by Friedberg and Lee in a framework where three right-handed neutrinos are added to the spectrum of the three-family minimal standard model. It is found that the right-handed neutrinos are very special, with respect to this symmetry. In the symmetry limit the neutrinos are massless, which could possibly be a hint about why they are light. Imposed as a condition and not as a full symmetry, we find that one of the three right-handed neutrinos simply decouples (has only gravitational interactions) and one of the interacting neutrinos is massless. The possible relation of the model to the seesaw mechanism is briefly discussed.
Discrete solitons in electromechanical resonators.
Syafwan, M; Susanto, H; Cox, S M
2010-02-01
We consider a particular type of parametrically driven discrete Klein-Gordon system describing microdevices and nanodevices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein-Gordon system through the discrete Schrödinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e., oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein-Gordon equation are performed, confirming the relevance of our analysis.
Distributed Relaxation for Conservative Discretizations
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2001-01-01
A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.
Lorentz symmetry and very long baseline interferometry
NASA Astrophysics Data System (ADS)
Le Poncin-Lafitte, C.; Hees, A.; Lambert, S.
2016-12-01
Lorentz symmetry violations can be described by an effective field theory framework that contains both general relativity and the Standard Model of particle physics called the Standard Model extension (SME). Recently, postfit analysis of Gravity Probe B and binary pulsars led to an upper limit at the 10-4 level on the time-time coefficient s¯T T of the pure-gravity sector of the minimal SME. In this work, we derive the observable of very long baseline interferometry (VLBI) in SME and then implement it into a real data analysis code of geodetic VLBI observations. Analyzing all available observations recorded since 1979, we compare estimates of s¯T T and errors obtained with various analysis schemes, including global estimations over several time spans, and with various Sun elongation cutoff angles, and by analysis of radio source coordinate time series. We obtain a constraint on s¯ T T=(-5 ±8 )×10-5 , directly fitted to the observations and improving by a factor of 5 previous postfit analysis estimates.
Critical-point symmetry in a finite system.
Leviatan, A; Ginocchio, J N
2003-05-30
At a critical point of a second-order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can describe the dynamics at the critical point. This effective deformation is determined by minimizing the energy surface after projection onto the appropriate symmetries. We derive analytic expressions for energies and quadrupole rates which provide good estimates for these observables at the critical point.
Two Higgs doublet models with an S3 symmetry
NASA Astrophysics Data System (ADS)
Cogollo, D.; Silva, João P.
2016-05-01
We study all implementations of the S3 symmetry in the two Higgs doublet models with quarks, consistent with nonzero quark masses and a Cabibbo-Kobayashi-Maskawa (CKM) matrix, which is not block diagonal. We study the impact of the various soft-breaking terms and vacuum expectation values and find an interesting relation between the mixing angles α and β . We also show that, in this minimal setting, only two types of assignments are possible: Either all field sectors are in singlets or all field sectors have a doublet.
Logarithmic superconformal minimal models
NASA Astrophysics Data System (ADS)
Pearce, Paul A.; Rasmussen, Jørgen; Tartaglia, Elena
2014-05-01
The higher fusion level logarithmic minimal models {\\cal LM}(P,P';n) have recently been constructed as the diagonal GKO cosets {(A_1^{(1)})_k\\oplus (A_1^ {(1)})_n}/ {(A_1^{(1)})_{k+n}} where n ≥ 1 is an integer fusion level and k = nP/(P‧- P) - 2 is a fractional level. For n = 1, these are the well-studied logarithmic minimal models {\\cal LM}(P,P')\\equiv {\\cal LM}(P,P';1). For n ≥ 2, we argue that these critical theories are realized on the lattice by n × n fusion of the n = 1 models. We study the critical fused lattice models {\\cal LM}(p,p')_{n\\times n} within a lattice approach and focus our study on the n = 2 models. We call these logarithmic superconformal minimal models {\\cal LSM}(p,p')\\equiv {\\cal LM}(P,P';2) where P = |2p - p‧|, P‧ = p‧ and p, p‧ are coprime. These models share the central charges c=c^{P,P';2}=\\frac {3}{2}\\big (1-{2(P'-P)^2}/{P P'}\\big ) of the rational superconformal minimal models {\\cal SM}(P,P'). Lattice realizations of these theories are constructed by fusing 2 × 2 blocks of the elementary face operators of the n = 1 logarithmic minimal models {\\cal LM}(p,p'). Algebraically, this entails the fused planar Temperley-Lieb algebra which is a spin-1 Birman-Murakami-Wenzl tangle algebra with loop fugacity β2 = [x]3 = x2 + 1 + x-2 and twist ω = x4 where x = eiλ and λ = (p‧- p)π/p‧. The first two members of this n = 2 series are superconformal dense polymers {\\cal LSM}(2,3) with c=-\\frac {5}{2}, β2 = 0 and superconformal percolation {\\cal LSM}(3,4) with c = 0, β2 = 1. We calculate the bulk and boundary free energies analytically. By numerically studying finite-size conformal spectra on the strip with appropriate boundary conditions, we argue that, in the continuum scaling limit, these lattice models are associated with the logarithmic superconformal models {\\cal LM}(P,P';2). For system size N, we propose finitized Kac character formulae of the form q^{-{c^{P,P';2}}/{24}+\\Delta ^{P,P';2} _{r
Integrable structure in discrete shell membrane theory
Schief, W. K.
2014-01-01
We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755
Travelling and standing envelope solitons in discrete non-linear cyclic structures
NASA Astrophysics Data System (ADS)
Grolet, Aurelien; Hoffmann, Norbert; Thouverez, Fabrice; Schwingshackl, Christoph
2016-12-01
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.
Gauge transformations of constrained discrete modified KP systems with self-consistent sources
NASA Astrophysics Data System (ADS)
Huang, Ran; Song, Tao; Li, Chuanzhong
In this paper, we firstly recall some basic facts about the discrete KP(d-KP) and discrete modified KP(d-mKP) hierarchies, and then we find that d-KP hierarchy and d-mKP hierarchy are linked by a gauge transformation. What’s more, we give three gauge transformation operators of the d-mKP hierarchy and give their successive applications. We further construct the ghost symmetry and use this symmetry to give the definition the d-mKP hierarchy with self-consistent sources. We also give gauge transformations of a newly defined constrained d-mKP(cd-mKP) hierarchy and the constrained d-mKP hierarchy with self-consistent sources(cd-mKPHSCSs).
Pilot-Wave Quantum Theory in Discrete Space and Time and the Principle of Least Action
NASA Astrophysics Data System (ADS)
Gluza, Janusz; Kosek, Jerzy
2016-11-01
The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a |Ψ |^2-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.
Geometry Of Discrete Sets With Applications To Pattern Recognition
NASA Astrophysics Data System (ADS)
Sinha, Divyendu
1990-03-01
In this paper we present a new framework for discrete black and white images that employs only integer arithmetic. This framework is shown to retain the essential characteristics of the framework for Euclidean images. We propose two norms and based on them, the permissible geometric operations on images are defined. The basic invariants of our geometry are line images, structure of image and the corresponding local property of strong attachment of pixels. The permissible operations also preserve the 3x3 neighborhoods, area, and perpendicularity. The structure, patterns, and the inter-pattern gaps in a discrete image are shown to be conserved by the magnification and contraction process. Our notions of approximate congruence, similarity and symmetry are similar, in character, to the corresponding notions, for Euclidean images [1]. We mention two discrete pattern recognition algorithms that work purely with integers, and which fit into our framework. Their performance has been shown to be at par with the performance of traditional geometric schemes. Also, all the undesired effects of finite length registers in fixed point arithmetic that plague traditional algorithms, are non-existent in this family of algorithms.
Meirovitch, E.
1986-10-23
The molecular motion of acetone-d/sub 6/ acting as guest in deoxycholic acid and apocholic acid host lattices in the solid state is interpreted in light of a broader concept assessing that very often the motion of the guest proceeds through discrete jumps rather than diffusively and its symmetry is congenial with the site symmetry of the host lattice. In particular, the acetone molecules are engaged in threefold jumps about a unique axis, compatible with the 32 site symmetry of the host lattice. The entire dynamic range of this process is investigated in terms of spectral consequences brought about by variations in jump rates, in the relative population of the three symmetry related sites, and in instrumental parameters such as the time interval between the two 90/sup 0/ pulses in the quadrupole echo sequence and the length of the 90/sup 0/ pulses.
Discrete cloud structure on Neptune
NASA Technical Reports Server (NTRS)
Hammel, H. B.
1989-01-01
Recent CCD imaging data for the discrete cloud structure of Neptune shows that while cloud features at CH4-band wavelengths are manifest in the southern hemisphere, they have not been encountered in the northern hemisphere since 1986. A literature search has shown the reflected CH4-band light from the planet to have come from a single discrete feature at least twice in the last 10 years. Disk-integrated photometry derived from the imaging has demonstrated that a bright cloud feature was responsible for the observed 8900 A diurnal variation in 1986 and 1987.
Dirac neutrinos with S4 flavor symmetry in warped extra dimensions
NASA Astrophysics Data System (ADS)
Ding, Gui-Jun; Zhou, Ye-Ling
2013-11-01
case of G being a finite group, there should be some integers n and mi such that Gln=(=1 with n⩾3 which results from the requirement that Gl is non-degenerate. We have performed a systematic scan of the possible values of n up to n=200, we are unable to find solutions for the integers mi such that (=1, and hence the symmetry groups in these cases are infinite. Therefore we conclude that there is no discrete flavor symmetry group that contains all of the symmetries needed for the DC mixing, although one cannot rule out the possibility of a discrete group with a very large order. This is the reason why the discrete flavor symmetry origin of the DC mixing has not been proposed so far. Note that the S×S symmetry can immediately lead to the so-called democratic mass matrix in which each matrix element has the same value [53], where S and S are symmetric groups of degree three acting on the left-handed and the right-handed fermion fields respectively. However, the DC mixing cannot be uniquely determined by the democratic mass matrix, and in fact only the third row of DC mixing matrix is fixed.
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
Minimally invasive valve surgery.
Woo, Y Joseph; Seeburger, Joerg; Mohr, Friedrich W
2007-01-01
As alternatives to standard sternotomy, surgeons have developed innovative, minimally invasive approaches to conducting valve surgery. Through very small skin incisions and partial upper sternal division for aortic valve surgery and right minithoracotomy for mitral surgery, surgeons have become adept at performing complex valve procedures. Beyond cosmetic appeal, apparent benefits range from decreased pain and bleeding to improved respiratory function and recovery time. The large retrospective studies and few small prospective randomized studies are herein briefly summarized. The focus is then directed toward describing specific intraoperative technical details in current clinical use, covering anesthetic preparation, incision, mediastinal access, cardiovascular cannulation, valve exposure, and valve reconstruction. Finally, unique situations such as pulmonic valve surgery, reoperations, beating heart surgery, and robotics are discussed.
Transanal Minimally Invasive Surgery
deBeche-Adams, Teresa; Nassif, George
2015-01-01
Transanal minimally invasive surgery (TAMIS) was first described in 2010 as a crossover between single-incision laparoscopic surgery and transanal endoscopic microsurgery (TEM) to allow access to the proximal and mid-rectum for resection of benign and early-stage malignant rectal lesions. The TAMIS technique can also be used for noncurative intent surgery of more advanced lesions in patients who are not candidates for radical surgery. Proper workup and staging should be done before surgical decision-making. In addition to the TAMIS port, instrumentation and set up include readily available equipment found in most operating suites. TAMIS has proven its usefulness in a wide range of applications outside of local excision, including repair of rectourethral fistula, removal of rectal foreign body, control of rectal hemorrhage, and as an adjunct in total mesorectal excision for rectal cancer. TAMIS is an easily accessible, technically feasible, and cost-effective alternative to TEM. PMID:26491410
Minimally invasive esophagectomy
Herbella, Fernando A; Patti, Marco G
2010-01-01
Esophageal resection is associated with a high morbidity and mortality rate. Minimally invasive esophagectomy (MIE) might theoretically decrease this rate. We reviewed the current literature on MIE, with a focus on the available techniques, outcomes and comparison with open surgery. This review shows that the available literature on MIE is still crowded with heterogeneous studies with different techniques. There are no controlled and randomized trials, and the few retrospective comparative cohort studies are limited by small numbers of patients and biased by historical controls of open surgery. Based on the available literature, there is no evidence that MIE brings clear benefits compared to conventional esophagectomy. Increasing experience and the report of larger series might change this scenario. PMID:20698044
Linear functional minimization for inverse modeling
Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...
2015-06-01
In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less
Use of switched capacitor filters to implement the discrete wavelet transform
NASA Technical Reports Server (NTRS)
Kaiser, Kraig E.; Peterson, James N.
1993-01-01
This paper analyzes the use of IIR switched capacitor filters to implement the discrete wavelet transform and the inverse transform, using quadrature mirror filters (QMF) which have the necessary symmetry for reconstruction of the data. This is done by examining the sensitivity of the QMF transforms to the manufacturing variance in the desired capacitances. The performance is evaluated at the outputs of the separate filter stages and the error in the reconstruction of the inverse transform is compared with the desired results.
Minimally invasive parathyroid surgery
Noureldine, Salem I.; Gooi, Zhen
2015-01-01
Traditionally, bilateral cervical exploration for localization of all four parathyroid glands and removal of any that are grossly enlarged has been the standard surgical treatment for primary hyperparathyroidism (PHPT). With the advances in preoperative localization studies and greater public demand for less invasive procedures, novel targeted, minimally invasive techniques to the parathyroid glands have been described and practiced over the past 2 decades. Minimally invasive parathyroidectomy (MIP) can be done either through the standard Kocher incision, a smaller midline incision, with video assistance (purely endoscopic and video-assisted techniques), or through an ectopically placed, extracervical, incision. In current practice, once PHPT is diagnosed, preoperative evaluation using high-resolution radiographic imaging to localize the offending parathyroid gland is essential if MIP is to be considered. The imaging study results suggest where the surgeon should begin the focused procedure and serve as a road map to allow tailoring of an efficient, imaging-guided dissection while eliminating the unnecessary dissection of multiple glands or a bilateral exploration. Intraoperative parathyroid hormone (IOPTH) levels may be measured during the procedure, or a gamma probe used during radioguided parathyroidectomy, to ascertain that the correct gland has been excised and that no other hyperfunctional tissue is present. MIP has many advantages over the traditional bilateral, four-gland exploration. MIP can be performed using local anesthesia, requires less operative time, results in fewer complications, and offers an improved cosmetic result and greater patient satisfaction. Additional advantages of MIP are earlier hospital discharge and decreased overall associated costs. This article aims to address the considerations for accomplishing MIP, including the role of preoperative imaging studies, intraoperative adjuncts, and surgical techniques. PMID:26425454
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.
On the partitioning strategy based on symmetry transformations
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, J. M.; Chien, L. S.
1990-01-01
A computational procedure is presented for the analysis of unsymmetric structures. The procedure is based on a modified version of the symmetry-transformation partitioning strategy, in which the response of the structure is approximated by a linear combination of symmetric/antisymmetric response vectors, each obtained by using only a fraction of the degrees of freedom of the original FEM model. The three key elements of the procedure are: (1) mixed (or primitive-variable) formulation with independent shape functions for the different fields; (2) restructuring of the governing discrete equations of the structure into uncoupled sets in the symmetric and antisymmetric response vectors; and (3) a stable and efficient iterative process for generating the response of the structure. The effectiveness of the proposed procedure and its advantages over classical substructuring are demonstrated by means of numerical examples.
Bilinear R-parity violation with flavor symmetry
NASA Astrophysics Data System (ADS)
Bazzocchi, F.; Morisi, S.; Peinado, E.; Valle, J. W. F.; Vicente, A.
2013-01-01
Bilinear R-parity violation (BRPV) provides the simplest intrinsically super-symmetric neutrino mass generation scheme. While neutrino mixing parameters can be probed in high energy accelerators, they are unfortunately not predicted by the theory. Here we propose a model based on the discrete flavor symmetry A 4 with a single R-parity violating parameter, leading to (i) correct Cabbibo mixing given by the Gatto-Sartori-Tonin formula, and a successful unification-like b-tau mass relation, and (ii) a correlation between the lepton mixing angles θ 13 and θ 23 in agreement with recent neutrino oscillation data, as well as a (nearly) massless neutrino, leading to absence of neutrinoless double beta decay.
Two-flavor QCD simulation with exact chiral symmetry
Aoki, S.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Yamada, N.; Ishikawa, K-I.; Okawa, M.; Kanaya, K.; Matsufuru, H.; Okamoto, M.; Onogi, T.; Ukawa, A; Yoshie, T.
2008-07-01
We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a 16{sup 3}x32 lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to m{sub s}/6, where m{sub s} is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.
Simultaneous optical flow and source estimation: Space–time discretization and preconditioning
Andreev, R.; Scherzer, O.; Zulehner, W.
2015-01-01
We consider the simultaneous estimation of an optical flow field and an illumination source term in a movie sequence. The particular optical flow equation is obtained by assuming that the image intensity is a conserved quantity up to possible sources and sinks which represent varying illumination. We formulate this problem as an energy minimization problem and propose a space–time simultaneous discretization for the optimality system in saddle-point form. We investigate a preconditioning strategy that renders the discrete system well-conditioned uniformly in the discretization resolution. Numerical experiments complement the theory. PMID:26435561
Singlet-stabilized minimal gauge mediation
NASA Astrophysics Data System (ADS)
Curtin, David; Tsai, Yuhsin
2011-04-01
We propose singlet-stabilized minimal gauge mediation as a simple Intriligator, Seiberg and Shih-based model of direct gauge mediation which avoids both light gauginos and Landau poles. The hidden sector is a massive s-confining supersymmetric QCD that is distinguished by a minimal SU(5) flavor group. The uplifted vacuum is stabilized by coupling the meson to an additional singlet sector with its own U(1) gauge symmetry via nonrenormalizable interactions suppressed by a higher scale ΛUV in the electric theory. This generates a nonzero vacuum expectation value for the singlet meson via the inverted hierarchy mechanism, but requires tuning to a precision ˜(Λ/ΛUV)2, which is ˜10-4. In the course of this analysis we also outline some simple model-building rules for stabilizing uplifted-ISS models, which lead us to conclude that meson deformations are required (or at least heavily favored) to stabilize the adjoint component of the magnetic meson.
Glial brain tumor detection by using symmetry analysis
NASA Astrophysics Data System (ADS)
Pedoia, Valentina; Binaghi, Elisabetta; Balbi, Sergio; De Benedictis, Alessandro; Monti, Emanuele; Minotto, Renzo
2012-02-01
In this work a fully automatic algorithm to detect brain tumors by using symmetry analysis is proposed. In recent years a great effort of the research in field of medical imaging was focused on brain tumors segmentation. The quantitative analysis of MRI brain tumor allows to obtain useful key indicators of disease progression. The complex problem of segmenting tumor in MRI can be successfully addressed by considering modular and multi-step approaches mimicking the human visual inspection process. The tumor detection is often an essential preliminary phase to solvethe segmentation problem successfully. In visual analysis of the MRI, the first step of the experts cognitive process, is the detection of an anomaly respect the normal tissue, whatever its nature. An healthy brain has a strong sagittal symmetry, that is weakened by the presence of tumor. The comparison between the healthy and ill hemisphere, considering that tumors are generally not symmetrically placed in both hemispheres, was used to detect the anomaly. A clustering method based on energy minimization through Graph-Cut is applied on the volume computed as a difference between the left hemisphere and the right hemisphere mirrored across the symmetry plane. Differential analysis involves the loss the knowledge of the tumor side. Through an histogram analysis the ill hemisphere is recognized. Many experiments are performed to assess the performance of the detection strategy on MRI volumes in presence of tumors varied in terms of shapes positions and intensity levels. The experiments showed good results also in complex situations.
Symmetry breaking in actin gels - Implications for cellular motility
NASA Astrophysics Data System (ADS)
John, Karin; Peyla, Philippe; Misbah, Chaouqi
2007-03-01
The physical origin of cell motility is not fully understood. Recently minimal model systems have shown, that polymerizing actin itself can produce a motile force, without the help of motor proteins. Pathogens like Shigella or Listeria use actin to propel themselves forward in their host cell. The same process can be mimicked with polystyrene beads covered with the activating protein ActA, which reside in a solution containing actin monomers. ActA induces the growth of an actin gel at the bead surface. Initially the gel grows symmetrically around the bead until a critical size is reached. Subsequently one observes a symmetry breaking and the gel starts to grow asymmetrically around the bead developing a tail of actin at one side. This symmetry breaking is accompanied by a directed movement of the bead, with the actin tail trailing behind the bead. Force generation relies on the combination of two properties: growth and elasticity of the actin gel. We study this phenomenon theoretically within the framework of a linear elasticity theory and linear flux-force relationships for the evolution of an elastic gel around a hard sphere. Conditions for a parity symmetry breaking are identified analytically and illustrated numerically with the help of a phasefield model.
A critical analysis of one-loop neutrino mass models with minimal dark matter
NASA Astrophysics Data System (ADS)
Ahriche, Amine; McDonald, Kristian L.; Nasri, Salah; Picek, Ivica
2016-06-01
A recent paper investigated minimal RνMDM models with the type T1-iii and T3 one-loop topologies. However, the candidate most-minimal model does not possess an accidental symmetry - the scalar potential contains an explicit symmetry breaking term, rendering the dark matter unstable. We present two models that cure this problem. However, we further show that all of the proposed minimal one-loop RνMDM models suffer from a second problem - an additional source of explicit Z2 symmetry breaking in the Yukawa sector. We perform a more-general analysis to show that neutrino mass models using either the type T3 or type T1-iii one-loop topologies do not give viable minimal dark matter candidates. Consequently, one-loop models of neutrino mass with minimal dark matter do not appear possible. Thus, presently there remains a single known (three-loop) model of neutrino mass that gives stable dark matter without invoking any new symmetries.
Reduced discretization error in HZETRN
Slaba, Tony C.; Blattnig, Steve R.; Tweed, John
2013-02-01
The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure. In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.
Discrete tomography in neutron radiography
NASA Astrophysics Data System (ADS)
Kuba, Attila; Rodek, Lajos; Kiss, Zoltán; Ruskó, László; Nagy, Antal; Balaskó, Márton
2005-04-01
Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori information (such as an approximate shape of the object) we can apply two DT methods in neutron imaging by reducing the problem to an optimization task. The first method is a special one because it is only suitable if the object is composed of cylinders and sphere shapes. The second method is a general one in the sense that it can be used for reconstructing objects of any shape. Software was developed and physical experiments performed in order to investigate the effects of several reconstruction parameters: the number of projections, noise levels, and complexity of the object to be reconstructed. We give a summary of the experimental results and make a comparison of the results obtained using a classical reconstruction technique (FBP). The programs we developed are available in our DT reconstruction program package DIRECT.
Police Discretion: A Selected Bibliography.
ERIC Educational Resources Information Center
Brenner, Robert N.; Kravitz, Marjorie
This bibliography was compiled with two goals. The first goal is to provide police administrators and officers with an overview of the issues involved in developing guidelines for police discretion and a discussion of the options available. The second goal is to demonstrate the need for continuing dialogue and interaction between lawmakers, law…
Tests of Discrete Symmetries in the Semileptonic Decays of Neutral Kaons at Cplear
NASA Astrophysics Data System (ADS)
Chertok, Maxwell Benjamin
The semileptonic decays of neutral kaon beams, K0/rightarrow/pi e/nu and /bar K0/rightarrow/pi e/nu, were measured in the CPLEAR experiment, and the parameters /Delta m, Re (x), Im (x), and Re (ɛ S) were extracted using the time-dependent asymmetries in the rates for these two decay channels. Here, /Delta m is the mass difference between the long and short lived components of the neutral kaons, Re (x) and Im (x) are proportional to the real and imaginary parts, respectively, of the /Delta S=-/Delta Q amplitude in semileptonic decays, and Re (ɛ S) is the real part of the [/cal CP] violating mixing parameter for the short lived neutral kaon. The experiment was performed at the Low Energy Antiproton Ring at CERN. Antiprotons were stopped in a gaseous hydrogen target, and the reactions pp /rightarrow K+/bar K0/pi/sp- and pp /rightarrow K/sp- K0π+ were selected. This resulted in beams of neutral kaons with known initial strangeness: K0 and K0. Using CPLEAR data taken during 1993 and 1994, 669K semileptonic events were selected. By fitting the decay rate asymmetries, the parameters were measured to be:/eqalign[/Delta m&=(0.5278/pm0.0029stat./pm0.0007syst.)×1010/hbar/s/cr [ Re]/ (x)&=(5.5/pm10.2stat./pm7.5syst.)×10- 3/cr [ Im]/ (x)&=(1.6/pm3.4stat./pm1.8syst.)×10- 3/cr [ Re]/ (ɛ S)&=(2.25/pm0.76stat./pm0.52syst.)×10- 3/cr]where the first error is statistical and the second error is systematic. The precision of Δm obtained from this analysis is on the same order as the best published values. The results for x are much better than previously published values, and are consistent with the standard model prediction of |x| ~10-6. This is the first experiment to make a measurement of Re (ɛ S), and the value obtained in this analysis is in agreement with the published value of Re (ɛ L), as predicted by [/cal CPT] invariance.
An Introduction to Non-Abelian Discrete Symmetries for Particle Physicists
NASA Astrophysics Data System (ADS)
Ishimori, Hajime; Kobayashi, Tatsuo; Ohki, Hiroshi; Okada, Hiroshi; Shimizu, Yusuke; Tanimoto, Morimitsu
In search of discrete symmetry violations beyond the standard model: Thorium monoxide reloaded
NASA Astrophysics Data System (ADS)
Denis, Malika; Fleig, Timo
2016-12-01
We present an updated electron electric dipole moment (EDM) effective electric field of Eeff= 75.2 GV/cm and 229Th magnetic hyperfine interaction constant A|| = -1266 MHz, the nucleon-electron scalar-pseudoscalar interaction constant WS = 106.0 kHz, and the molecule-frame static electric dipole moment D = -4.41 D for the Δ31 science state of ThO. The criticisms of the results from Fleig and Nayak [J. Mol. Spectrosc. 300, 16 (2014)] made in Skripnikov and Titov [J. Chem. Phys. 142, 024301 (2015)] are addressed and largely found to be unsubstantiated within the framework of the present approach. The present findings confirm the slightly relaxed constraints on relevant beyond-standard-model parameters, in particular the electron EDM, de, and the nucleon-electron scalar-pseudoscalar coupling constant, CS.
3D toroidal physics: testing the boundaries of symmetry breaking
NASA Astrophysics Data System (ADS)
Spong, Don
2014-10-01
Toroidal symmetry is an important concept for plasma confinement; it allows the existence of nested flux surface MHD equilibria and conserved invariants for particle motion. However, perfect symmetry is unachievable in realistic toroidal plasma devices. For example, tokamaks have toroidal ripple due to discrete field coils, optimized stellarators do not achieve exact quasi-symmetry, the plasma itself continually seeks lower energy states through helical 3D deformations, and reactors will likely have non-uniform distributions of ferritic steel near the plasma. Also, some level of designed-in 3D magnetic field structure is now anticipated for most concepts in order to lead to a stable, steady-state fusion reactor. Such planned 3D field structures can take many forms, ranging from tokamaks with weak 3D ELM-suppression fields to stellarators with more dominant 3D field structures. There is considerable interest in the development of unified physics models for the full range of 3D effects. Ultimately, the questions of how much symmetry breaking can be tolerated and how to optimize its design must be addressed for all fusion concepts. Fortunately, significant progress is underway in theory, computation and plasma diagnostics on many issues such as magnetic surface quality, plasma screening vs. amplification of 3D perturbations, 3D transport, influence on edge pedestal structures, MHD stability effects, modification of fast ion-driven instabilities, prediction of energetic particle heat loads on plasma-facing materials, effects of 3D fields on turbulence, and magnetic coil design. A closely coupled program of simulation, experimental validation, and design optimization is required to determine what forms and amplitudes of 3D shaping and symmetry breaking will be compatible with future fusion reactors. The development of models to address 3D physics and progress in these areas will be described. This work is supported both by the US Department of Energy under Contract DE
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.
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.
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.
Are supersymmetric models with minimal particle content under tension for testing at LHC?
NASA Astrophysics Data System (ADS)
Samanta, Abhijit; Mandal, Sujoy Kumar; Manna, Himadri
2016-12-01
In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses O (10) TeV, far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4-5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as √{mt˜Lmt˜R }, to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.
Minimal Marking: A Success Story
ERIC Educational Resources Information Center
McNeilly, Anne
2014-01-01
The minimal-marking project conducted in Ryerson's School of Journalism throughout 2012 and early 2013 resulted in significantly higher grammar scores in two first-year classes of minimally marked university students when compared to two traditionally marked classes. The "minimal-marking" concept (Haswell, 1983), which requires…
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.
Quasiprobability Representations of Quantum Mechanics with Minimal Negativity.
Zhu, Huangjun
2016-09-16
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has profound implications for quantum computation. However, little is known about the minimal negativity that is necessary in general quasiprobability representations. Here we focus on a natural class of quasiprobability representations that is distinguished by simplicity and economy. We introduce three measures of negativity concerning the representations of quantum states, unitary transformations, and quantum channels, respectively. Quite surprisingly, all three measures lead to the same representations with minimal negativity, which are in one-to-one correspondence with the elusive symmetric informationally complete measurements. In addition, most representations with minimal negativity are automatically covariant with respect to the Heisenberg-Weyl groups. Furthermore, our study reveals an interesting tradeoff between negativity and symmetry in quasiprobability representations.
Peccei-Quinn symmetry from dynamical supersymmetry breaking
NASA Astrophysics Data System (ADS)
Harigaya, Keisuke; Ibe, Masahiro; Schmitz, Kai; Yanagida, Tsutomu T.
2015-10-01
The proximity of the Peccei-Quinn scale to the scale of supersymmetry breaking in models of pure gravity mediation hints at a common dynamical origin of these two scales. To demonstrate how to make such a connection manifest, we embed the Peccei-Quinn mechanism into the vectorlike model of dynamical supersymmetry breaking à la Izawa and Yanagida as well as Intriligator and Thomas (IYIT). Here, we rely on the anomaly-free discrete Z4R symmetry required in models of pure gravity mediation to solve the μ problem to protect the Peccei-Quinn symmetry from the dangerous effect of higher-dimensional operators. This results in a rich phenomenology featuring a QCD axion with a decay constant of O (1010) GeV and mixed dark matter in the form of weakly interacting massive particles and axions. In addition, exactly five pairs of extra 5 and 5* matter multiplets, directly coupled to the supersymmetry breaking sector and with masses close to the gravitino mass, m3 /2˜100 TeV , are needed to cancel the Z4R anomalies.
Transverse discrete breathers in unstrained graphene
NASA Astrophysics Data System (ADS)
Barani, Elham; Lobzenko, Ivan P.; Korznikova, Elena A.; Soboleva, Elvira G.; Dmitriev, Sergey V.; Zhou, Kun; Marjaneh, Aliakbar Moradi
2017-02-01
Discrete breathers (DB) are spatially localized vibrational modes of large amplitude in defect-free nonlinear lattices. The search for DBs in graphene is of high importance, taking into account that this one atom thick layer of carbon is promising for a number of applications. There exist several reports on successful excitation of DBs in graphene, based on molecular dynamics and ab initio simulations. In a recent work by Hizhnyakov with co-authors the possibility to excite a DB with atoms oscillating normal to the graphene sheet has been reported. In the present study we use a systematic approach for finding initial conditions to excite transverse DBs in graphene. The approach is based on the analysis of the frequency-amplitude dependence for a delocalized, short-wavelength vibrational mode. This mode is a symmetry-dictated exact solution to the dynamic equations of the atomic motion, regardless the mode amplitude and regardless the type of interatomic potentials used in the simulations. It is demonstrated that if the AIREBO potential is used, the mode frequency increases with the amplitude bifurcating from the upper edge of the phonon spectrum for out-of-plane phonons. Then a bell-shaped function is superimposed on this delocalized mode to obtain a spatially localized vibrational mode, i.e., a DB. Placing the center of the bell-shaped function at different positions with respect to the lattice sites, three different DBs are found. Typically, the degree of spatial localization of DBs increases with the DB amplitude, but the transverse DBs in graphene reported here demonstrate the opposite trend. The results are compared to those obtained with the use of the Savin interatomic potential and no transverse DBs are found in this case. The results of this study contribute to a better understanding of the nonlinear dynamics of graphene and they call for the ab initio simulations to verify which of the two potentials used in this study is more precise.
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.
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.
Exploring Discretization Error in Simulation-Based Aerodynamic Databases
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Nemec, Marian
2010-01-01
This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2016-08-01
We study SU(8) symmetry breaking induced by minimizing the Coleman-Weinberg effective potential for a third rank antisymmetric tensor scalar field in the 56 representation. Instead of breaking {SU}(8)\\supset {SU}(3)× {SU}(5), we find that the stable minimum of the potential breaks the original symmetry according to {SU}(8)\\supset {SU}(3)× {Sp}(4). Using both numerical and analytical methods, we present results for the potential minimum, the corresponding Goldstone boson structure and BEH mechanism, and the group-theoretic classification of the residual states after symmetry breaking.
Vadimov, Vasily; Silaev, Mihail
2013-10-25
We show that time reversal symmetry-breaking p(x)+ip(y) wave superconductors undergo several phase transitions subjected to an external magnetic field or supercurrent. In such a system, the discrete Z(2) symmetry can recover before a complete destruction of the order parameter. The domain walls associated with Z(2) symmetry can be created in a controllable way by a magnetic field or current sweep according to the Kibble-Zurek scenario. Such domain wall generation can take place in exotic superconductors like Sr(2)RuO(4), thin films of superfluid (3)He-A, and some heavy fermion compounds.
Ras activation and symmetry breaking during Dictyostelium chemotaxis.
Kortholt, Arjan; Keizer-Gunnink, Ineke; Kataria, Rama; Van Haastert, Peter J M
2013-10-01
Central to chemotaxis is the molecular mechanism by which a shallow spatial gradient of chemoattractant induces symmetry breaking of activated signaling molecules. Previously, we have used Dictyostelium mutants to investigate the minimal requirements for chemotaxis, and identified a basal signaling module providing activation of Ras and F-actin at the leading edge. Here, we show that Ras activation after application of a pipette releasing the chemoattractant cAMP has three phases, each depending on specific guanine-nucleotide-exchange factors (GEFs). Initially a transient activation of Ras occurs at the entire cell boundary, which is proportional to the local cAMP concentrations and therefore slightly stronger at the front than in the rear of the cell. This transient Ras activation is present in gα2 (gpbB)-null cells but not in gβ (gpbA)-null cells, suggesting that Gβγ mediates the initial activation of Ras. The second phase is symmetry breaking: Ras is activated only at the side of the cell closest to the pipette. Symmetry breaking absolutely requires Gα2 and Gβγ, but not the cytoskeleton or four cAMP-induced signaling pathways, those dependent on phosphatidylinositol (3,4,5)-triphosphate [PtdIns(3,4,5)P3], cGMP, TorC2 and PLA2. As cells move in the gradient, the crescent of activated Ras in the front half of the cell becomes confined to a small area at the utmost front of the cell. Confinement of Ras activation leads to cell polarization, and depends on cGMP formation, myosin and F-actin. The experiments show that activation, symmetry breaking and confinement of Ras during Dictyostelium chemotaxis uses different G-protein subunits and a multitude of Ras GEFs and GTPase-activating proteins (GAPs).
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
Dynamical supersymmetry breaking and late-time R symmetry breaking as the origin of cosmic inflation
NASA Astrophysics Data System (ADS)
Schmitz, Kai; Yanagida, Tsutomu T.
2016-10-01
Spontaneously broken supersymmetry (SUSY) and a vanishingly small cosmological constant imply that R symmetry must be spontaneously broken at low energies. Based on this observation, we suppose that, in the sector responsible for low-energy R symmetry breaking, a discrete R symmetry remains preserved at high energies and only becomes dynamically broken at relatively late times in the cosmological evolution, i.e., after the dynamical breaking of SUSY. Prior to R symmetry breaking, the Universe is then bound to be in a quasi-de Sitter phase—which offers a dynamical explanation for the occurrence of cosmic inflation. This scenario yields a new perspective on the interplay between SUSY breaking and inflation, which neatly fits into the paradigm of high-scale SUSY: inflation is driven by the SUSY-breaking vacuum energy density, while the chiral field responsible for SUSY breaking, the Polonyi field, serves as the inflaton. Because R symmetry is broken only after inflation, slow-roll inflation is not spoiled by otherwise dangerous gravitational corrections in supergravity. We illustrate our idea by means of a concrete example, in which both SUSY and R symmetry are broken by strong gauge dynamics and in which late-time R symmetry breaking is triggered by a small inflaton field value. In this model, the scales of inflation and SUSY breaking are unified, the inflationary predictions are similar to those of F-term hybrid inflation in supergravity, reheating proceeds via gravitino decay at temperatures consistent with thermal leptogenesis, and the sparticle mass spectrum follows from pure gravity mediation. Dark matter consists of thermally produced winos with a mass in the TeV range.
NASA Astrophysics Data System (ADS)
Motrunich, Olexei; Geraedts, Scott
2015-03-01
We construct models realizing distinct confining phases of lattice gauge theories envisioned in a formal classification of gapped phases of gauge theories by Kapustin and Thorngreen, arXiv:1309.4721. This generalizes ideas of Symmetry-Protected Topological (SPT) phases in Condensed Matter to systems where fundamental microscopic objects are quantum lines, which is of interest in High Energy Theory. Specifically, in (3+1)D, we consider discrete ZN lattice gauge theory models, with two copies of ZN, and construct N distinct confining phases by engineering condensation of bound states of magnetic fluxes (which are quantum lines in 3d) and ZN electric field lines. In (4+1)D, we consider compact quantum electrodynamics (CQED) models, with two copies of CQED, and engineer condensation of bound states of monopoles (which are quantum lines in 4d) and U(1) electric field lines. When the bound states contain a single monopole, we find SPT-like phases of the lattice gauge theory, while when the bound states contain multiple monopoles, we find analogs of Symmetry-Enriched Topological phases, where in the present case we also have fractionalization of Faraday lines. The distinct character of these topological phases of quantum lines is revealed by unusual physics at a boundary.
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.
Scattering States of HULTHÉN Interaction in Minimal Length Quantum Mechanics
NASA Astrophysics Data System (ADS)
Hassanabadi, H.; Zarrinkamar, S.; Maghsoodi, E.
2013-05-01
We first revisit the nonrelativistic minimal length quantum mechanics and reveal an interesting symmetry of the problem. In fact, we will show that the cumbersome problem can be cast into the ordinary Schrödinger equation with a new effective potential. Next, as a typical example, we show the minimal length Schrödinger equation in the presence of a nonminimal Hulthén vector interaction. The transmission and reflection coefficients are reported as well.
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.
Spatial data discretization methods for geocomputation
NASA Astrophysics Data System (ADS)
Cao, Feng; Ge, Yong; Wang, Jinfeng
2014-02-01
Geocomputation provides solutions to complex geographic problems. Continuous and discrete spatial data are involved in the geocomputational process; however, geocomputational methods for discrete spatial data cannot be directly applied to continuous or mixed spatial data. Therefore, discretization methods for continuous or mixed spatial data are involved in the process. Since spatial data has spatial features, such as association, heterogeneity and spatial structure, these features cannot be handled by traditional discretization methods. Therefore, this work develops feature-based spatial data discretization methods that achieve optimal discretization results for spatial data using spatial information implicit in those features. Two discretization methods considering the features of spatial data are presented. One is an unsupervised method considering autocorrelation of spatial data and the other is a supervised method considering spatial heterogeneity. Discretization processes of the two methods are exemplified using neural tube defects (NTD) for Heshun County in Shanxi Province, China. Effectiveness is also assessed.
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.
Holographic nonlinear hydrodynamics from AdS/CFT with multiple/non-abelian symmetries
NASA Astrophysics Data System (ADS)
Torabian, Mahdi; Yee, Ho-Ung
2009-08-01
We study viscous hydrodynamics of hot conformal field theory plasma with multiple/non-Abelian symmetries in the framework of AdS/CFT correspondence, using a recently proposed method of directly solving bulk gravity in derivative expansion of local plasma parameters. Our motivation is to better describe the real QCD plasma produced at RHIC, incorporating its U(1)Nf flavor symmetry as well as SU(2)I non-Abelian iso-spin symmetry. As concrete examples, we choose to study the STU model for multiple U(1)3 symmetries, which is a sub-sector of 5D N=4 gauged SUGRA dual to N=4 Super Yang-Mills theory, capturing Cartan U(1)3 dynamics inside the full R-symmetry. For SU(2), we analyze the minimal 4D N=3 gauged SUGRA whose bosonic action is simply an Einstein-Yang-Mills system, which corresponds to SU(2) R-symmetry dynamics on M2-branes at a Hyper-Kahler cone. By generalizing the bosonic action to arbitrary dimensions and Lie groups, we present our analysis and results for any non-Abelian plasma in arbitrary dimensions.
Systoles in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Fernandes, Sara; Grácio, Clara; Ramos, Carlos Correia
2013-01-01
The fruitful relationship between Geometry and Graph Theory has been explored by several authors benefiting also the Theory of discrete dynamical systems seen as Markov chains in graphs. In this work we will further explore the relation between these areas, giving a geometrical interpretation of notions from dynamical systems. In particular, we relate the topological entropy with the systole, here defined in the context of discrete dynamical systems. We show that for continuous interval maps the systole is trivial; however, for the class of interval maps with one discontinuity point the systole acquires relevance from the point of view of the dynamical behavior. Moreover, we define the geodesic length spectrum associated to a Markov interval map and we compute the referred spectrum in several examples.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
On the complexity of discrete feature selection for optimal classification.
Peña, Jose M; Nilsson, Roland
2010-08-01
Consider a classification problem involving only discrete features that are represented as random variables with some prescribed discrete sample space. In this paper, we study the complexity of two feature selection problems. The first problem consists in finding a feature subset of a given size k that has minimal Bayes risk. We show that for any increasing ordering of the Bayes risks of the feature subsets (consistent with an obvious monotonicity constraint), there exists a probability distribution that exhibits that ordering. This implies that solving the first problem requires an exhaustive search over the feature subsets of size k. The second problem consists of finding the minimal feature subset that has minimal Bayes risk. In the light of the complexity of the first problem, one may think that solving the second problem requires an exhaustive search over all of the feature subsets. We show that, under mild assumptions, this is not true. We also study the practical implications of our solutions to the second problem.
Observability of discretized partial differential equations
NASA Technical Reports Server (NTRS)
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
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.
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.
Umbral Deformations on Discrete SPACE TIME
NASA Astrophysics Data System (ADS)
Zachos, Cosmas K.
Given a minimum measurable length underlying spacetime, the latter may be effectively regarded as discrete, at scales of order the Planck length. A systematic discretization of continuum physics may be effected most efficiently through the umbral deformation. General functionals yielding such deformations at the level of solutions are furnished and illustrated, and broad features of discrete oscillations and wave propagation are outlined.
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…
Soto-Quiros, Pablo
2015-01-01
This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase. PMID:26451390
Soto-Quiros, Pablo
2015-01-01
This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT): the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.