NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Fermion mass hierarchies and flavour mixing from a minimal discrete symmetry
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio; Lin, Yin
2008-09-01
We construct a simple model of fermion masses based on a spontaneously broken S×Z flavour group. At the leading order, in the neutrino sector S is broken down to a ν-ν parity subgroup that enforces a maximal atmospheric mixing angle and a vanishing θ. In the charged lepton sector the ν-ν parity is maximally broken and the resulting mass matrix is nearly diagonal. The charged lepton mass hierarchy is automatically reproduced by the S symmetry breaking parameter alone. A careful analysis shows that, after the inclusion of all relevant subleading effects, the model predicts θ=π/4+O(λc2) and θ=O(λc2), λ denoting the Cabibbo angle. A simple extension to the quark sector is also illustrated, where the mass spectrum and the mixing angles are naturally reproduced, with the exception of the mixing angle between the first two generations, that requires a small accidental enhancement.
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
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.
`t Hooft anomaly matching for discrete symmetries
Csaki, C.; Murayama, Hitoshi |
1998-05-01
The authors show how to extend the `t Hooft anomaly matching conditions to discrete symmetries. They check these discrete anomally matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N = 1 supersymmetric yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N = 1 supersymmetric theories based on exceptional groups.
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
NASA Astrophysics Data System (ADS)
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.
Breaking and Restoring of Diffeomorphism Symmetry in Discrete Gravity
Bahr, B.; Dittrich, B.
2009-12-15
We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so-called perfect actions, with exact symmetries and we will review first steps towards this end.
Symmetry breaking for drag minimization
NASA Astrophysics Data System (ADS)
Roper, Marcus; Squires, Todd M.; Brenner, Michael P.
2005-11-01
For locomotion at high Reynolds numbers drag minimization favors fore-aft asymmetric slender shapes with blunt noses and sharp trailing edges. On the other hand, in an inertialess fluid the drag experienced by a body is independent of whether it travels forward or backward through the fluid, so there is no advantage to having a single preferred swimming direction. In fact numerically determined minimum drag shapes are known to exhibit almost no fore-aft asymmetry even at moderate Re. We show that asymmetry persists, albeit extremely weakly, down to vanishingly small Re, scaling asymptotically as Re^3. The need to minimize drag to maximize speed for a given propulsive capacity gives one possible mechanism for the increasing asymmetry in the body plans seen in nature, as organisms increase in size and swimming speed from bacteria like E-Coli up to pursuit predator fish such as tuna. If it is the dominant mechanism, then this signature scaling will be observed in the shapes of motile micro-organisms.
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.
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
NASA Astrophysics Data System (ADS)
Kapustin, Anton; Thorngren, Ryan
2014-06-01
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 G1×G2 such that gauging G1 necessarily breaks G2 and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.
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. PMID:24972194
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: Gν=Zn with n ≥3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry Gℓ=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries Gℓ, an agreement with the data can be achieved if ˜10 % corrections related to breaking of Gℓ and Gν are included.
On discrete symmetries and torsion homology in F-theory
NASA Astrophysics Data System (ADS)
Mayrhofer, Christoph; Palti, Eran; Till, Oskar; Weigand, Timo
2015-06-01
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a gauge symmetry. We show that the resulting five-dimensional theories do not have a symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
Gravity cutoff in theories with large discrete symmetries.
Dvali, Gia; Redi, Michele; Sibiryakov, Sergey; Vainshtein, Arkady
2008-10-10
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z(N) discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories that address the hierarchy problem by lowering the gravitational cutoff due to the existence of large Z(10(32))-type symmetries. PMID:18999587
On discrete symmetries for a whole Abelian model
NASA Astrophysics Data System (ADS)
Chauca, J.; Doria, R.
2012-10-01
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 {Dμ,Xiμ} and the physical basis {GμI}. 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 {GμI} 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.
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.
Testing discrete symmetries at a super τ -charm factory
NASA Astrophysics Data System (ADS)
Bevan, Adrian John
2016-02-01
Tests of discrete symmetry violation have played an important role in understanding the structure of weak interactions in the Standard Model of particle physics. Historically, these measurements have been extensively performed in experiments with large samples of K and B mesons. A high luminosity τ-charm facility presents physicists with the opportunity to comprehensively explore discrete symmetry violation and test the Standard Model using τ leptons, charm mesons, and charmed baryons. This paper discusses several possible measurements for a future τ-charm factory.
Peculiar symmetry structure of some known discrete nonautonomous equations
NASA Astrophysics Data System (ADS)
Garifullin, R. N.; Habibullin, I. T.; Yamilov, R. I.
2015-06-01
We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler-Bobenko-Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler-Bobenko-Suris list.
Discretized Weyl-orbit functions: modified multiplication and Galois symmetry
NASA Astrophysics Data System (ADS)
Hrivnák, J.; Walton, M. A.
2015-05-01
We note a remarkable similarity between the discretized Weyl-orbit functions and affine modular data associated with Wess-Zumino-Novikov-Witten (WZNW) conformal field theories. Known properties of the modular data are exploited here to uncover analogous results for the discretized orbit functions. We show that the product of orbit functions is modified in analogy with the truncation of tensor products known as affine fusion, governing the interactions in WZNW models. A Galois symmetry, like that of affine modular data, is also described for the discretized orbit functions.
Chirality and Symmetry Breaking in a Discrete Internal Space
NASA Astrophysics Data System (ADS)
Lampe, Bodo
2012-10-01
In previous papers the permutation group S 4 has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S 4 is the pyritohedral group A 4× Z 2 because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S 4→ A 4. Since A 4 is a chiral group, while S 4 is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.
Discrete symmetries in the heterotic-string landscape
NASA Astrophysics Data System (ADS)
Athanasopoulos, P.
2015-07-01
We describe a new type of discrete symmetry that relates heterotic-string models. It is based on the spectral flow operator which normally acts within a general N = (2, 2) model and we use this operator to construct a map between N = (2, 0) models. The landscape of N = (2, 0) models is of particular interest among all heterotic-string models for two important reasons: Firstly, N =1 spacetime SUSY requires (2, 0) superconformal invariance and secondly, models with the well motivated by the Standard Model SO(10) unification structure are of this type. This idea was inspired by a new discrete symmetry in the space of fermionic ℤ2 × ℤ2 heterotic-string models that exchanges the spinors and vectors of the SO(10) GUT group, dubbed spinor-vector duality. We will describe how to generalize this to arbitrary internal rational Conformal Field Theories.
Leptonic Dirac CP violation predictions from residual discrete symmetries
NASA Astrophysics Data System (ADS)
Girardi, I.; Petcov, S. T.; Stuart, Alexander J.; Titov, A. V.
2016-01-01
Assuming that the observed pattern of 3-neutrino mixing is related to the existence of a (lepton) flavour symmetry, corresponding to a non-Abelian discrete symmetry group Gf, and that Gf is broken to specific residual symmetries Ge and Gν of the charged lepton and neutrino mass terms, we derive sum rules for the cosine of the Dirac phase δ of the neutrino mixing matrix U. The residual symmetries considered are: i) Ge =Z2 and Gν =Zn, n > 2 or Zn ×Zm, n , m ≥ 2; ii) Ge =Zn, n > 2 or Zn ×Zm, n , m ≥ 2 and Gν =Z2; iii) Ge =Z2 and Gν =Z2; iv) Ge is fully broken and Gν =Zn, n > 2 or Zn ×Zm, n , m ≥ 2; and v) Ge =Zn, n > 2 or Zn ×Zm, n , m ≥ 2 and Gν is fully broken. For given Ge and Gν, the sum rules for cos δ thus derived are exact, within the approach employed, and are valid, in particular, for any Gf containing Ge and Gν as subgroups. We identify the cases when the value of cos δ cannot be determined, or cannot be uniquely determined, without making additional assumptions on unconstrained parameters. In a large class of cases considered the value of cos δ can be unambiguously predicted once the flavour symmetry Gf is fixed. We present predictions for cos δ in these cases for the flavour symmetry groups Gf =S4, A4, T‧ and A5, requiring that the measured values of the 3-neutrino mixing parameters sin2 θ12, sin2 θ13 and sin2 θ23, taking into account their respective 3σ uncertainties, are successfully reproduced.
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.
Discrete-time minimal control synthesis adaptive algorithm
NASA Astrophysics Data System (ADS)
di Bernardo, M.; di Gennaro, F.; Olm, J. M.; Santini, S.
2010-12-01
This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.
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
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Flocking with discrete symmetry: The two-dimensional active Ising model
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Li, Chuanzhong; He, Jingsong
2016-06-01
We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev-Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy.
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
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
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.
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
2014-09-01
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
Discrete Symmetries and 1/3-Quantum Vortices in Condensates of F=2 Cold Atoms
Semenoff, Gordon W.; Zhou, Fei
2007-03-09
In this Letter we study discrete symmetries of mean field manifolds of condensates of F=2 cold atoms, and various unconventional quantum vortices. Discrete quaternion symmetries result in two species of spin defects that can only appear in integer vortices while cyclic symmetries are found to result in a phase shift of 2{pi}/3 (or 4{pi}/3) and therefore 1/3- (or 2/3-) quantum vortices in condensates. We also briefly discuss 1/3-quantum vortices in condensates of trimers.
Fermionic Renormalization Group Flow at All Scales: Breaking a Discrete Symmetry
NASA Astrophysics Data System (ADS)
Gersch, Roland; Honerkamp, Carsten; Rohe, Daniel; Metzner, Walter
2006-07-01
We extend the functional renormalization group technique in a modi cation of the one-particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry-broken phase of a charge-density wave mean- eld model. We study the half- lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry-breaking eld allows us to access the symmetry-broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature.
Neutrino transitional magnetic moment and non-Abelian discrete symmetry
Chang, D. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Keung, W. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Senjanovic, G. Bartol Research Institute, University of Delaware, Newark, DE )
1990-09-01
We propose a mechanism which naturally will give rise to a small mass but a large transitional magnetic moment for the neutrino such that the solar-neutrino deficit problem can be explained. The idea is a discrete version of Voloshin's SU(2) mechanism. An example of such a mechanism using the quaternion group is illustrated.
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
Molfetta, G. di; Debbasch, F.
2012-12-15
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.
Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
Carbone, Lisa; Murray, Scott H.; Sati, Hisham
2015-10-15
For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(ℤ) on K∖G. We give explicit results for the action of the discrete U-duality groups SL{sub 2}(ℤ) and E{sub 7}(ℤ) on the scalar cosets SO(2)∖SL{sub 2}(ℝ) and [SU(8)/( ± Id)]∖E{sub 7(+7)}(ℝ) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.
Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories
NASA Astrophysics Data System (ADS)
Carbone, Lisa; Murray, Scott H.; Sati, Hisham
2015-10-01
For G = G(ℝ), a split, simply connected, semisimple Lie group of rank n and K the maximal compact subgroup of G, we give a method for computing Iwasawa coordinates of K∖G using the Chevalley generators and the Steinberg presentation. When K∖G is a scalar coset for a supergravity theory in dimensions ≥3, we determine the action of the integral form G(ℤ) on K∖G. We give explicit results for the action of the discrete U-duality groups SL2(ℤ) and E7(ℤ) on the scalar cosets SO(2)∖SL2(ℝ) and [SU(8)/{ ± Id}]∖E7(+7)(ℝ) for type IIB supergravity in ten dimensions and 11-dimensional supergravity reduced to D = 4 dimensions, respectively. For the former, we use this to determine the discrete U-duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum-generating symmetry group for fundamental BPS solitons of type IIB supergravity in D = 10 dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U-duality groups in general.
Precision measurements of θ12 for testing models of discrete leptonic flavour symmetries
NASA Astrophysics Data System (ADS)
Ballett, P.; King, S. F.; Luhn, C.; Pascoli, S.; Schmidt, M. A.
2015-04-01
Models of leptonic flavour with discrete symmetries can provide an attractive explanation of the pattern of elements found in the leptonic mixing matrix. The next generation of neutrino oscillation experiments will allow the mixing parameters to be tested to a new level of precision, crucially measuring the CP violating phase δ for the first time. In this contribution, we present results of a systematic survey of the predictions of a class of models based on residual discrete symmetries and the prospects for excluding such models at medium- and long-term oscillation experiments. We place particular emphasis on the complementary role that a future circa 50 km reactor experiment, e.g. JUNO, can play in constraining these models.
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. PMID:25396355
NASA Astrophysics Data System (ADS)
Campoamor-Stursberg, R.; Rodríguez, M. A.; Winternitz, P.
2016-01-01
Ordinary differential equations (ODEs) and ordinary difference systems (OΔSs) invariant under the actions of the Lie groups {{SL}}x(2),{{SL}}y(2) and {{SL}}x(2)× {{SL}}y(2) of projective transformations of the independent variables x and dependent variables y are constructed. The ODEs are continuous limits of the OΔSs, or conversely, the OΔSs are invariant discretizations of the ODEs. The invariant OΔSs are used to calculate numerical solutions of the invariant ODEs of order up to five. The solutions of the invariant numerical schemes are compared to numerical solutions obtained by standard Runge-Kutta methods and to exact solutions, when available. The invariant method performs at least as well as standard ones and much better in the vicinity of singularities of solutions.
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.
Bezuglova, G S; Chechin, G M; Goncharov, P P
2011-09-01
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in two- and three-dimensional lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined invariant manifolds admitting existence of localized vibrations are found, and some types of discrete breathers are constructed on these manifolds. A general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed. This method allows one to decompose the corresponding system of linear differential equations with time-dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system. PMID:22060521
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.
Magnetic moment generation from non-minimal couplings in a scenario with Lorentz-symmetry violation
NASA Astrophysics Data System (ADS)
Belich, H.; Colatto, L. P.; Costa-Soares, T.; Helayël-Neto, J. A.; Orlando, M. T. D.
2009-07-01
This paper deals with situations that illustrate how the violation of Lorentz symmetry in the gauge sector may contribute to magnetic moment generation of massive neutral particles with spin- frac {1}{2} and spin-1. The procedure we adopt here is based on Relativistic Quantum Mechanics. We work out the non-relativistic regime that follows from the wave equation corresponding to a certain particle coupled to an external electromagnetic field and a background that accounts for the Lorentz-symmetry violation, and we thereby read off the magnetic dipole moment operator for the particle under consideration. We keep track of the parameters that govern the non-minimal electromagnetic coupling and the breaking of Lorentz symmetry in the expressions we get for the magnetic moments in the different cases we contemplate. Our claim is that the tiny magnetic dipole moment of truly-elementary neutral particles might signal Lorentz-symmetry violation.
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.
A UV-complete Composite Higgs model for Electroweak Symmetry Breaking: Minimal Conformal Technicolor
NASA Astrophysics Data System (ADS)
Tacchi, Ruggero Altair
The Large Hadron Collider is currently collecting data. One of the main goals of the experiment is to find evidence of the mechanism responsible for the breaking of the electroweak symmetry. There are many different models attempting to explain this breaking and traditionally most of them involve the use of supersymmetry near the scale of the breaking. This work is focused on exploring a viable model that is not based on a weakly coupled low scale supersymmetry sector to explain the electroweak symmetry breaking. We build a model based on a new strong interaction, in the fashion of theories commonly called "technicolor", name that is reminiscent of one of the first attempts of explaining the electroweak symmetry breaking using a strong interaction similar to the one whose charges are called colors. We explicitly study the minimal model of conformal technicolor, an SU(2) gauge theory near a strongly coupled conformal fixed point, with conformal symmetry softly broken by technifermion mass terms. Conformal symmetry breaking triggers chiral symmetry breaking in the pattern SU(4) → Sp (4), which gives rise to a pseudo-Nambu-Goldstone boson that can act as a composite Higgs boson. There is an additional composite pseudoscalar A with mass larger than mh and suppressed direct production at LHC. We discuss the electroweak fit in this model in detail. A good fit requires fine tuning at the 10% level. We construct a complete, realistic, and natural UV completion of the model, that explains the origin of quark and lepton masses and mixing angles. We embed conformal technicolor in a supersymmetric theory, with supersymmetry broken at a high scale. The effective theory below the supersymmetry breaking scale is minimal conformal technicolor with an additional light technicolor gaugino that might give rise to an additional pseudo Nambu-Goldstone boson that is observable at the LHC.
Large field excursions and approximate discrete symmetries from a clockwork axion
NASA Astrophysics Data System (ADS)
Kaplan, David E.; Rattazzi, Riccardo
2016-04-01
We present a renormalizable theory of scalars in which the low-energy effective theory contains a pseudo-Goldstone boson with a compact field space of 2 π F and an approximate discrete shift symmetry ZQ with Q ≫1 , yet the number of fields in the theory goes as log Q . Such a model can serve as a UV completion to models of relaxions and is a new source of exponential scale separation in field theory. While the model is local in "theory space," it appears not to have a continuum generalization (i.e., it cannot be a deconstructed extra dimension). Our framework shows that super-Planckian field excursions can be mimicked while sticking to renormalizable four-dimensional quantum field theory. We show that a supersymmetric extension is straightforwardly obtained, and we illustrate possible UV completions based on a compact extra dimension, where all global symmetries arise accidentally as a consequence of gauge invariance and five-dimensional locality.
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. PMID:25295295
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
Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures
NASA Astrophysics Data System (ADS)
Bihlo, Alexander; Staufer, Johannes
2011-03-01
A typical problem with the conventional Galerkin approach for the construction of finite-mode models is to keep structural properties unaffected in the process of discretization. We present two examples of finite-mode approximations that in some respect preserve the geometric attributes inherited from their continuous models: a three-component model of the barotropic vorticity equation known as Lorenz' maximum simplification equations [E.N. Lorenz, Maximum simplification of the dynamic equations, Tellus 12 (3) (1960) 243-254] and a six-component model of the two-dimensional Rayleigh-Bénard convection problem. It is reviewed that the Lorenz-1960 model respects both the maximal set of admitted point symmetries and an extension of the noncanonical Hamiltonian form (Nambu form). In a similar fashion, it is proved that the famous Lorenz-1963 model violates the structural properties of the Saltzman equations and hence cannot be considered as the maximum simplification of the Rayleigh-Bénard convection problem. Using a six-component truncation, we show that it is again possible to retain both symmetries and the Nambu representation in the course of discretization. The conservative part of this six-component reduction is related to the Lagrange top equations. Dissipation is incorporated using a metric tensor.
Constraining non-minimally coupled tachyon fields by the Noether symmetry
NASA Astrophysics Data System (ADS)
de Souza, Rudinei C.; Kremer, Gilberto M.
2009-07-01
A model for a homogeneous and isotropic Universe whose gravitational sources are a pressureless matter field and a tachyon field non-minimally coupled to the gravitational field is analyzed. The Noether symmetry is used to find expressions for the potential density and for the coupling function, and it is shown that both must be exponential functions of the tachyon field. Two cosmological solutions are investigated: (i) for the early Universe whose only source of gravitational field is a non-minimally coupled tachyon field which behaves as an inflaton and leads to an exponential accelerated expansion and (ii) for the late Universe whose gravitational sources are a pressureless matter field and a non-minimally coupled tachyon field which plays the role of dark energy and is responsible for the decelerated-accelerated transition period.
Hidden conformal symmetry of rotating black holes in minimal five-dimensional gauged supergravity
Setare, M. R.; Kamali, V.
2010-10-15
In the present paper we show that for a low frequency limit the wave equation of a massless scalar field in the background of nonextremal charged rotating black holes in five-dimensional minimal gauged and ungauged supergravity can be written as the Casimir of an SL(2,R) symmetry. Our result shows that the entropy of the black hole is reproduced by the Cardy formula. Also the absorption cross section is consistent with the finite temperature absorption cross section for a two-dimensional conformal field theory.
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)
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.
Higher-rank discrete symmetries in the IBM I. Octahedral shapes: General Hamiltonian
NASA Astrophysics Data System (ADS)
Van Isacker, P.; Bouldjedri, A.; Zerguine, S.
2015-06-01
In the context of the interacting boson model with s, d and g bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.
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.
Behbahani, Siavosh R.; Dymarsky, Anatoly; Mirbabayi, Mehrdad; Senatore, Leonardo; /Stanford U., Phys. Dept. /KIPAC, Menlo Park
2012-06-06
We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson {pi} is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory inspired models of Inflation based on Axion Monodromy. The models we study have the property that the 2-point function oscillates as a function of the wavenumber, leading to oscillations in the CMB power spectrum. The non-linear realization of time diffeomorphisms induces some self-interactions for the Goldstone boson that lead to a peculiar non-Gaussianity whose shape oscillates as a function of the wavenumber. We find that in the regime of validity of the effective theory, the oscillatory signal contained in the n-point correlation functions, with n > 2, is smaller than the one contained in the 2-point function, implying that the signature of oscillations, if ever detected, will be easier to find first in the 2-point function, and only then in the higher order correlation functions. Still the signal contained in higher-order correlation functions, that we study here in generality, could be detected at a subleading level, providing a very compelling consistency check for an approximate discrete shift symmetry being realized during inflation.
Spontaneous breaking of discrete symmetries in QCD on a small volume
Lucini, B.; Patella, A.; Pica, C.
2007-11-20
In a compact space with non-trivial cycles, for sufficiently small values of the compact dimensions, charge conjugation (C), spatial reflection (P) and time reversal (J) are spontaneously broken in QCD. The order parameter for the symmetry breaking is the trace of the Wilson line wrapping around the compact dimension, which acquires an imaginary part in the broken phase. We show that a physical signature for the symmetry breaking is a persistent baryonic current wrapping in the compact directions. The existence of such a current is derived analytically at first order in perturbation theory and confirmed in the non-perturbative regime by lattice simulations.
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.
Lepton masses in a minimal model with triplet Higgs bosons and S{sub 3} flavor symmetry
Mitra, Manimala; Choubey, Sandhya
2008-12-01
Viable neutrino and charged lepton masses and mixings are obtained by imposing a S{sub 3}xZ{sub 4}xZ{sub 3} flavor symmetry in a model with a few additional Higgs. We use two SU(2){sub L} triplet Higgs which are arranged as a doublet of S{sub 3}, and standard model singlet Higgs which are also put as doublets of S{sub 3}. We break the S{sub 3} symmetry in this minimal model by giving vacuum expectation values (VEV) to the additional Higgs fields. Dictated by the minimum condition for the scalar potential, we obtain certain VEV alignments which allow us to maintain {mu}-{tau} symmetry in the neutrino sector, while breaking it maximally for the charged leptons. This helps us to simultaneously explain the hierarchical charged lepton masses, and the neutrino masses and mixings. In particular, we obtain maximal {theta}{sub 23} and zero {theta}{sub 13}. We allow for a mild breaking of the {mu}-{tau} symmetry for the neutrinos and study the phenomenology. We give predictions for {theta}{sub 13} and the CP violating Jarlskog invariant J{sub CP}, as a function of the {mu}-{tau} symmetry breaking parameter. We also discuss possible collider signatures and phenomenology associated with lepton flavor violating processes.
Optically isotropic responses induced by discrete rotational symmetry of nanoparticle clusters
NASA Astrophysics Data System (ADS)
Hopkins, Ben; Liu, Wei; Miroshnichenko, Andrey E.; Kivshar, Yuri S.
2013-06-01
Fostered by the recent progress of the fields of plasmonics and metamaterials, the seminal topic of light scattering by clusters of nanoparticles is attracting enormous renewed interest gaining more attention than ever before. Related studies have not only found various new applications in different branches of physics and chemistry, but also spread rapidly into other fields such as biology and medicine. Despite the significant achievements, there still exists unsolved but vitally important challenges of how to obtain robust polarisation-invariant responses of different types of scattering systems. In this paper, we demonstrate polarisation-independent responses of any scattering system with a rotational symmetry with respect to an axis parallel to the propagation direction of the incident wave. We demonstrate that the optical responses such as extinction, scattering, and absorption, can be made independent of the polarisation of the incident wave for all wavelengths. Such polarisation-independent responses are proven to be a robust and generic feature that is purely due to the rotational symmetry of the whole structure. We anticipate our finding will play a significant role in various applications involving light scattering such as sensing, nanoantennas, optical switches, and photovoltaic devices.
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. PMID:27089174
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.
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)
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].
Riazuddin
2010-05-01
The degenerate leptogenesis is studied when the degeneracy in two of the heavy right-handed neutrinos [the third one is irrelevant if {mu}-{tau} symmetry is assumed] is due to L{identical_to}(L{sub e}-L{sub {mu}-}L{sub {tau}}) discrete symmetry. It is shown that a sizable leptogenesis asymmetry ({epsilon}{>=}10{sup -6}) is possible. The level of degeneracy required also predicts the Majorana phase needed for the asymmetry and this prediction is testable since it is the same phase, which appears in the double {beta} decay. Implications of nonzero reactor angle {theta}{sub 13} are discussed. It is shown that the contribution from sin{sup 2{theta}}{sub 13} to the leptogenesis asymmetry parameter may even dominate. An accurate measurement of sin{sup 2{theta}}{sub 13} would have important implications for the mass degeneracy of heavy right-handed neutrinos.
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.
Adler, S.L.
1999-01-01
We construct extensions of the standard model based on the hypothesis that Higgs bosons also exhibit a family structure and that the flavor weak eigenstates in the three families are distinguished by a discrete Z{sub 6} chiral symmetry that is spontaneously broken by the Higgs sector. We study in detail at the tree level models with three Higgs doublets and with six Higgs doublets comprising two weakly coupled sets of three. In a leading approximation of S{sub 3} cyclic permutation symmetry the three-Higgs-doublet model gives a {open_quotes}democratic{close_quotes} mass matrix of rank 1, while the six-Higgs-doublet model gives either a rank-1 mass matrix or, in the case when it spontaneously violates {ital CP}, a rank-2 mass matrix corresponding to nonzero second family masses. In both models, the CKM matrix is exactly unity in the leading approximation. Allowing small explicit violations of cyclic permutation symmetry generates small first family masses in the six-Higgs-doublet model, and first and second family masses in the three-Higgs-doublet model, and gives a nontrivial CKM matrix in which the mixings of the first and second family quarks are naturally larger than mixings involving the third family. Complete numerical fits are given for both models, flavor-changing neutral current constraints are discussed in detail, and the issues of unification of couplings and neutrino masses are addressed. On a technical level, our analysis uses the theory of circulant and retrocirculant matrices, the relevant parts of which are reviewed. {copyright} {ital 1998} {ital The American Physical Society}
Nehaniv, Chrystopher L; Rhodes, John; Egri-Nagy, Attila; Dini, Paolo; Morris, Eric Rothstein; Horváth, Gábor; Karimi, Fariba; Schreckling, Daniel; Schilstra, Maria J
2015-07-28
Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions. PMID:26078349
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.
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
Quantum oscillations in a bilayer with broken mirror symmetry: A minimal model for YBa2Cu3O6+δ
NASA Astrophysics Data System (ADS)
Maharaj, Akash V.; Zhang, Yi; Ramshaw, B. J.; Kivelson, S. A.
2016-03-01
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.
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).
Symmetries of Spectral Problems
NASA Astrophysics Data System (ADS)
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Whitaker, Thomas J. Beltran, Chris; Tryggestad, Erik; Kruse, Jon J.; Remmes, Nicholas B.; Tasson, Alexandria; Herman, Michael G.; Bues, Martin
2014-08-15
Purpose: Delayed charge is a small amount of charge that is delivered to the patient after the planned irradiation is halted, which may degrade the quality of the treatment by delivering unwarranted dose to the patient. This study compares two methods for minimizing the effect of delayed charge on the dose delivered with a synchrotron based discrete spot scanning proton beam. Methods: The delivery of several treatment plans was simulated by applying a normally distributed value of delayed charge, with a mean of 0.001(SD 0.00025) MU, to each spot. Two correction methods were used to account for the delayed charge. Method one (CM1), which is in active clinical use, accounts for the delayed charge by adjusting the MU of the current spot based on the cumulative MU. Method two (CM2) in addition reduces the planned MU by a predicted value. Every fraction of a treatment was simulated using each method and then recomputed in the treatment planning system. The dose difference between the original plan and the sum of the simulated fractions was evaluated. Both methods were tested in a water phantom with a single beam and simple target geometry. Two separate phantom tests were performed. In one test the dose per fraction was varied from 0.5 to 2 Gy using 25 fractions per plan. In the other test the number fractions were varied from 1 to 25, using 2 Gy per fraction. Three patient plans were used to determine the effect of delayed charge on the delivered dose under realistic clinical conditions. The order of spot delivery using CM1 was investigated by randomly selecting the starting spot for each layer, and by alternating per layer the starting spot from first to last. Only discrete spot scanning was considered in this study. Results: Using the phantom setup and varying the dose per fraction, the maximum dose difference for each plan of 25 fractions was 0.37–0.39 Gy and 0.03–0.05 Gy for CM1 and CM2, respectively. While varying the total number of fractions, the maximum dose
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
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.
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Cao, N.; Chen, S.; Jin, S.; Martinez, D.
1997-01-01
The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}
Combining Flavour and CP Symmetries
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio
2013-07-01
I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.
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.
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Flavor symmetry based MSSM: Theoretical models and phenomenological analysis
NASA Astrophysics Data System (ADS)
Babu, K. S.; Gogoladze, Ilia; Raza, Shabbar; Shafi, Qaisar
2014-09-01
We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM—for flavor symmetry-based minimal supersymmetric standard model—that respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)H and SO(3)H with the three families transforming as 2+1 and 3 representations, respectively. A simple solution is found in the case of SU(2)H for suppressing the flavor violating D-terms based on an exchange symmetry. Explicit models based on SO(3)H without the D-term problem are developed. In addition, models based on discrete non-Abelian flavor groups are presented which are automatically free from D-term issues. The permutation group S3 with a 2+1 family assignment, as well as the tetrahedral group A4 with a 3 assignment are studied. In all cases, a simple solution to the SUSY CP problem is found, based on spontaneous CP violation leading to a complex quark mixing matrix. We develop the phenomenology of the resulting sMSSM, which is controlled by seven soft SUSY breaking parameters for both the 2+1 assignment and the 3 assignment of fermion families. These models are special cases of the phenomenological MSSM (pMSSM), but with symmetry restrictions. We discuss the parameter space of sMSSM compatible with LHC searches, B-physics constraints and dark matter relic abundance. Fine-tuning in these models is relatively mild, since all SUSY particles can have masses below about 3 TeV.
A Twin Higgs Model from Left-Right Symmetry
Chacko, Z.; Goh, Hock-Seng; Harnik, Roni; /SLAC /Stanford U., Phys. Dept.
2005-12-14
We present twin Higgs models based on the extension of the Standard Model to left-right symmetry that protect the weak scale against radiative corrections up to scales of order 5 TeV. In the ultraviolet the Higgs sector of these theories respects an approximate global symmetry, in addition to the discrete parity symmetry characteristic of left-right symmetric models. The Standard Model Higgs field emerges as the pseudo-Goldstone boson associated with the breaking of the global symmetry. The parity symmetry tightly constrains the form of radiative corrections to the Higgs potential, allowing natural electroweak breaking. The minimal model predicts a rich spectrum of exotic particles that will be accessible to upcoming experiments, and which are necessary for the cancellation of one-loop quadratic divergences. These include right-handed gauge bosons with masses not to exceed a few TeV and a pair of vector-like quarks with masses of order several hundred GeV.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
Symmetry fractionalization and twist defects
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction. PMID:26086581
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.
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.
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.
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
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
Crystalline condensates in the chiral symmetry breaking phase diagram
Dunne, Gerald V.
2010-07-27
The existence of crystalline condensates in the temperature and chemcial potential phase diagram of the Gross-Neveu models can be traced to intricate symmetries of the associated inhomogeneous gap equation, which in turn reflect the form of chiral symmetry (discrete or continuous) that is broken. The gap equation based on the Ginzburg-Landau expansion is precisely the mKdV or AKNS hierarchy of integrable nonlinear equations for the Gross-Neveu model with discrete or continuous chiral symmetry, respectively.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
A K3 sigma model with : symmetry
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto; Wendland, Katrin
2014-02-01
The K3 sigma model based on the -orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra . By combining these different viewpoints we show that the = (4 , 4) preserving symmetries of this theory are described by the discrete symmetry group : . This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.
Symmetry in finite phase plane
NASA Astrophysics Data System (ADS)
Zak, J.
2010-03-01
The known symmetries in one-dimensional systems are inversion and translations. These symmetries persist in finite phase plane, but a novel symmetry arises in view of the discrete nature of the coordinate xi and the momentum pi : xi and pi can undergo permutations. Thus, if xi assumes M discrete values, i = 0, 1,2,..., M - 1, a permutation will change the order of the set x0,x1,..., xM-1 into a new ordered set. Such a symmetry element does not exist for a continuous x-coordinate in an infinite phase plane. Thus, in a finite phase plane, translations can be replaced by permutations. This is also true for the inversion operator. The new permutation symmetry has been used for the construction of conjugate representations and for the splitting of the M-dimensional vector space into independent subspaces. This splitting is exhaustive in the sense that if M = iMi with Mi being prime numbers, the M-dimensional space splits into M1,M2,...Mn-dimensional independent subspaces. It is shown that following this splitting one can design new potentials with appropriate constants of motion. A related problem is the Weyl-Heisenberg group in the M-dimensional space which turns into a direct product of its subgroups in the Mi-dimensional subspaces. As an example we consider the case of M = 8.
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
2015-12-01
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
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…
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
Time-reversal symmetry violation in several Lepton-Flavor-Violating processes
NASA Astrophysics Data System (ADS)
Vasquez, Juan Carlos
2015-09-01
We compute a T-odd triple vector correlation for the μ → eγ decay and the μ → e conversion process, finding simple results in terms of the CP violating phases of the effective Hamiltonians. Then we focus on the minimal Left-Right symmetric extension of the Standard Model, which can lead to an appreciable correlation. We show that under rather general assumptions, this correlation can be used to discriminate between Parity or Charge-conjugation as the discrete Left-Right symmetry.
NASA Astrophysics Data System (ADS)
Wang, Xiaoting; Byrd, Mark; Jacobs, Kurt
2016-03-01
A system subjected to noise contains a decoherence-free subspace or subsystem (DFS) only if the noise possesses an exact symmetry. Here we consider noise models in which a perturbation breaks a symmetry of the noise, so that if S is a DFS under a given noise process it is no longer so under the new perturbed noise process. We ask whether there is a subspace or subsystem that is more robust to the perturbed noise than S . To answer this question we develop a numerical method that allows us to search for subspaces or subsystems that are maximally robust to arbitrary noise processes. We apply this method to a number of examples, and find that a subsystem that is a DFS is often not the subsystem that experiences minimal noise when the symmetry of the noise is broken by a perturbation. We discuss which classes of noise have this property.
None
2011-10-06
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ?renormalizable?. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged ?vector? particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of ?massless? modes
Novel approach to data discretization
NASA Astrophysics Data System (ADS)
Borowik, Grzegorz; Kowalski, Karol; Jankowski, Cezary
2015-09-01
Discretization is an important preprocessing step in data mining. The data discretization method involves determining the ranges of values for numeric attributes, which ultimately represent discrete intervals for new attributes. The ranges for the proposed set of cuts are analyzed, in order to obtain a minimal set of ranges while retaining the possibility of classification. For this purpose, a special discernibility function can be constructed as a conjunction of alternative cuts set for each pair of different objects of different decisions- cuts discern these objects. However, the data mining methods based on discernibility matrix are insufficient for large databases. The purpose of this paper is the idea of implementation of a new data discretization algorithm that is based on statistics of attribute values and that avoids building the discernibility matrix explicitly. Evaluation of time complexity has shown that the proposed method is much more efficient than currently available solutions for large data sets.
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.
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 odometry. Results…
Symmetric Discrete Orthonormal Stockwell Transform
NASA Astrophysics Data System (ADS)
Wang, Yanwei; Orchard, Jeff
2008-09-01
The Stockwell Transform (ST) is a time-frequency signal decomposition that is gaining in popularity, likely because of its direct relation with the Fourier Transform (FT). A discrete and non-redundant version of the ST, denoted the Discrete Orthonormal Stockwell Transform (DOST), has made the use of the ST more feasible. However, the matrix multiplication required by the DOST can still be a formidable computation, especially for high-dimensional data. Moreover, the symmetric property of the ST and FT is not present in the DOST. In this paper, we investigate a new Symmetric Discrete Orthonormal Stockwell Transform (SDOST) that still keeps the non-redundant multiresolution features of the DOST, while maintaining a symmetry property similar to that of the FT. First, we give a brief introduction for the ST and the DOST. Then we analyze the DOST coefficients and modify the transform to get a symmetric version. A small experiment shows that the SDOST has kept the abilities of the DOST and demonstrates the advantage of symmetry when applying the SDOST.
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.
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.
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.
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
Hidden flavor symmetries of SO(10) GUT
NASA Astrophysics Data System (ADS)
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Symmetric Potential Lattice and Smooth Propagation of Tail-Free Discrete Breathers.
Doi, Yusuke; Yoshimura, Kazuyuki
2016-07-01
We present a particular type of one-dimensional nonlinear lattice that supports smoothly propagating discrete breathers. The lattice is constructed by imposing a particular symmetry on its potential function. This symmetry crucially affects the profile and motion of a traveling discrete breather. We show that any traveling discrete breather is truly localized with no tail and can smoothly propagate with a constant velocity. Theoretical analysis using an average Lagrangian explains this numerical observation. PMID:27419571
Symmetric Potential Lattice and Smooth Propagation of Tail-Free Discrete Breathers
NASA Astrophysics Data System (ADS)
Doi, Yusuke; Yoshimura, Kazuyuki
2016-07-01
We present a particular type of one-dimensional nonlinear lattice that supports smoothly propagating discrete breathers. The lattice is constructed by imposing a particular symmetry on its potential function. This symmetry crucially affects the profile and motion of a traveling discrete breather. We show that any traveling discrete breather is truly localized with no tail and can smoothly propagate with a constant velocity. Theoretical analysis using an average Lagrangian explains this numerical observation.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2⊂SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
ERIC Educational Resources Information Center
Ghezzi, Patrick M.
2007-01-01
The advantages of emphasizing discrete trials "teaching" over discrete trials "training" are presented first, followed by a discussion of discrete trials as a method of teaching that emerged historically--and as a matter of necessity for difficult learners such as those with autism--from discrete trials as a method for laboratory research. The…
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
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.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
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.
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.
S{sub 4}xZ{sub 2} flavor symmetry in supersymmetric extra U(1) model
Daikoku, Y.; Okada, H.
2010-08-01
We propose a E{sub 6} inspired supersymmetric model with a non-Abelian discrete flavor symmetry (S{sub 4} group); that is, SU(3){sub c}xSU(2){sub W}xU(1){sub Y}xU(1){sub X}xS{sub 4}xZ{sub 2}. In our scenario, the additional Abelian gauge symmetry, U(1){sub X}, not only solves the {mu} problem in the minimal supersymmetric standard model but also requires new exotic fields which play an important role in solving flavor puzzles. If our exotic quarks can be embedded into a S{sub 4} triplet, which corresponds to the number of the generation, one finds that dangerous proton decay can be well suppressed. Hence, it might be expected that the generation structure for lepton and quark in the standard model can be understood as a new system in order to stabilize the proton in a supersymmetric standard model. Moreover, because of the nature of the discrete non-Abelian symmetry itself, Yukawa coupling constants of our model are drastically reduced. In our paper, we show two predictive examples of the models for quark sector and lepton sector, respectively.
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ≥Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator χ ˆ =Rˆy (π) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
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. PMID:26871085
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)
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
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.
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
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.
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.
Beattle, A J; Oliver, I
1994-12-01
Biological surveys are in increasing demand while taxonomic resources continue to decline. How much formal taxonomy is required to get the job done? The answer depends on the kind of job but it is possible that taxonomic minimalism, especially (1) the use of higher taxonomic ranks, (2) the use of morphospecies rather than species (as identified by Latin binomials), and (3) the involvement of taxonomic specialists only for training and verification, may offer advantages for biodiversity assessment, environmental monitoring and ecological research. As such, formal taxonomy remains central to the process of biological inventory and survey but resources may be allocated more efficiently. For example, if formal Identification is not required, resources may be concentrated on replication and increasing sample sizes. Taxonomic minimalism may also facilitate the inclusion in these activities of important but neglected groups, especially among the invertebrates, and perhaps even microorganisms. PMID:21236933
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.
Construction of Superconvergent Discretizations with Differential-Difference Invariants
R.A. Axford
2005-08-12
To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations.
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.
Spinor Structure and Internal Symmetries
NASA Astrophysics Data System (ADS)
Varlamov, V. V.
2015-10-01
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
A discretization of Boltzmann's collision operator with provable convergence
NASA Astrophysics Data System (ADS)
Brechtken, Stefan
2014-12-01
The discretization of the right-hand side of the Boltzmann equation (aka the collision operator) on uniform grids generally suffers from some well known problems prohibiting the construction of deterministic high order discretizations which exactly sustain the basic properties of the collision operator. These problems mainly relate to problems arising from the discretization of spheres on uniform grids and the necessity that the discretization must possess some symmetry properties in order to provide the discrete versions of properties stemming from the continuous collision operator (number of collision invariants, avoidance of artificial collision invariants, type of equilibrium solutions, H-Theorem). We present a scheme to construct discretizations in 2 dimensions with arbitrarily high convergence orders on uniform grids, which are comparable to the approach by Rogier and Schneider [1] and the subsequent works by Michel and Schneider as well as Panferov and Heintz [2, 3] who used Farey sequences for the discretization. Moreover we take a closer look at this discretization in the framework of discrete velocity models to present results governing the correct collision invariants, lack of artificial collision invariants, the H-Theorem and the correct equilibrium solutions. Furthermore we classify lattice group models (LGpM) in the context of DVMs to transfer the high convergence order of these discretizations into the context of LGpMs and finally we take a short look at the numerical complexity.
Sekhar Chivukula
2010-01-08
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was present at the classical level. Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter.
Gray, J E; Vogt, A
1997-01-01
Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation. PMID:9224554
A left-right symmetric flavor symmetry model
NASA Astrophysics Data System (ADS)
Rodejohann, Werner; Xu, Xun-Jie
2016-03-01
We discuss flavor symmetries in left-right symmetric theories. We show that such frameworks are a different environment for flavor symmetry model building compared to the usually considered cases. This does not only concern the need to obey the enlarged gauge structure, but also more subtle issues with respect to residual symmetries. Furthermore, if the discrete left-right symmetry is charge conjugation, potential inconsistencies between the flavor and charge conjugation symmetries should be taken care of. In our predictive model based on A_4 we analyze the correlations between the smallest neutrino mass, the atmospheric mixing angle and the Dirac CP phase, the latter prefers to lie around maximal values. There is no lepton flavor violation from the Higgs bi-doublet.
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
Global convergence analysis of a discrete time nonnegative ICA algorithm.
Ye, Mao
2006-01-01
When the independent sources are known to be nonnegative and well-grounded, which means that they have a nonzero pdf in the region of zero, Oja and Plumbley have proposed a "Nonnegative principal component analysis (PCA)" algorithm to separate these positive sources. Generally, it is very difficult to prove the convergence of a discrete-time independent component analysis (ICA) learning algorithm. However, by using the skew-symmetry property of this discrete-time "Nonnegative PCA" algorithm, if the learning rate satisfies suitable condition, the global convergence of this discrete-time algorithm can be proven. Simulation results are employed to further illustrate the advantages of this theory. PMID:16526495
Broken flavor symmetries in high energy particle phenomenology
Antaramian, A.
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.
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.
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.
Symmetry Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
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.
Symmetry Breaking and Optical Negative Index of Closed Nanorings
NASA Astrophysics Data System (ADS)
Kante, Boubacar; Park, Yong-Shik; O'Brien, Kevin; Shuldman, Daniel; Lanzillotti-Kimura, Norberto; Wong, Zi; Yin, Xiaobo; Zhang, Xiang; UC Berkeley Team
2013-03-01
We report the first experimental demonstration of broadband negative-index metamaterial made solely of closed metallic nanorings. Using symmetry breaking that negatively couples the discrete nanorings, we measured negative phase delay in our composite chess metamaterial. Our approach open avenues towards topological nanophotonics with on demand linear and non-linear responses.
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.
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.
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.
Topological classification of crystalline insulators with space group symmetry
Jadaun, Priyamvada; Xiao, Di; Niu, Q.; Banerjee, Sanjay K.
2013-01-01
We show that in crystalline insulators, space group symmetry alone gives rise to a topological classification based on the discretization of electric polarization. Using C3 rotational symmetry as an example, we first prove that the polarization is discretized into three distinct classes, i.e., it can only take three inequivalent values. We then prove that these classes are topologically distinct. Therefore, a Z3 topological classification exists, with polarization as a topological class index. A concrete tight-binding model is derived to demonstrate the Z3 topological phase transition. Using first-principles calculations, we identify graphene on a BN substrate as a possible candidate to realize these Z3 topological states. To complete our analysis, we extend the classification of band structures to all 17 two-dimensional space groups. This work will contribute to a complete theory of symmetry-conserved topological phases and also elucidate topological properties of graphenelike systems.
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
Anomalous Abelian symmetry in the standard model
Ramond, P.
1995-12-31
The observed hierarchy of quark and lepton masses can be parametrized by nonrenormalizable operators with dimensions determined by an anomalous Abelian family symmetry, a gauge extension to the minimal supersymmetric standard model. Such an Abelian symmetry is generic to compactified superstring theories, with its anomalies compensated by the Green-Schwarz mechanism. If we assume these two symmetries to be the same, we find the electroweak mixing angle to be sin {sup 2}{theta}{sub {omega}} = 3/8 at the string scale, just by setting the ratio of the product of down quark to charged lepton masses equal to one at the string scale. This assumes no GUT structure. The generality of the result suggests a superstring origin for the standard model. We generalize our analysis to massive neutrinos, and mixings in the lepton sector.
New Algorithms For Automated Symmetry Recognition
NASA Astrophysics Data System (ADS)
Paul, Jody; Kilgore, Tammy Elaine; Klinger, Allen
1988-02-01
In this paper we present new methods for computer-based symmetry identification that combine elements of group theory and pattern recognition. Detection of symmetry has diverse applications including: the reduction of image data to a manageable subset with minimal information loss, the interpretation of sensor data,1 such as the x-ray diffraction patterns which sparked the recent discovery of a new "quasicrystal" phase of solid matter,2 and music analysis and composition.3,4,5 Our algorithms are expressed as parallel operations on the data using the matrix representation and manipulation features of the APL programming language. We demonstrate the operation of programs that characterize symmetric and nearly-symmetric patterns by determining the degree of invariance with respect to candidate symmetry transformations. The results are completely general; they may be applied to pattern data of arbitrary dimension and from any source.
Exact evolution of discrete relativistic cosmological models
Clifton, Timothy; Tavakol, Reza; Gregoris, Daniele; Rosquist, Kjell E-mail: danielegregoris@libero.it E-mail: r.tavakol@qmul.ac.uk
2013-11-01
We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.
Holography and Mottness: A Discrete Marriage
NASA Astrophysics Data System (ADS)
Phillips, Philip
2012-02-01
Gauge-gravity duality has allowed us to solve the physics of certain strongly coupled quantum mechanical systems using gravity. I will show how a space-time consisting of a charged black hole and a bulk Pauli coupling corresponds to a boundary theory with a dynamically generated gap (with no obvious symmetry breaking) and a massive rearrangement of the spectral weight as in classic Mott systems such as VO2. In this holographic set-up, the gap opens only when discrete scale invariance is present. This raises the possibility that the elusive symmetry that might be broken in Mott insulators, in general, might pertain to scale invariance. The relevance of this claim to recent theories of Mott systems that possess massless charged bosons is explored.
Aspects of emergent symmetries
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.
2016-03-01
These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
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.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
2010-06-01
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Carlsten, B.E.; Haynes, W.B.
1996-08-01
The authors theoretically and numerically investigate the operation and behavior of the discrete monotron oscillator, a novel high-power microwave source. The discrete monotron differs from conventional monotrons and transit time oscillators by shielding the electron beam from the monotron cavity`s RF fields except at two distinct locations. This makes the discrete monotron act more like a klystron than a distributed traveling wave device. As a result, the oscillator has higher efficiency and can operate with higher beam powers than other single cavity oscillators and has more stable operation without requiring a seed input signal than mildly relativistic, intense-beam klystron oscillators.
Molecular symmetry with quaternions.
Fritzer, H P
2001-09-01
A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry. PMID:11666072
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
Symmetry Breaking in Topological Quantum Gravity
NASA Astrophysics Data System (ADS)
Mielke, Eckehard W.
2013-04-01
A SL(5, ℝ) gauge-invariant topological field theory of gravity and possible gauge unifications are considered in four-dimensions (4D). The problem of quantization is evaluated in the asymptotic safety scenario. "Minimal" BF type models for the high energy limit are physically not quite realistic, a tiny symmetry breaking is needed to recover standard Einsteinian gravity for the macroscopic metrical background with induced cosmological constant.
Symmetry Breaking in Topological Quantum Gravity
NASA Astrophysics Data System (ADS)
Mielke, Eckehard W.
2015-01-01
A SL(5, R) gauge-invariant topological field theory of gravity and possible gauge unifications are considered in four-dimensions. The problem of quantization is evaluated in the asymptotic safety scenario. `Minimal' BF type models for the high energy limit are physically not quite realistic, a tiny symmetry breaking is needed to recover standard Einsteinian gravity for the oscopic metrical background with induced cosmological constant.
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.
Discretizations of axisymmetric systems
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg
2002-11-01
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.
Origin of constrained maximal CP violation in flavor symmetry
NASA Astrophysics Data System (ADS)
He, Hong-Jian; Rodejohann, Werner; Xu, Xun-Jie
2015-12-01
Current data from neutrino oscillation experiments are in good agreement with δ = -π/2 and θ23 =π/4 under the standard parametrization of the mixing matrix. We define the notion of "constrained maximal CP violation" (CMCPV) for predicting these features and study their origin in flavor symmetry. We derive the parametrization-independent solution of CMCPV and give a set of equivalent definitions for it. We further present a theorem on how the CMCPV can be realized. This theorem takes the advantage of residual symmetries in neutrino and charged lepton mass matrices, and states that, up to a few minor exceptions, (| δ | ,θ23) = (π/2 ,π/4) is generated when those symmetries are real. The often considered μ- τ reflection symmetry, as well as specific discrete subgroups of O(3), is a special case of our theorem.
Minimal distances between SCFTs
NASA Astrophysics Data System (ADS)
Buican, Matthew
2014-01-01
We study lower bounds on the minimal distance in theory space between four-dimensional superconformal field theories (SCFTs) connected via broad classes of renormalization group (RG) flows preserving various amounts of supersymmetry (SUSY). For = 1 RG flows, the ultraviolet (UV) and infrared (IR) endpoints of the flow can be parametrically close. On the other hand, for RG flows emanating from a maximally supersymmetric SCFT, the distance to the IR theory cannot be arbitrarily small regardless of the amount of (non-trivial) SUSY preserved along the flow. The case of RG flows from =2 UV SCFTs is more subtle. We argue that for RG flows preserving the full =2 SUSY, there are various obstructions to finding examples with parametrically close UV and IR endpoints. Under reasonable assumptions, these obstructions include: unitarity, known bounds on the c central charge derived from associativity of the operator product expansion, and the central charge bounds of Hofman and Maldacena. On the other hand, for RG flows that break = 2 → = 1, it is possible to find IR fixed points that are parametrically close to the UV ones. In this case, we argue that if the UV SCFT possesses a single stress tensor, then such RG flows excite of order all the degrees of freedom of the UV theory. Furthermore, if the UV theory has some flavor symmetry, we argue that the UV central charges should not be too large relative to certain parameters in the theory.
Parida, Mina K.; Sahu, Pradip K.; Bora, Kalpana
2011-05-01
We show how gauge coupling unification is successfully implemented through nonsupersymmetric grand unified theory, SO(10)xG{sub f}(G{sub f}=S{sub 4},SO(3){sub f},SU(3){sub f}), using a low-scale flavor-symmetric model of the type SU(2){sub L}xU(1){sub Y}xSU(3){sub C}xS{sub 4} recently proposed by Hagedorn, Lindner, and Mohapatra, while assigning matter-parity discrete symmetry for the dark matter stability. For gauge coupling unification in the single-step-breaking case, we show that a color-octet fermion and a hyperchargeless weak triplet fermionic dark matter are the missing particles needed to complete its minimal supersymmetric standard model-equivalent degrees of freedom. When these are included, the model automatically predicts the nonsupersymmetric grand unification with a scale identical to the minimal supersymmetric standard model/grand unified theory scale. We also find a two-step-breaking model with Pati-Salam intermediate symmetry where the dark matter and a low-mass color-octet scalar or the fermion are signaled by grand unification. The proton-lifetime predictions are found to be accessible to ongoing or planned searches in a number of models. We discuss the grand unified origin of the light fermionic triplet dark matter, the color-octet fermion, and their phenomenology.
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.
Minimal vectorlike leptonic dark matter and signatures at the LHC
NASA Astrophysics Data System (ADS)
Bhattacharya, Subhaditya; Sahoo, Nirakar; Sahu, Narendra
2016-06-01
We propose a minimal vectorlike leptonic dark matter (DM) with renormalizable interaction in a beyond-the-Standard-Model (SM) scenario, in which the SM is augmented with a vectorlike doublet and a singlet lepton. The additional fermions are odd under a discrete Z2 symmetry, while the rest of the SM particles are singlets, thus providing stability to the DM. In this scenario, we show that the DM emerges as an admixture of the neutral component of the vectorlike doublet and the singlet leptons. The singlet-doublet mixing (sin θ ) plays a crucial role in yielding the correct relic density as well as in obtaining null direct DM search results through an interplay of interactions via Z and Higgs mediation. The mixing is also strongly constrained from the invisible Z and Higgs decay width. We found that the correct relic abundance of DM can be obtained in a large region of parameter space for a DM mass larger than MZ/2 and sin θ ≲0.1 . The details of model phenomenology with collider signatures at the Large Hadron Collider (LHC) are discussed. In particular, we show that for sin θ ≲0.01 , the charged companion of the DM can give rise to an observable displaced vertex signature, marking a significant departure from other fermionic DM scenarios, while keeping the relic abundance intact.
A discrete fractional random transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2005-11-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
NASA Astrophysics Data System (ADS)
Fang, Yi-Nan; Dong, Guo-Hui; Zhou, Duan-Lu; Sun, Chang-Pu
2016-04-01
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking. Supported by the National Natural Science Foundation of China under Grant Nos. 11421063, 11534002, 11475254 and the National 973 Program under Grant Nos. 2014CB921403, 2012CB922104, and 2014CB921202
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
Surface-Assisted Cyclodehydrogenation; Break the Symmetry, Enhance the Selectivity.
Wiengarten, Alissa; Lloyd, Julian A; Seufert, Knud; Reichert, Joachim; Auwärter, Willi; Han, Runyuan; Duncan, David A; Allegretti, Francesco; Fischer, Sybille; Oh, Seung Cheol; Sağlam, Özge; Jiang, Li; Vijayaraghavan, Saranyan; Écija, David; Papageorgiou, Anthoula C; Barth, Johannes V
2015-08-24
Selectivity in chemical reactions is a major objective in industrial processes to minimize spurious byproducts and to save scarce resources. In homogeneous catalysis the most important factor which determines selectivity is structural symmetry. However, a transfer of the symmetry concept to heterogeneous catalysis still requires a detailed comprehension of the underlying processes. Here, we investigate a ring-closing reaction in surface-confined meso-substituted porphyrin molecules by scanning tunneling microscopy, temperature-programmed desorption, and computational modeling. The identification of reaction intermediates enables us to analyze the reaction pathway and to conclude that the symmetry of the porphyrin core is of pivotal importance regarding product yields. PMID:26211450
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.
NASA Astrophysics Data System (ADS)
Ismael, Jenann Tareq
1997-04-01
Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.
Clash of symmetries in a Randall-Sundrum-like spacetime
Dando, Gareth; George, Damien P.; Volkas, Raymond R.; Davidson, Aharon; Wali, K.C.
2005-08-15
We present a toy model that exhibits clash-of-symmetries style Higgs field kink configurations in a Randall-Sundrum-like spacetime. The model has two complex scalar fields {phi}{sub 1,2}, with a sextic potential obeying global U(1)xU(1) and discrete {phi}{sub 1}{r_reversible}{phi}{sub 2} interchange symmetries. The scalar fields are coupled to 4+1 dimensional gravity endowed with a bulk cosmological constant. We show that the coupled Einstein-Higgs field equations have an interesting analytic solution provided the sextic potential adopts a particular form. The 4+1 metric is shown to be that of a smoothed-out Randall-Sundrum type of spacetime. The thin-brane Randall-Sundrum limit, whereby the Higgs field kinks become step functions, is carefully defined in terms of the fundamental parameters in the action. The 'clash-of-symmetries' feature, defined in previous papers, is manifested here through the fact that both of the U(1) symmetries are spontaneously broken at all nonasymptotic points in the extra dimension w. One of the U(1)'s is asymptotically restored as w{yields}-{infinity}, with the other U(1) restored as w{yields}+{infinity}. The spontaneously broken discrete symmetry ensures topological stability. In the gauged version of this model we find new flat-space solutions, but in the warped metric case we have been unable to find any solutions with nonzero gauge fields.
NASA Astrophysics Data System (ADS)
West, Carl T.; Kottos, Tsampikos; Prosen, Tomaz
2010-03-01
We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time PT symmetry. For a value γPT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT-phase. Our results will have applications to the design of optical elements with PT-symmetry.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
NASA Astrophysics Data System (ADS)
Moore, Gregory
The vanishing of the one-loop string cosmological constant in nontrivial non supersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions. For special backgrounds the string theory has an extra symmetry, expressed as a transformation on moduli space. When left- and right-moving wave functions transform in different representations of this symmetry the cosmological constant must vanish. Specific examples of the mechanism are given at one loop for theories in two and four dimensions. Various suggestions are made for the higher loop extension of this idea.
Discrete Newtonian cosmology: perturbations
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2015-03-01
In a previous paper (Gibbons and Ellis 2014 Discrete Newtonian cosmology Class. Quantum Grav. 31 025003), we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of general relativity theory, provided the distribution of particles obeys the central configuration equation. In this paper we show that one can obtain perturbed such Newtonian solutions that give the same linearized structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zel’dovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.
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
Symmetry, Equivalence and Self-Assembly
NASA Astrophysics Data System (ADS)
Douglas, Jack
2006-03-01
Molecular self-assembly at equilibrium is central to the formation of many biological structures and the emulation of this process through the creation of synthetic counterparts offers great promise for nanofabrication. The central problems in this field are an understanding of how the symmetry of the interacting particles encodes the geometrical structure of the organized structure and the nature of the thermodynamic transitions involved. Our approach is inspired by the self-assembly of actin, tubulin and icosahedral structures of plant and animal viruses. We observe chain, membrane,`nanotube' and hollow icosahedron structures using `equivalent' particles exhibiting an interplay between directional (dipolar and multi-polar) interactions and short-range (van der Waals) interactions. Specifically, a dipolar potential (continuous rotational symmetry) gives rise to chain formation, while potentials having discrete rotational symmetries (e.g., square quadrupole or triangular ring of dipoles) led to the self-organization of nanotube and icosahedral structures with some resemblance to tubulin and icosahedral viruses. The simulations are compared to theoretical models of molecular self-assembly, especially in the case of dipolar fluids where the corresponding analytic theory of equilibrium polymerization is well developed. These computations give insights into the design elements required for the development of synthetic systems exhibiting this type of organization.
Extended spin symmetry and the standard model
Besprosvany, J.; Romero, R.
2010-12-23
We review unification ideas and explain the spin-extended model in this context. Its consideration is also motivated by the standard-model puzzles. With the aim of constructing a common description of discrete degrees of freedom, as spin and gauge quantum numbers, the model departs from q-bits and generalized Hilbert spaces. Physical requirements reduce the space to one that is represented by matrices. The classification of the representations is performed through Clifford algebras, with its generators associated with Lorentz and scalar symmetries. We study a reduced space with up to two spinor elements within a matrix direct product. At given dimension, the demand that Lorentz symmetry be maintained, determines the scalar symmetries, which connect to vector-and-chiral gauge-interacting fields; we review the standard-model information in each dimension. We obtain fermions and bosons, with matter fields in the fundamental representation, radiation fields in the adjoint, and scalar particles with the Higgs quantum numbers. We relate the fields' representation in such spaces to the quantum-field-theory one, and the Lagrangian. The model provides a coupling-constant definition.
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
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
NASA Astrophysics Data System (ADS)
Maes, Christian; Salazar, Alberto
2014-01-01
In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary-driven particle systems such as the open Kawasaki lattice gas and the zero-range model. As a measure of time-symmetric dynamical activity over time T we count the difference (Nℓ - Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo-type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.
ERIC Educational Resources Information Center
McGehe, Carol
1991-01-01
Presents math activities, problems, and games for teaching elementary students to recognize the world's natural symmetry and understand the mathematical qualities it represents; suggests activities with construction paper, blocks, and calculators. Instructions for using the calculator to create palindromes are included. (SM)
Symmetry breaking in reconstituted actin cortices.
Abu Shah, Enas; Keren, Kinneret
2014-01-01
The actin cortex plays a pivotal role in cell division, in generating and maintaining cell polarity and in motility. In all these contexts, the cortical network has to break symmetry to generate polar cytoskeletal dynamics. Despite extensive research, the mechanisms responsible for regulating cortical dynamics in vivo and inducing symmetry breaking are still unclear. Here we introduce a reconstituted system that self-organizes into dynamic actin cortices at the inner interface of water-in-oil emulsions. This artificial system undergoes spontaneous symmetry breaking, driven by myosin-induced cortical actin flows, which appears remarkably similar to the initial polarization of the embryo in many species. Our in vitro model system recapitulates the rich dynamics of actin cortices in vivo, revealing the basic biophysical and biochemical requirements for cortex formation and symmetry breaking. Moreover, this synthetic system paves the way for further exploration of artificial cells towards the realization of minimal model systems that can move and divide.DOI: http://dx.doi.org/10.7554/eLife.01433.001. PMID:24843007
Symmetry breaking in reconstituted actin cortices
Abu Shah, Enas; Keren, Kinneret
2014-01-01
The actin cortex plays a pivotal role in cell division, in generating and maintaining cell polarity and in motility. In all these contexts, the cortical network has to break symmetry to generate polar cytoskeletal dynamics. Despite extensive research, the mechanisms responsible for regulating cortical dynamics in vivo and inducing symmetry breaking are still unclear. Here we introduce a reconstituted system that self-organizes into dynamic actin cortices at the inner interface of water-in-oil emulsions. This artificial system undergoes spontaneous symmetry breaking, driven by myosin-induced cortical actin flows, which appears remarkably similar to the initial polarization of the embryo in many species. Our in vitro model system recapitulates the rich dynamics of actin cortices in vivo, revealing the basic biophysical and biochemical requirements for cortex formation and symmetry breaking. Moreover, this synthetic system paves the way for further exploration of artificial cells towards the realization of minimal model systems that can move and divide. DOI: http://dx.doi.org/10.7554/eLife.01433.001 PMID:24843007
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Gauging without initial symmetry
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Σ, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Σ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ∼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
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.
Minimal D = 7 supergravity and the supersymmetry of Arnold-Beltrami flux branes
NASA Astrophysics Data System (ADS)
Fré, P.; Grassi, P. A.; Ravera, L.; Trigiante, M.
2016-06-01
In this paper we study some properties of the newly found Arnold-Beltrami flux-brane solutions to the minimal D = 7 supergravity. To this end we first single out the appropriate Free Differential Algebra containing both a gauge 3-form B [3] and a gauge 2-form B [2]: then we present the complete rheonomic parametrization of all the generalized curvatures. This allows us to identify two-brane configurations with Arnold-Beltrami fluxes in the transverse space with exact solutions of supergravity and to analyze the Killing spinor equation in their background. We find that there is no preserved supersymmetry if there are no additional translational Killing vectors. Guided by this principle we explicitly construct Arnold-Beltrami flux two-branes that preserve 0, 1/8 and 1/4 of the original supersymmetry. Two-branes without fluxes are instead BPS states and preserve 1/2 supersymmetry. For each two-brane solution we carefully study its discrete symmetry that is always given by some appropriate crystallographic group Γ. Such symmetry groups Γ are transmitted to the D = 3 gauge theories on the brane world-volume that would occur in the gauge/gravity correspondence. Furthermore we illustrate the intriguing relation between gauge fluxes in two-brane solutions and hyperinstantons in D = 4 topological sigma-models.
Gravity from Lorentz Symmetry Violation
Potting, Robertus
2006-06-19
In general relativity, the masslessness of gravitons can be traced to symmetry under diffeomorphisms. In this talk, we consider another possibility, whereby the masslessness arises from spontaneous violation of Lorentz symmetry.
Symmetry breaking and optical negative index of closed nanorings
NASA Astrophysics Data System (ADS)
Kanté, Boubacar; Park, Yong-Shik; O'Brien, Kevin; Shuldman, Daniel; Lanzillotti-Kimura, Norberto D.; Jing Wong, Zi; Yin, Xiaobo; Zhang, Xiang
2012-11-01
Metamaterials have extraordinary abilities, such as imaging beyond the diffraction limit and invisibility. Many metamaterials are based on split-ring structures, however, like atomic orbital currents, it has long been believed that closed rings cannot produce negative refractive index. Here we report a low-loss and polarization-independent negative-index metamaterial made solely of closed metallic nanorings. Using symmetry breaking that negatively couples the discrete nanorings, we measured negative phase delay in our composite ‘chess metamaterial’. The formation of an ultra-broad Fano-resonance-induced optical negative-index band, spanning wavelengths from 1.3 to 2.3 μm, is experimentally observed in this structure. This discrete and mono-particle negative-index approach opens exciting avenues towards symmetry-controlled topological nanophotonics with on-demand linear and nonlinear responses.
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
Mechanochemical symmetry breaking in Hydra aggregates.
Mercker, Moritz; Köthe, Alexandra; Marciniak-Czochra, Anna
2015-05-01
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
Electroweak symmetry breaking: Higgs/whatever
Chanowitz, M.S.
1989-10-16
In the first of these two lectures the Higgs mechanism is reviewed in its most general form, which does not necessarily require the existence of Higgs bosons. The general consequences of the hypothesis that electroweak symmetry breaking is due to the Higgs mechanism are deduced just from gauge invariance and unitarity. In the second lecture the general properties are illustrated with three specific models: the Weinberg-Salam model, its minimal supersymmetric extension, and technicolor. The second lecture concludes with a discussion of the experiment signals for strong WW scattering, whose presence or absence will allow us to determine whether the symmetry breaking sector lies above or below 1 TeV. 57 refs.
Chivukula, R. Sekhar; Simmons, Elizabeth H.; Di Chiara, Stefano; Foadi, Roshan
2009-11-01
We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zb{sub L}b{sub L} coupling from large corrections. This 'doublet-extended standard model' adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4)xU(1){sub X}{approx}SU(2){sub L}xSU(2){sub R}xP{sub LR}xU(1){sub X} symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2){sub L}xU(1){sub Y} electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M{yields}0) and standard-model-like (M{yields}{infinity}) limits. In this simple model, we find that the experimental limits on the Zb{sub L}b{sub L} coupling favor smaller M while the presence of a potentially sizable negative contribution to {alpha}T strongly favors large M. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to {alpha}T, {alpha}S, and the Zb{sub L}b{sub L} coupling in this model arise from an effective operator coupling right-handed top quarks to the Z boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to {alpha}T and the Zb{sub L}b{sub L} coupling, while leaving the standard model contributions essentially unchanged.
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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.
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…
Bubble divergences and gauge symmetries in spin foams
NASA Astrophysics Data System (ADS)
Bonzom, Valentin; Dittrich, Bianca
2013-12-01
The divergence structure of spin foam models and its relation to diffeomorphism symmetry has attracted renewed interest. We will discuss in detail the (nonoccurrence of) divergencies in the Barrett-Crane spin foam model, which with our choice of weights can be understood as an integral of delta functions only. We will present furthermore a simple method to estimate the occurrence of so-called bubble divergencies for general spin foam models. We expect divergencies in spin foams related to the existence of (diffeomorphism) gauge symmetries. Thus we have to conclude that such gauge symmetries are not (fully) present in the model we consider. But we will identify a class of gauge symmetries that occur at special solutions of equations imposed by the delta function weights. This situation is surprisingly similar to the case of broken diffeomorphism symmetries in discrete gravity, which are present around flat solutions. We introduce a method to derive (Ward identity-like) equations for the vertex amplitudes of the model in the case of broken gauge symmetries.
Continuous limit of discrete quantum walks
NASA Astrophysics Data System (ADS)
M N, Dheeraj; Brun, Todd A.
2015-06-01
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time walks. Quantum mechanically, in the discrete-time case, an additional "coin space" must be appended for the walk to have nontrivial time evolution. Continuous-time quantum walks, however, have no such constraints. This means that there is no completely straightforward way to treat a CTQW as a limit of a DTQW, as can be done in the classical case. Various approaches to this problem have been taken in the past. We give a construction for walks on d -regular, d -colorable graphs when the coin flip operator is Hermitian: from a standard DTQW we construct a family of discrete-time walks with a well-defined continuous-time limit on a related graph. One can think of this limit as a "coined" continuous-time walk. We show that these CTQWs share some properties with coined DTQWs. In particular, we look at a spatial search by a DTQW over the two-dimensional (2D) torus (a grid with periodic boundary conditions) of size √{N }×√{N } , where it was shown that a coined DTQW can search in time O (√{N }logN ) , but a standard CTQW takes Ω (N ) time to search for a marked element. The continuous limit of the DTQW search over the 2D torus exhibits the O (√{N }logN ) scaling, like the coined walk it is derived from. We also look at the effects of graph symmetry on the limiting walk, and show that the properties are similar to those of the DTQW as shown in Krovi and Brun, Phys. Rev. A 75, 062332 (2007), 10.1103/PhysRevA.75.062332.
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Chiral symmetry and pentaquarks
Dmitri Diakonov
2004-07-01
Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Discreteness induced extinction
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira; da Silva, Linaena Méricy
2015-11-01
Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the "Discreteness Inducing Extinction" (DIE). The results are interpreted in the context of the "paradox of sex", an old problem of evolutionary biology.
NASA Astrophysics Data System (ADS)
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
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.
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.
Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications
NASA Astrophysics Data System (ADS)
Blaszczyk, Michael; Oehlmann, Paul-Konstantin
2016-04-01
We are considering the class of heterotic N=(2,2) Landau-Ginzburg orbifolds with 9 fields corresponding to A 1 9 Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N=1 , 2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a Z_3 orbifold on an E6 lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric Z_3× Z_{3,free} orbifold regime.
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.
The minimal composite Higgs model
NASA Astrophysics Data System (ADS)
Agashe, Kaustubh; Contino, Roberto; Pomarol, Alex
2005-07-01
We study the idea of a composite Higgs in the framework of a five-dimensional AdS theory. We present the minimal model of the Higgs as a pseudo-Goldstone boson in which electroweak symmetry is broken dynamically via top loop effects, all flavour problems are solved, and contributions to electroweak precision observables are below experimental bounds. Since the 5D theory is weakly coupled, we are able to fully determine the Higgs potential and other physical quantities. The lightest resonances are expected to have a mass around 2 TeV and should be discovered at the LHC. The top sector is mostly composite and deviations from Standard Model couplings are expected.
NASA Astrophysics Data System (ADS)
Barceló, Roberto; Masip, Manuel
2008-11-01
We discuss a little Higgs scenario that introduces below the TeV scale just the two minimal ingredients of these models, a vectorlike T quark and a singlet component (implying anomalous couplings) in the Higgs field, together with a pseudoscalar singlet η. In the model, which is a variation of Schmaltz’s simplest little Higgs model, all the extra vector bosons are much heavier than the T quark. In the Yukawa sector the global symmetry is approximate, implying a single large coupling per flavor, whereas in the scalar sector it is only broken at the loop level. We obtain the one-loop effective potential and show that it provides acceptable masses for the Higgs h and for the singlet η with no need for an extra μ term. We find that mη can be larger than mh/2, which would forbid the (otherwise dominant) decay mode h→ηη.
Chemical basis for minimal cognition.
Hanczyc, Martin M; Ikegami, Takashi
2010-01-01
We have developed a simple chemical system capable of self-movement in order to study the physicochemical origins of movement. We propose how this system may be useful in the study of minimal perception and cognition. The system consists simply of an oil droplet in an aqueous environment. A chemical reaction within the oil droplet induces an instability, the symmetry of the oil droplet breaks, and the droplet begins to move through the aqueous phase. The complement of physical phenomena that is then generated indicates the presence of feedback cycles that, as will be argued, form the basis for self-regulation, homeostasis, and perhaps an extended form of autopoiesis. We discuss the result that simple chemical systems are capable of sensory-motor coupling and possess a homeodynamic state from which cognitive processes may emerge. PMID:20586578
Twisted supersymmetry: Twisted symmetry versus renormalizability
Dimitrijevic, Marija; Nikolic, Biljana; Radovanovic, Voja
2011-03-15
We discuss a deformation of superspace based on a Hermitian twist. The twist implies a *-product that is noncommutative, Hermitian and finite when expanded in a power series of the deformation parameter. The Leibniz rule for the twisted supersymmetry transformations is deformed. A minimal deformation of the Wess-Zumino action is proposed and its renormalizability properties are discussed. There is no tadpole contribution, but the two-point function diverges. We speculate that the deformed Leibniz rule, or more generally the twisted symmetry, interferes with renormalizability properties of the model. We discuss different possibilities to render a renormalizable model.
NASA Astrophysics Data System (ADS)
Cai, Jian; Modest, Michael F.
2016-01-01
In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.
Discrete translational invariance and mass-renormalization in the two-dimensional sine-Gordon model
NASA Astrophysics Data System (ADS)
Neudecker, Bernhard
1982-06-01
We consider the sine-Gordon model as a field-theory in which the interaction has a discrete translational invariance. It is shown that apart from a Gaussian contribution the Helmholtz free-energy exhibits this symmetry as well. Thus in an originally massless theory, the insertion of a mass term can be considered as a rather “weak” symmetry-breaking. Within the Amit-Goldschmidt-Grinstein renormalization-scheme we show that mass-renormalization is trivial.
Thermal symmetry in isoscaling
Escudero, C. R.; Lopez, J. A.; Dorso, C. O.
2007-02-12
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
NASA Astrophysics Data System (ADS)
Kotulski, Zbigniew; Szczepaski, Janusz
In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
NASA Astrophysics Data System (ADS)
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
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
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
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
NASA Astrophysics Data System (ADS)
Duguet, T.
2015-02-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree-Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.
Radiatively broken symmetries of nonhierarchical neutrinos
Dighe, Amol; Roy, Probir; Goswami, Srubabati
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 {lambda}{approx}10{sup 12} GeV 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 {lambda}{approx}10{sup 3} GeV 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 {alpha}{sub 2,3} 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 {alpha}{sub 2}{approx_equal}{pi} (i.e., m{sub 1}{approx_equal}-m{sub 2}) emerges in each case. We also show how a future accurate measurement of {theta}{sub 13} may enable some discrimination among these four cases in spite of renormalization group evolution.
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.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2011-08-01
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞.
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.
Minimal change nephrotic syndrome; Nil disease; Lipoid nephrosis; Idiopathic nephrotic syndrome of childhood ... which filter blood and produce urine. In minimal change disease, there is damage to the glomeruli. These ...
... 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.
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.
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.
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 of Magnetically Ordered Quasicrystals
NASA Astrophysics Data System (ADS)
Lifshitz, Ron
1998-03-01
The notion of magnetic symmetry is reexamined in light of the recent observation of long-range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals, is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.
Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow
Ishii, Katsuyuki; Omata, Seiro
2011-12-15
We consider the approximation scheme to the American call option via the discrete Morse semiflow, which is a minimizing scheme of a time semi-discretized variational functional. In this paper we obtain a rate of convergence of approximate solutions and the convergence of approximate free boundaries. We mainly apply the theory of variational inequalities and that of viscosity solutions to prove our results.
Multi-Interval Discretization of Continuous-Valued Attributes for Classification Learning
NASA Technical Reports Server (NTRS)
Fayyad, U.; Irani, K.
1993-01-01
Since most real-world applications of classification learning involve continuous-valued attributes, properly addressing the discretization process is an important problem. This paper addresses the use of the entropy minimization heuristic for discretizing the range of a continuous-valued attribute into multiple intervals.
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.
Discrete Sibson interpolation.
Park, Sung W; Linsen, Lars; Kreylos, Oliver; Owens, John D; Hamann, Bernd
2006-01-01
Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds. PMID:16509383
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.
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
Discrete stability in stochastic programming
Lepp, R.
1994-12-31
In this lecture we study stability properties of stochastic programs with recourse where the probability measure is approximated by a sequence of weakly convergent discrete measures. Such discrete approximation approach gives us a possibility to analyze explicitly the behavior of the second stage correction function. The approach is based on modern functional analytical methods of an approximation of extremum problems in function spaces, especially on the notion of the discrete convergence of vectors to an essentially bounded measurable function.
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.
Applications of flavor symmetry to the phenomenology of elementary particles
Kaeding, T.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.
Black Hole Spacetimes with Killing-Yano Symmetries
NASA Astrophysics Data System (ADS)
Kubizňák, David
2010-03-01
We present a brief overview of black hole spacetimes admitting Killing-Yano tensors. In vacuum these include Kerr-NUT-(A)dS metrics and certain black brane solutions. In the presence of matter fields, (conformal) Killing-Yano symmetries are known to exist for the Plebanski-Demianski solution and (trivially) for any spacetime with spherical symmetry. Special attention is devoted to generalized Killing-Yano tensors of black holes in minimal gauged supergravity Several aspects directly related to the existence of Killing-Yano tensors--such as the Kerr-Schild form, algebraic type of spacetimes, and separability of field equations--are also briefly discussed.
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…
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
Generalized Atkin-Lehner symmetry
NASA Astrophysics Data System (ADS)
Dienes, Keith R.
1990-09-01
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner ``selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Generalized Atkin-Lehner symmetry
Dienes, K.R. )
1990-09-15
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Ultraviolet completion without symmetry restoration
NASA Astrophysics Data System (ADS)
Endlich, Solomon; Nicolis, Alberto; Penco, Riccardo
2014-03-01
We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Minimal models for axion and neutrino
NASA Astrophysics Data System (ADS)
Ahn, Y. H.; Chun, Eung Jin
2016-01-01
The PQ mechanism resolving the strong CP problem and the seesaw mechanism explaining the smallness of neutrino masses may be related in a way that the PQ symmetry breaking scale and the seesaw scale arise from a common origin. Depending on how the PQ symmetry and the seesaw mechanism are realized, one has different predictions on the color and electromagnetic anomalies which could be tested in the future axion dark matter search experiments. Motivated by this, we construct various PQ seesaw models which are minimally extended from the (non-) supersymmetric Standard Model and thus set up different benchmark points on the axion-photon-photon coupling in comparison with the standard KSVZ and DFSZ models.
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.
Discrete Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
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…
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.
Khan, M M; Varma, M P; Cleland, J; O'Kane, H O; Webb, S W; Mulholland, H C; Adgey, A A
1981-01-01
Data concerning 17 consecutive patients with discrete subaortic stenosis are recorded. Twelve patients underwent operative resection of the obstructing lesion. Of these all except one were symptomatic and all had electrocardiographic evidence of left ventricular hypertrophy or left ventricular hypertrophy with strain. They had a peak resting systolic left ventricular outflow tract gradient of greater than 50 mmHg as predicted from the combined cuff measurement of systolic blood pressure and the echocardiographically estimated left ventricular systolic pressure and/or as determined by cardiac catheterisation. The outflow tract gradient as predicted from M-mode echocardiography and peak systolic pressure showed close correlation with that measured at cardiac catheterisation or operation. During the postoperative follow-up from one month to 11 years, of 11 patients, one patient required a further operation for recurrence of the obstruction four years after the initial operation. All patients are now asymptomatic. Five patients have not had an operation. The left ventricular outflow tract gradient as assessed at the time of cardiac catheterisation was greater than 50 mmHg. One patient has been lost to follow-up. The remaining four have been followed from four to eight years and have remained asymptomatic and the electrocardiograms have remained unchanged. Careful follow-up of all patients is essential with continuing clinical assessment, electrocardiograms, M-mode and two-dimensional echocardiograms, and if necessary cardiac catheterisation. Prophylaxis against bacterial endocarditis is also essential. Images PMID:6457617
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Hidden symmetries and black holes
NASA Astrophysics Data System (ADS)
Frolov, Valeri P.
2009-10-01
The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.
Minimal decaying Dark Matter and the LHC
Arcadi, Giorgio; Covi, Laura E-mail: covi@theorie.physik.uni-goettingen.de
2013-08-01
We consider a minimal Dark Matter model with just two additional states, a Dark Matter Majorana fermion and a colored or electroweakly charged scalar, without introducing any symmetry to stabilize the DM state. We identify the parameter region where an indirect DM signal would be within the reach of future observations and the DM relic density generated fits the observations. We find in this way two possible regions in the parameter space, corresponding to a FIMP/SuperWIMP or a WIMP DM. We point out the different collider signals of this scenario and how it will be possible to measure the different couplings in case of a combined detection.
Linear functional minimization for inverse modeling
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Wohlberg, B. E.; Vesselinov, V. V.; Tartakovsky, D. M.
2015-06-01
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. Addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.
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.
Spontaneous CP Violation in E{sub 6} GUT with horizontal symmetry
Maekawa, Nobuhiro
2010-02-10
We consider spontaneous CP violation in E{sub 6} grand unified theory (GUT) with horizontal symmetry and anomalous U(1){sub A} gauge symmetry in order to solve the SUSY CP problem. To realize the sufficiently small phases of SUSY Higgs mass mu 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 V{sub ub}approxgamma{sup 4}, which is quite good agreement with the measured value. This talk is based on the works in Ref. [1].
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
Quark mixing from Δ (6N2) family symmetry
NASA Astrophysics Data System (ADS)
Ishimori, Hajime; King, Stephen F.; Okada, Hiroshi; Tanimoto, Morimitsu
2015-04-01
We consider a direct approach to quark mixing based on the discrete family symmetry Δ (6N2) in which the Cabibbo angle is determined by a residual Z2 ×Z2 subgroup to be |Vus | = 0.222521, for N being a multiple of 7. We propose a particular model in which unequal smaller quark mixing angles and CP phases may occur without breaking the residual Z2 ×Z2 symmetry. We perform a numerical analysis of the model for N = 14, where small Z2 ×Z2 breaking effects of order 3% are allowed by model, allowing perfect agreement within the uncertainties of the experimentally determined best fit quark mixing values.
Spontaneous CP violation in A4 flavor symmetry and leptogenesis
NASA Astrophysics Data System (ADS)
Ahn, Y. H.; Kang, Sin Kyu; Kim, C. S.
2013-06-01
We propose a simple renormalizable model for the spontaneous CP violation based on SU(2)L×U(1)Y×A4 symmetry in a radiative seesaw mechanism, which can be guaranteed by an extra Z2 symmetry. In our model CP is spontaneously broken at high energies, after the breaking of flavor symmetry, by a complex vacuum expectation value of the A4 triplet and gauge-singlet scalar field. We show that the spontaneously generated CP phase could become a natural source of leptogenesis, and also investigate CP violation at low energies in the lepton sector and show how the CP phases in the Pontecorvo-Maki-Nakagawa-Sakata formalism could arise through a spontaneous symmetry-breaking mechanism. As a numerical study, interestingly, we show that the normal mass hierarchy favors relatively large values of θ13, large deviations from maximality of θ23<π/4, and the Dirac-CP phase 0°≤δCP≤50° and 300°≤δCP≤360°. For the inverted hierarchy case, the experimentally measured values of θ13 favors θ23>π/4 and discrete values of δCP around 100°, 135°, 255°, and 300°. Finally, with a successful leptogenesis our numerical results give more predictive values on the Dirac CP phase: for the normal mass hierarchy 1°≲δCP≲10° and for inverted one δCP˜100°, 135°, 300°.
Polarization properties of optical metasurfaces of different symmetries
NASA Astrophysics Data System (ADS)
Kruk, Sergey S.; Poddubny, Alexander N.; Powell, David A.; Helgert, Christian; Decker, Manuel; Pertsch, Thomas; Neshev, Dragomir N.; Kivshar, Yuri S.
2015-05-01
Optical metasurfaces have become a new paradigm for creating flat optical devices. While being typically an order of magnitude thinner than the wavelength of light, metasurfaces allow control of the phase of propagating light waves across the full 2 π range and therefore enable the realization of optical elements such as lenses, waveplates, and beam converters. Currently one of the limiting factors of functional metasurfaces is their small range of operational angles. Here we demonstrate both theoretically and experimentally that the angular range can be broadened by increasing the rotational symmetry of metasurfaces. We develop an analytical model based on the discrete dipole approximation that quantitatively describes the response of metasurfaces under oblique excitation. It shows that the effective optical symmetry is doubled for structures with odd rotational symmetry, increasing the angular range correspondingly. We apply and experimentally verify our model for metasurfaces consisting of identical meta-atoms, arranged into square lattices, hexagonal lattices, and on the vertices of a Penrose tiling. The results demonstrate the increasing angular performance with increasing rotational symmetry.
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.
Liu, Y.; Keller, J.
1996-09-01
It is proved that there exists an additional intrinsic symmetry in the left-handed and right-handed fermions (and other fields). The corresponding group of transformations is induced by the Poincar{acute e} translations in the space{endash}time manifold. This symmetry predicts an additional intrinsic energy-momentum for fermions. Considering this symmetry as local leads to introduction of a gauge field and of a nonintegrable phase angle, the corresponding Berry-type phase depends on the topology of the Riemannian space{endash}time manifold as determined by the vierbein. This additional symmetry provides us with the possibility of considering the fermions as gauge fields on the nonvector bundle. {copyright} {ital 1996 American Institute of Physics.}
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
The discrete variational derivative method based on discrete differential forms
NASA Astrophysics Data System (ADS)
Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki
2012-05-01
As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.
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.
Momentum dependence of symmetry energy
NASA Astrophysics Data System (ADS)
Coupland, Daniel D.; Youngs, Michael; Chajecki, Zbigniew; Lynch, William; Tsang, Betty; Zhang, Yingxun; Famiano, Michael; Ghosh, Tilak; Giacherio, B.; Kilburn, Micha; Lee, Jenny; Lu, Fei; Russotto, Paulo; Sanetullaev, Alisher; Showalter, Rachel; Verde, Giuseppe; Winkelbauer, Jack
2014-09-01
One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn +124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn+124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. PHY-1102511.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; Rodríguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
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
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}.
Probabilistic minimal disturbance measurement of symmetrical qubit states
Filip, R.; Mista, L. Jr.; De Martini, F.; Ricci, M.; Sciarrino, F.
2006-11-15
We derive fidelity tradeoffs for probabilistic minimal disturbance measurements for certain discrete sets of symmetrical single qubit states. We propose and experimentally demonstrate a simple linear optical scheme saturating these tradeoffs in which the degree of disturbance is controlled only by measurement of a single ancillary photon.
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.
Discreteness-induced transitions in multibody reaction systems.
Saito, Yohei; Sughiyama, Yuki; Kaneko, Kunihiko; Kobayashi, Tetsuya J
2016-08-01
A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a one- and three-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior. PMID:27627279
Exact discretization by Fourier transforms
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.
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. PMID:20059064
Minimally Invasive Valve Surgery
Pope, Nicolas H.; Ailawadi, Gorav
2014-01-01
Cardiac valve surgery is life saving for many patients. The advent of minimally invasive surgical techniques has historically allowed for improvement in both post-operative convalescence and important clinical outcomes. The development of minimally invasive cardiac valve repair and replacement surgery over the past decade is poised to revolutionize the care of cardiac valve patients. Here, we present a review of the history and current trends in minimally invasive aortic and mitral valve repair and replacement, including the development of sutureless bioprosthetic valves. PMID:24797148
Algorithms for error localization of discrete data
Liepins, G.E.
1984-07-01
A self-contained derivation and evaluation of the three principal algorithms for error localization of discrete data are provided: (1) generation of a sufficient set of edits by single-sweep with fathoming (suggested by the original work by Fellegi and Holt), and (2) sequential row generation (developed by Garfinkel), and (3) modifications of the Chernikova algorithm (suggested by work of Rubin and Sande). The first two approaches can be characterized as Boolean-based, whereas the last is a nonpivoting extremal ray search. The background to the Boolean approaches to data editing is provided, as are Burger's results on extremal rays, Chernikova's original algorithm, and Rubin's modifications. For selected results, new elementary proofs are given in the appendix. For the Chernikova algorithm, novel use is made of the problem structure of localization to minimize the undesirable tendency to generate excessively large matrices.
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
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.
Prostate resection - minimally invasive
... are: Erection problems (impotence) No symptom improvement Passing semen back into your bladder instead of out through ... Whelan JP, Goeree L. Systematic review and meta-analysis of transurethral resection of the prostate versus minimally ...
Minimizing Shortness of Breath
... Top Doctors in the Nation Departments & Divisions Home Health Insights Stress & Relaxation Breathing and Relaxation Minimizing Shortness of Breath ... Management Assess Your Stress Coping Strategies Identifying ... & Programs Health Insights Doctors & Departments Research & Science Education & Training Make ...
Minimally invasive hip replacement
... Smits SA, Swinford RR, Bahamonde RE. A randomized, prospective study of 3 minimally invasive surgical approaches in total hip arthroplasty: comprehensive gait analysis. J Arthroplasty . 2008;23:68-73. PMID: 18722305 ...
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.
ERIC Educational Resources Information Center
Hubbard, Guy
2002-01-01
Provides background information on the art movement called "Minimalism" discussing why it started and its characteristics. Includes learning activities and information on the artist, Donald Judd. Includes a reproduction of one of his art works and discusses its content. (CMK)
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
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.
Unification of standard and exotic matter through a Z{sub 2} symmetry
Matute, Ernesto A.
2006-03-01
We consider a scenario in which the discrete weak symmetry between quarks and leptons is extended to the weak force by introducing exotic partners. We conjecture that there exists a hidden discrete symmetry P-tilde, defining a Z{sub 2} group, between standard and exotic quarks and leptons. The unified model SU(3){sub q}xSU(3){sub q-tilde}xSU(2){sub ql-tilde}xSU(2){sub q-tildel}xU(1){sub Y}= xP-tilde is discussed, where the unifying discrete symmetry extends over particles and forces. It is shown that the lighter neutral and charged weak bosons generated upon spontaneous symmetry breaking have the same properties as those of the standard model. Cabbibo-Kobayashi-Maskawa unitarity is used to set a mass of order 2.8 TeV for the nonstandard weak bosons, which do not exhibit quark-lepton universality. A grand unified theory of (GUT){sub ql-tilde}x(GUT){sub q-tildel}xP-tilde type, with decay of exotic matter into standard matter and no decay of the ordinary nucleon, is put forward.
NASA Astrophysics Data System (ADS)
Mohamad, Sannay
2001-11-01
Convergence dynamics of continuous-time bidirectional neural networks with constant transmission delays are studied. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, Lyapunov functionals and Halanay-type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous-time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks. Discrete-time analogues of the continuous-time networks are formulated and we study their dynamical characteristics. It is shown that the convergence dynamics of the continuous-time networks are preserved by the discrete-time analogues without any restriction on the discretization step-size. Several examples are given to illustrate the advantages of the discrete-time analogues in numerically simulating the continuous-time networks.
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.
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 .
Symmetries and fundamental interactions—selected topics
NASA Astrophysics Data System (ADS)
Jungmann, Klaus P.
2014-06-01
High precision experiments at low energies on discrete and continuous symmetries offer the possibility to search for New Physics beyond the Standard Model. Examples are dedicated searches for violations of the C, P, CP and CPT as well as of Lorentz Invariance using matter and anti-matter. Atomic parity violation was not only essential in the past to verify the Standard Model, still today it has a potential to find Z' bosons, leptoquarks or dark matter. Electric Dipole Moments (EDMs) may provide clues to explain the matter-antimatter asymmetry in the universe. There is at present a some 4 standard deviations discrepancy between theory and experiment for the muon magnetic anomaly. At the same time while providing important information on physics beyond the Standard Model, new technology such as precise clocks is developed along with the experiments motivated by fundamental physics questions. This article summarizes an overview talk that was concerned primarily with a selection of topics from a very rich field, in particular such that were not covered otherwise at this conference.
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.
Hyperspherical slow variable discretization method for weakly bound triatomic molecules.
Suno, Hiroya
2011-02-14
We develop a method for calculating the bound state energies and the wave functions of weakly bound triatomic molecular systems. The method is based on the use of hyperspherical coordinates, combined with the slow variable discretization approach. The finite-element methods-discrete variable representation scheme provides an efficient means to solve the coupled-channel hyper-radial equations. Our method is applied to searching for bound states of the (20)Ne(2)H and (4)He(20)NeH triatomic molecules, using the best empirical pairwise interaction potentials. We consider not only zero total nuclear orbital momentum, J = 0, states but also J > 0 states. The (20)Ne(2)H system has been found to possess one bound state each for the J(Π)=0(+),1(-), and 2(+) symmetries, while there exist only one bound state for the (4)He(20)NeH system in the 0(+) symmetry. We shall calculate the bound state energies and analyze the molecular structures of these species in detail. PMID:21322691
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.
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
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.
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
Symmetry breaking in molecular ferroelectrics.
Shi, Ping-Ping; Tang, Yuan-Yuan; Li, Peng-Fei; Liao, Wei-Qiang; Wang, Zhong-Xia; Ye, Qiong; Xiong, Ren-Gen
2016-07-11
Ferroelectrics are inseparable from symmetry breaking. Accompanying the paraelectric-to-ferroelectric phase transition, the paraelectric phase adopting one of the 32 crystallographic point groups is broken into subgroups belonging to one of the 10 ferroelectric point groups, i.e. C1, C2, C1h, C2v, C4, C4v, C3, C3v, C6 and C6v. The symmetry breaking is captured by the order parameter known as spontaneous polarization, whose switching under an external electric field results in a typical ferroelectric hysteresis loop. In addition, the responses of spontaneous polarization to other external excitations are related to a number of physical effects such as second-harmonic generation, piezoelectricity, pyroelectricity and dielectric properties. Based on these, this review summarizes recent developments in molecular ferroelectrics since 2011 and focuses on the relationship between symmetry breaking and ferroelectricity, offering ideas for exploring high-performance molecular ferroelectrics. PMID:27051889
CKM matrix and flavor symmetries
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Ishida, Hiroyuki; Ishimori, Hajime; Kobayashi, Tatsuo; Ogasahara, Atsushi
2013-11-01
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both θ13 and θ23 or only θ13 are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The Z7 symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the Δ(6N2) series are also briefly discussed.
Symmetries in geometrical optics: theory
NASA Astrophysics Data System (ADS)
Szilagyi, M.; Mui, P. H.
1995-12-01
A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
Cheraghi-Sohi, Sudeh; Calnan, Michael
2013-11-01
There has much debate about the extent to which professional discretion has been challenged by recent organisational changes such as through the new forms of governance associated with the introduction of the principles of the New Public Management (NPM) into health systems and other public sector services. What appears to be missing from these debates is a detailed analysis of the concept of professional discretion itself. This paper attempts to fill this gap by delineating the key concepts of professional discretion evident in the literature and exploring their significance in an empirical study of the influence of the 2004 new general medical services contract (nGMS) and the introduction of the Quality and Outcomes Framework (QOF), a prescriptive pay-for-performance system designed to standardise the quality of care provision in general medical practice in the United Kingdom. The study adopted a longitudinal design using semi-structured interviews with general practitioners (GPs, N = 62) working in the English National Health Service (NHS) between 2007 and 2009. A multi-dimensional conception of discretion was used to explore how GP discretion might have been influenced by contractual changes and in particular, QOF. The findings suggest that through a complex interplay of factors, a post-QOF reduction in GP discretion was identifiable, highlighting different potential sources of constraint such as in the social, organisational and economic dimensions of discretion. The evidence also suggested the emergence of a new form of organisational medical professionalism within general practice characterised by standardisation, bureaucracy and performance management. PMID:24034951
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
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).
Discrete representations for the deformed su(1, 1) algebra via the magnetic monopole harmonics
NASA Astrophysics Data System (ADS)
Dehghani, A.; Fakhri, H.
2008-07-01
It is well known that the magnetic quantum number m of monopole harmonics describes quantization corresponding to the z-component of the angular momentum operator in the framework of su(2) symmetry algebra. Here, it is shown that the azimuthal quantum number l allocates itself a ladder symmetry by the operators which are described in terms of l. Furthermore, quantization of both quantum numbers l and m leads to extracting positive and negative irreducible discrete representations of the deformed su(1, 1) algebra for l - m and l + m, respectively. It will also be shown in detail how they in turn lead to the spectrum-generating algebra for all monopole harmonics.
Minimally Invasive Radiofrequency Devices.
Sadick, Neil; Rothaus, Kenneth O
2016-07-01
This article reviews minimally invasive radiofrequency options for skin tightening, focusing on describing their mechanism of action and clinical profile in terms of safety and efficacy and presenting peer-reviewed articles associated with the specific technologies. Treatments offered by minimally invasive radiofrequency devices (fractional, microneedling, temperature-controlled) are increasing in popularity due to the dramatic effects they can have without requiring skin excision, downtime, or even extreme financial burden from the patient's perspective. Clinical applications thus far have yielded impressive results in treating signs of the aging face and neck, either as stand-alone or as postoperative maintenance treatments. PMID:27363771
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Inverse Modeling Via Linearized Functional Minimization
NASA Astrophysics Data System (ADS)
Barajas-Solano, D. A.; Wohlberg, B.; Vesselinov, V. V.; Tartakovsky, D. M.
2014-12-01
We present a novel parameter estimation methodology for transient models of geophysical systems with uncertain, spatially distributed, heterogeneous and piece-wise continuous parameters.The methodology employs a bayesian approach to propose an inverse modeling problem for the spatial configuration of the model parameters.The likelihood of the configuration is formulated using sparse measurements of both model parameters and transient states.We propose using total variation regularization (TV) as the prior reflecting the heterogeneous, piece-wise continuity assumption on the parameter distribution.The maximum a posteriori (MAP) estimator of the parameter configuration is then computed by minimizing the negative bayesian log-posterior using a linearized functional minimization approach. The computation of the MAP estimator is a large-dimensional nonlinear minimization problem with two sources of nonlinearity: (1) the TV operator, and (2) the nonlinear relation between states and parameters provided by the model's governing equations.We propose a a hybrid linearized functional minimization (LFM) algorithm in two stages to efficiently treat both sources of nonlinearity.The relation between states and parameters is linearized, resulting in a linear minimization sub-problem equipped with the TV operator; this sub-problem is then minimized using the Alternating Direction Method of Multipliers (ADMM). The methodology is illustrated with a transient saturated groundwater flow application in a synthetic domain, stimulated by external point-wise loadings representing aquifer pumping, together with an array of discrete measurements of hydraulic conductivity and transient measurements of hydraulic head.We show that our inversion strategy is able to recover the overall large-scale features of the parameter configuration, and that the reconstruction is improved by the addition of transient information of the state variable.
ERIC Educational Resources Information Center
Mueller, Mary Ellen; Parisi, Mary Joy
This report delineates a series of interventions aimed at minimizing incidences of bullying in a suburban elementary school. The social services staff was scheduled to initiate an anti-bullying incentive in fall 2001 due to the increased occurrences of bullying during the prior year. The target population consisted of third- and fourth-grade…
Minimally invasive pancreatic surgery.
Yiannakopoulou, E
2015-12-01
Minimally invasive pancreatic surgery is feasible and safe. Laparoscopic distal pancreatectomy should be widely adopted for benign lesions of the pancreas. Laparoscopic pancreaticoduodenectomy, although technically demanding, in the setting of pancreatic ductal adenocarcinoma has a number of advantages including shorter hospital stay, faster recovery, allowing patients to recover in a timelier manner and pursue adjuvant treatment options. Furthermore, it seems that progression-free survival is longer in patients undergoing laparoscopic pancreaticoduodenectomy in comparison with those undergoing open pancreaticoduodenectomy. Minimally invasive middle pancreatectomy seems appropriate for benign or borderline tumors of the neck of the pancreas. Technological advances including intraoperative ultrasound and intraoperative fluorescence imaging systems are expected to facilitate the wide adoption of minimally invasive pancreatic surgery. Although, the oncological outcome seems similar with that of open surgery, there are still concerns, as the majority of relevant evidence comes from retrospective studies. Large multicenter randomized studies comparing laparoscopic with open pancreatectomy as well as robotic assisted with both open and laparoscopic approaches are needed. Robotic approach could be possibly shown to be less invasive than conventional laparoscopic approach through the less traumatic intra-abdominal handling of tissues. In addition, robotic approach could enable the wide adoption of the technique by surgeon who is not that trained in advanced laparoscopic surgery. A putative clinical benefit of minimally invasive pancreatic surgery could be the attenuated surgical stress response leading to reduced morbidity and mortality as well as lack of the detrimental immunosuppressive effect especially for the oncological patients. PMID:26530291
ERIC Educational Resources Information Center
Van Ness, Wilhelmina
1974-01-01
Described the development of Minimal Art, a composite name that has been applied to the scattering of bland, bleak, non-objective fine arts painting and sculpture forms that proliferated slightly mysteriously in the middle 1960's as Pop Art began to decline. (Author/RK)
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.
Enhanced gauge symmetry and winding modes in double field theory
NASA Astrophysics Data System (ADS)
Aldazabal, G.; Graña, M.; Iguri, S.; Mayo, M.; Nuñez, C.; Rosabal, J. A.
2016-03-01
We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1) × U(1) symmetry to SU(2) × SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with Oleft(d+3,d+3right)/Oleft(d+3right)× Oleft(d+3right) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Entanglement renormalization and gauge symmetry
Tagliacozzo, L.; Vidal, G.
2011-03-15
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Quantitative Analysis of Face Symmetry.
Tamir, Abraham
2015-06-01
The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait. PMID:26080172
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. PMID:23599060
Symmetry reduction in high dimensions, illustrated in a turbulent pipe
NASA Astrophysics Data System (ADS)
Willis, Ashley P.; Short, Kimberly Y.; Cvitanović, Predrag
2016-02-01
Equilibrium solutions are believed to structure the pathways for ergodic trajectories in a dynamical system. However, equilibria are atypical for systems with continuous symmetries, i.e., for systems with homogeneous spatial dimensions, whereas relative equilibria (traveling waves) are generic. In order to visualize the unstable manifolds of such solutions, a practical symmetry reduction method is required that converts relative equilibria into equilibria, and relative periodic orbits into periodic orbits. In this article we extend the fixed Fourier mode slice approach, previously applied one-dimensional PDEs, to a spatially three-dimensional fluid flow, and show that it is substantially more effective than our previous approach to slicing. Application of this method to a minimal flow unit pipe leads to the discovery of many relative periodic orbits that appear to fill out the turbulent regions of state space. We further demonstrate the value of this approach to symmetry reduction through projections (projections only possible in the symmetry-reduced space) that reveal the interrelations between these relative periodic orbits and the ways in which they shape the geometry of the turbulent attractor.
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.
Some discrete multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Discrete implementations of scale transform
NASA Astrophysics Data System (ADS)
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
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
CKM and PMNS mixing matrices from discrete subgroups of SU(2)
NASA Astrophysics Data System (ADS)
Potter, Franklin
2015-07-01
Remaining within the realm of the Standard Model(SM) local gauge group, this first principles derivation of both the PMNS and CKM matrices utilizes quaternion generators of the three discrete (i.e., finite) binary rotational subgroups of SU(2) called [3,3,2], [4,3,2], and [5,3,2] for three lepton families in R3 and four related discrete binary rotational subgroups [3,3,3], [4,3,3], [3,4,3], and [5,3,3] represented by four quark families in R4. The traditional 3x3 CKM matrix is extracted as a submatrix of the 4x4 CKM4 matrix. If these two additional quarks b' and t' of a 4th quark family exist, there is the possibility that the SM lagrangian may apply all the way down to the Planck scale. There are then numerous other important consequences. The Weinberg angle is derived using these same quaternion generators, and the triangle anomaly cancellation is satisfied even though there is an obvious mismatch of three lepton families to four quark families. In a discrete space, one can also use these generators to derive a unique connection from the electroweak local gauge group SU(2)L x U(1)Y acting in R4 to the discrete group Weyl E8 in R8. By considering Lorentz transformations in discrete (3,1)-D spacetime, one obtains another Weyl E8 discrete symmetry group in R8, so that the combined symmetry is Weyl E8 x Weyl E8 = "discrete" SO(9,1) in 10-D spacetime. This unique connection is in direct contrast to the 10500 possible connections for superstring theory!
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Instanton effects in lattice models of bosonic symmetry-protected topological states
NASA Astrophysics Data System (ADS)
Santos, Luiz H.; Fradkin, Eduardo
2016-04-01
Bosonic symmetry-protected topological (SPT) states are gapped disordered phases of matter possessing symmetry-preserving boundary excitations. It has been proposed that, at long wavelengths, the universal properties of an SPT system are captured by an effective nonlinear sigma model field theory in the presence of a quantized topological θ term. By studying lattice models of bosonic SPT states, we are able to identify, in their Euclidean path integral formulation, (discrete) Berry phases that hold relevant physical information on the nature of the SPT ground states. These discrete Berry phases are given intuitive physical interpretation in terms of instanton effects that capture the presence of a θ term on the microscopic scale.
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}.
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.
Minimally invasive radioguided parathyroidectomy.
Costello, D; Norman, J
1999-07-01
The last decade has been characterized by an emphasis on minimizing interventional techniques, hospital stays, and overall costs of patient care. It is clear that most patients with sporadic HPT do not require a complete neck exploration. We now know that a minimal approach is appropriate for this disease. Importantly, the MIRP technique can be applied to most patients with sporadic HPT and can be performed by surgeons with modest advanced training. The use of a gamma probe as a surgical tool converts the sestamibi to a functional and anatomical scan eliminating the need for any other preoperative localizing study. Quantification of the radioactivity within the removed gland eliminates the need for routine frozen section histologic examination and obviates the need for costly intraoperative parathyroid hormone measurements. This radioguided technique allows the benefit of local anesthesia, dramatically reduces operative times, eliminates postoperative blood tests, provides a smaller scar, requires minimal time spent in the hospital, and almost assures a rapid, near pain-free recovery. This combination is beneficial to the patient whereas helping achieve a reduction in overall costs. PMID:10448697
Landfill gas recovery system and method with pressure symmetry
Zison, S.W.; Roqueta, A.
1984-09-04
In a landfill gas recovery system, the breakthrough danger is minimized, and the system efficiency is improved, by providing pressure-equalizing low-impedance gas paths such as aggregate-filled symmetry trenches positioned within the landfill and surrounding, at least partially, the primary collection zone. The symmetry trenches may be connected to the system's low-pressure source to serve as secondary collectors. A sensing trench positioned within the landfill along the periphery of the collector's zone of influence can be used to monitor the collector pressure and to automatically maintain it at a safe level. The sensing trench can also serve as a secondary equalizing path in heterogeneous landfills. Hot spots may advantageously be tapped by auxiliary collectors whose pressure level bears a predetermined proportional relationship to the primary collector pressure.
Streamwise-Localized Solutions with natural 1-fold symmetry
NASA Astrophysics Data System (ADS)
Altmeyer, Sebastian; Willis, Ashley; Hof, Björn
2014-11-01
It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.
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.
Quantizing the Discrete Painlevé VI Equation: The Lax Formalism
NASA Astrophysics Data System (ADS)
Hasegawa, Koji
2013-08-01
A discretization of Painlevé VI equation was obtained by Jimbo and Sakai (Lett Math Phys 38:145-154, 1996). There are two ways to quantize it: (1) use the affine Weyl group symmetry (of {D_5^{(1)}}) (Hasegawa in Adv Stud Pure Math 61:275-288, 2011), (2) Lax formalism, i.e. monodromy preserving point of view. It turns out that the second approach is also successful and gives the same quantization as in the first approach.
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.
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
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
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
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.
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
Applications of Symmetry to Problem Solving.
ERIC Educational Resources Information Center
Leikin, Roza; Berman, Abraham; Zaslavsky, Orit
2000-01-01
Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…
Quantum-field coherent control: Preparation of broken-symmetry entangled states
Kral, Petr; Thanopulos, Ioannis; Shapiro, Moshe
2005-08-15
We show that entangled radiation-matter states with broken symmetries can be prepared by using nonclassical light in the coherent control techniques. We demonstrate the method by realizing the entanglement in degenerate continuum electronic momentum states of opposite directionality and discrete states of opposite handedness in chiral molecules. When the material system is excited simultaneously by classical light and quantum light in a state with several semiclassical phases, the interference conditions guide the system to such entangled radiation-matter states.
Beyond minimal lepton-flavored Dark Matter
NASA Astrophysics Data System (ADS)
Chen, Mu-Chun; Huang, Jinrui; Takhistov, Volodymyr
2016-02-01
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.
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.
An adaptive mesh refinement algorithm for the discrete ordinates method
Jessee, J.P.; Fiveland, W.A.; Howell, L.H.; Colella, P.; Pember, R.B.
1996-03-01
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.
NASA Astrophysics Data System (ADS)
Tanaka, Satoshi; Garmon, Savannah; Kanki, Kazuki; Petrosky, Tomio
2016-08-01
We have theoretically investigated the time-symmetry-breaking phase-transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue problem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy dependence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry-breaking phase transition: As a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.
CP symmetry in optical systems
NASA Astrophysics Data System (ADS)
Dana, Brenda; Bahabad, Alon; Malomed, Boris A.
2015-04-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Simulating granular materials by energy minimization
NASA Astrophysics Data System (ADS)
Krijgsman, D.; Luding, S.
2016-03-01
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
Symmetry and Stochastic Gene Regulation
NASA Astrophysics Data System (ADS)
Ramos, Alexandre F.; Hornos, José E. M.
2007-09-01
Lorentz-like noncompact Lie symmetry SO(2,1) is found in a spin-boson stochastic model for gene expression. The invariant of the algebra characterizes the switch decay to equilibrium. The azimuthal eigenvalue describes the affinity between the regulatory protein and the gene operator site. Raising and lowering operators are constructed and their actions increase or decrease the affinity parameter. The classification of the noise regime of the gene arises from the group theoretical numbers.
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. PMID:24312502
Class of discrete Gabor expansion
NASA Astrophysics Data System (ADS)
Li, Shidong; Healy, Dennis M., Jr.
1994-03-01
We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.
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
Symmetry analysis of talus bone
Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.
2014-01-01
Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391
Dark matter and global symmetries
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.
2016-09-01
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system
NASA Astrophysics Data System (ADS)
Lian, Zeng-Ju; Chen, Li-Li; Lou, Sen-Yue
2005-08-01
The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.
Large transition magnetic moment of the neutrino from horizontal symmetry
NASA Astrophysics Data System (ADS)
Babu, K. S.; Mohapatra, Rabindra N.
1990-12-01
The apparent anticorrelation of the solar-neutrino signal with the 11-yr sunspot cycle observed by Davis can be understood if the electron neutrino has a large magnetic moment. We discuss extensions of the standard model, where the existence of a leptonic SU(2)H-horizontal symmetry between the electron and muon generations provides a way to understand such a large magnetic moment, while keeping the neutrino mass naturally small. A global le-lμ symmetry (li=ith lepton number) is maintained even after spontaneous gauge symmetry breaking, so that the neutrino is of Zeldovich-Konopinski-Mahmoud type with m2νe-m2νμ=0. This condition automatically guarantees that the neutrino spin precession in the magnetic field of the Sun is not suppressed. Of the two extensions of the standard model that we discuss, the first one is a local SU(2)H model with the horizontal symmetry broken completely at a TeV scale. We show how a global U(1)le-lμ can be maintained although le-lμ is a subgroup of the gauged SU(2)H. The second example is the minimal supersymmetric extension of the standard model with R-parity-violating [but (le-lμ)-conserving] interactions. An approximate SU(2)H symmetry between the e-μ families is imposed in order to suppress the neutrino mass, but not its magnetic moment. We provide a detailed theoretical and phenomenological investigation of these two models and discuss their tests at the colliders as well as in low-energy experiments. The models generally predict mνe~=1-10 eV and the existence of charged scalar particles in the mass range of 100 GeV.
A FORTRAN Program for Discrete Discriminant Analysis
ERIC Educational Resources Information Center
Boone, James O.; Brewer, James K.
1976-01-01
A Fortran program is presented for discriminant analysis of discrete variables. The program assumes discrete, nominal data with no distributional, variance-covariance assumptions. The program handles a maximum of fifty predictor variables and twelve outcome groups. (Author/JKS)
Efficient genetic algorithms using discretization scheduling.
McLay, Laura A; Goldberg, David E
2005-01-01
In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling. PMID:16156928
Discrete vortex representation of magnetohydrodynamics
Kinney, R.; Tajima, T.; Petviashvili, N.; McWilliams, J.C.
1993-02-01
We present an alternative approach to statistical analysis of an intermittent ideal MHD fluid in two dimensions, based on the hydrodynamical discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamical turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.
Discrete-contact nanowire photovoltaics
NASA Astrophysics Data System (ADS)
Chitambar, Michelle J.; Wen, Wen; Maldonado, Stephen
2013-11-01
A series of finite-element simulations have been performed to assess the operational characteristics of a new semiconductor nanowire solar cell design operating under high-level injection conditions. Specifically, the steady-state current-voltage behavior of a cylindrical silicon (Si) nanowire with a series of discrete, ohmic-selective contacts under intense sunlight illumination was investigated. The scope of the analysis was limited to only the factors that impact the net internal quantum yield for solar to electricity conversion. No evaluations were performed with regards to optical light trapping in the modeled structures. Several aspects in a discrete-contact nanowire device that could impact operation were explored, including the size and density of ohmic-selective contacts, the size of the nanowire, the electronic quality and conductivity of the nanowire, the surface defect density of the nanowire, and the type of ohmic selectivity employed at each contact. The analysis showed that there were ranges of values for each parameter that supported good to excellent photoresponses, with certain combinations of experimentally attainable material properties yielding internal energy conversion efficiencies at the thermodynamic limit for a single junction cell. The merits of the discrete-contact nanowire cell were contrasted with "conventional" nanowire photovoltaic cells featuring a uniform conformal contact and also with planar point-contact solar cells. The unique capacity of the discrete-contact nanowire solar cell design to operate at useful energy conversion efficiencies with low quality semiconductor nanowires (i.e., possessing short charge-carrier lifetimes) with only light doping is discussed. This work thus defines the impetus for future experimental work aimed at developing this photovoltaic architecture.
NASA Astrophysics Data System (ADS)
Blanco, Celia; Ribó, Josep M.; Hochberg, David
2015-02-01
We derive the class of population balance equations (PBE), recently applied to model the Viedma deracemization experiment, from an underlying microreversible kinetic reaction scheme. The continuum limit establishing the relationship between the micro- and macroscopic processes and the associated particle fluxes erases the microreversible nature of the molecular interactions in the population growth rate functions and limits the scope of such PBE models to strict kinetic control. The irreversible binary agglomeration processes modeled in those PBEs contribute an additional source of kinetic control. These limitations are crucial regarding the question of the origin of biological homochirality, where the interest in any model lies precisely in its ability for absolute asymmetric synthesis and the amplification of the tiny inherent statistical chiral fluctuations about the ideal racemic composition up to observable enantiometric excess levels.
Interference in discrete Wigner functions
Cormick, Cecilia; Paz, Juan Pablo
2006-12-15
We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider ''cat'' states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.
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
Minimally invasive mediastinal surgery.
Melfi, Franca M A; Fanucchi, Olivia; 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 invasive
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.
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.
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.
Minimally Invasive Parathyroidectomy
Starker, Lee F.; Fonseca, Annabelle L.; Carling, Tobias; Udelsman, Robert
2011-01-01
Minimally invasive parathyroidectomy (MIP) is an operative approach for the treatment of primary hyperparathyroidism (pHPT). Currently, routine use of improved preoperative localization studies, cervical block anesthesia in the conscious patient, and intraoperative parathyroid hormone analyses aid in guiding surgical therapy. MIP requires less surgical dissection causing decreased trauma to tissues, can be performed safely in the ambulatory setting, and is at least as effective as standard cervical exploration. This paper reviews advances in preoperative localization, anesthetic techniques, and intraoperative management of patients undergoing MIP for the treatment of pHPT. PMID:21747851
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.
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.
Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED
Griffin, P.A.
1992-07-01
Staggered fermions are constructed for the transverse lattice regularization scheme. The weak perturbation theory of transverse lattice non-compact QED is developed in light-cone gauge, and we argue that for fixed lattice spacing this theory is ultraviolet finite, order by order in perturbation theory. However, by calculating the anomalous scaling dimension of the link fields, we find that the interaction Hamiltonian becomes non-renormalizable for g{sup 2}(a) > 4{pi}, where g(a) is the bare (lattice) QED coupling constant. We conjecture that this is the critical point of the chiral symmetry breaking phase transition in QED. Non-perturbative chiral symmetry breaking is then studied in the strong coupling limit. The discrete remnant of chiral symmetry that remains on the lattice is spontaneously broken, and the ground state to lowest order in the strong coupling expansion corresponds to the classical ground state of the two-dimensional spin one-half Heisenberg antiferromagnet.
Approaching Minimal Flavour Violation from an SU(5) × S 4 × U(1) SUSY GUT
NASA Astrophysics Data System (ADS)
Dimou, Maria; King, Stephen F.; Luhn, Christoph
2016-02-01
We show how approximate Minimal Flavour Violation (MFV) can emerge from an SU(5) Supersymmetric Grand Unified Theory (SUSY GUT) supplemented by an S 4 × U(1) family symmetry, which provides a good description of all quark and lepton (including neutrino) masses, mixings and CP violation. Assuming a SUSY breaking mechanism which respects the family symmetry, we calculate in full explicit detail the low energy mass insertion parameters in the super-CKM basis, including the effects of canonical normalisation and renormalisation group running. We find that the very simple family symmetry S 4 ×U(1) is sufficient to approximately reproduce the effects of low energy MFV.
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.
2014-06-01
In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.
Polyhedra with noncrystallographic symmetry as the orbits of crystallographic point symmetry groups
NASA Astrophysics Data System (ADS)
Ovsetsina, T. I.; Chuprunov, E. V.
2015-11-01
Polyhedra with noncrystallographic symmetry are analyzed as the orbits of crystallographic point symmetry groups on a set of smooth or structured ("hatched") planes. Polyhedra with symmetrically equivalent faces, obtained using crystallographic point groups but having noncrystallographic symmetry, and polyhedra, the symmetry group T of which is crystallographic but can be implemented only on the assumption of a noncrystallographic character of the internal structure of polyhedron, are studied. The results of the analysis for all 32 point symmetry groups are listed in table.
Black holes and Abelian symmetry breaking
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Niz, Gustavo; Tasinato, Gianmassimo
2016-09-01
Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector–tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector–tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.
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
Symmetry measures of the electron density.
Casanova, David; Alemany, Pere; Alvarez, Santiago
2010-10-01
In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983
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.
DeClue, S.C.
1996-06-01
Hazardous waste minimization is a broad term often associated with pollution prevention, saving the environment or protecting Mother Earth. Some associate hazardous waste minimization with saving money. Thousands of hazardous materials are used in processes every day, but when these hazardous materials become hazardous wastes, dollars must be spent for disposal. When hazardous waste is reduced, an organization will spend less money on hazardous waste disposal. In 1993, Fort Bragg reduced its hazardous waste generation by over 100,000 pounds and spent nearly $90,000 less on hazardous waste disposal costs than in 1992. Fort Bragg generates a variety of wastes: Vehicle maintenance wastes such as antifreeze, oil, grease and solvents; helicopter maintenance wastes, including solvents, adhesives, lubricants and paints; communication operation wastes such as lithium, magnesium, mercury and nickel-cadmium batteries; chemical defense wastes detection, decontamination, and protective mask filters. The Hazardous Waste Office has the responsibility to properly identify, characterize, classify and dispose of these waste items in accordance with US Environmental Protection Agency (EPA) and US Department of Transportation (DOT) regulations.
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.
Geometric reductions of ABS equations on an n-cube to discrete Painlevé systems
NASA Astrophysics Data System (ADS)
Joshi, N.; Nakazono, N.; Shi, Y.
2014-12-01
In this paper, we show how to relate n-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlevé equations. We here focus on the reduction from the four-dimensional cube to the q-discrete third Painlevé equation, which is a dynamical system on a rational surface of type A5(1) with the extended affine Weyl group \\tilde{W}({{({{A}2}+{{A}1})}(1)}). We provide general theorems to show that this reduction also extends to other discrete Painlevé equations at least of type A. This research was supported by an Australian Laureate Fellowship # FL 120100094 and grant # DP130100967 from the Australian Research Council.
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
Motion Mode Decomposition Based on Discrete Fourier Series Expansion
NASA Astrophysics Data System (ADS)
Hatta, Yoshiyuki; Shimono, Tomoyuki
In recent years, several methods for decomposing the whole motion of a parallel multi-degrees-of-freedom (MDOF) system into motion modes have been proposed. A motion mode is a motion element that corresponds to a specific physical action, such as grasping, manipulating, and rotating. Modal decomposition is effective for the expression and analysis of a complicated motion. However, conventional methods can extract motion modes only if the arrangement of actuators in the system has spatial linearity and symmetry. Therefore, the actuators cannot be arranged arbitrarily when the conventional methods are applied. In order to solve this problem, a novel method for modal decomposition is proposed; this method is based on the discrete Fourier series expansion. The proposed method is applied to a parallel MDOF bilateral system in which the arrangement of actuators is spatially asymmetric. Finally, the validity of the proposed method is confirmed on the basis of the experimental results.
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.
Berenstein, David; Pinansky, Samuel
2007-05-01
This paper discusses the minimal quiver gauge theory embedding of the standard model that could arise from brane world type string theory constructions. It is based on the low energy effective field theory of D branes in the perturbative regime. The model differs from the standard model by the addition of one extra massive gauge boson, and contains only one additional parameter to the standard model: the mass of this new particle. The coupling of this new particle to the standard model is uniquely determined by input from the standard model and consistency conditions of perturbative string theory. We also study some aspects of the phenomenology of this model and bounds on its possible observation at the Large Hadron Collider.
[Minimally invasive breast surgery].
Mátrai, Zoltán; Gulyás, Gusztáv; Kunos, Csaba; Sávolt, Akos; Farkas, Emil; Szollár, András; Kásler, Miklós
2014-02-01
Due to the development in medical science and industrial technology, minimally invasive procedures have appeared in the surgery of benign and malignant breast diseases. In general , such interventions result in significantly reduced breast and chest wall scars, shorter hospitalization and less pain, but they require specific, expensive devices, longer surgical time compared to open surgery. Furthermore, indications or oncological safety have not been established yet. It is quite likely, that minimally invasive surgical procedures with high-tech devices - similar to other surgical subspecialties -, will gradually become popular and it may form part of routine breast surgery even. Vacuum-assisted core biopsy with a therapeutic indication is suitable for the removal of benign fibroadenomas leaving behind an almost invisible scar, while endoscopically assisted skin-sparing and nipple-sparing mastectomy, axillary staging and reconstruction with latissimus dorsi muscle flap are all feasible through the same short axillary incision. Endoscopic techniques are also suitable for the diagnostics and treatment of intracapsular complications of implant-based breast reconstructions (intracapsular fluid, implant rupture, capsular contracture) and for the biopsy of intracapsular lesions with uncertain pathology. Perception of the role of radiofrequency ablation of breast tumors requires further hands-on experience, but it is likely that it can serve as a replacement of surgical removal in a portion of primary tumors in the future due to the development in functional imaging and anticancer drugs. With the reduction of the price of ductoscopes routine examination of the ductal branch system, guided microdochectomy and targeted surgical removal of terminal ducto-lobular units or a "sick lobe" as an anatomical unit may become feasible. The paper presents the experience of the authors and provides a literature review, for the first time in Hungarian language on the subject. Orv. Hetil
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
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.
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.
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.
Control of discrete event systems modeled as hierarchical state machines
NASA Technical Reports Server (NTRS)
Brave, Y.; Heymann, M.
1991-01-01
The authors examine a class of discrete event systems (DESs) modeled as asynchronous hierarchical state machines (AHSMs). For this class of DESs, they provide an efficient method for testing reachability, which is an essential step in many control synthesis procedures. This method utilizes the asynchronous nature and hierarchical structure of AHSMs, thereby illustrating the advantage of the AHSM representation as compared with its equivalent (flat) state machine representation. An application of the method is presented where an online minimally restrictive solution is proposed for the problem of maintaining a controlled AHSM within prescribed legal bounds.
Killing symmetries as Hamiltonian constraints
NASA Astrophysics Data System (ADS)
Lusanna, Luca
2016-02-01
The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.
Hidden symmetries in jammed systems
NASA Astrophysics Data System (ADS)
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
Driven discrete time quantum walks
NASA Astrophysics Data System (ADS)
Hamilton, Craig S.; Barkhofen, Sonja; Sansoni, Linda; Jex, Igor; Silberhorn, Christine
2016-07-01
We introduce the driven discrete time quantum walk (QW), where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original QW. These dynamics have two regimes, which we illustrate using the one-dimensional line. Then, we explore a search application which has certain advantages over current search protocols, namely that it does not require a complicated initial state nor a specific measurement time to observe the marked state. Finally, we describe a potential experimental implementation using existing technology.
Singlet-stabilized minimal gauge mediation
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 {Lambda}{sub UV} 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 {approx}({Lambda}/{Lambda}{sub UV}){sup 2}, which is {approx}10{sup -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.
Design of minimally strained nucleic Acid nanotubes.
Sherman, William B; Seeman, Nadrian C
2006-06-15
A practical theoretical framework is presented for designing and classifying minimally strained nucleic acid nanotubes. The structures are based on the double crossover motif where each double-helical domain is connected to each of its neighbors via two or more Holliday-junction-like reciprocal exchanges, such that each domain is parallel to the main tube axis. Modeling is based on a five-parameter characterization of the segmented double-helical structure. Once the constraint equations have been derived, the primary design problem for a minimally strained N-domain structure is reduced to solving three simultaneous equations in 2N+2 variables. Symmetry analysis and tube merging then allow for the design of a wide variety of tubes, which can be tailored to satisfy requirements such as specific inner and outer radii, or multiple lobed structures. The general form of the equations allows similar techniques to be applied to various nucleic acid helices: B-DNA, A-DNA, RNA, DNA-PNA, or others. Possible applications for such tubes include nanoscale scaffolding as well as custom-shaped enclosures for other nano-objects. PMID:16581842
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.
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.
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
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…
NASA Astrophysics Data System (ADS)
Mikhalev, A. S.; Rouban, A. I.
2016-04-01
The algorithms of global non-differentiable minimization of functions on set of the mixed variables: continuous and discrete with unordered specific possible values are constructed. The method of optimization is based on selective averaging of required variables, on adaptive reorganization of the sizes of admissible domain of trial movements and on use of relative values for minimised functions. Existence of discrete variables leads to solution of a sequence of global minimization problems of the functions in space of only continuous variables at the presence: 1) of their inequality restrictions for each problem; 2) of the general inequality restrictions for all problems (i.e. at the absence of dependence of functions fore inequality restrictions from discrete variables). In the first case, presence of discrete variables with unordered non-numeric possible values leads to solution of sequence of problems of global minimization of multiextreme functions on set only of continuous variables at the presence of their inequality restrictions. As a result, among the received optimum solutions the best is selected. In the second variant all minimized functions is convoluted in each sampling point in one multiextreme function and this function is minimised on continuous variables.
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Duality symmetries in string theory
Nunez, Carmen A.
1999-10-25
The search for a unified theory of quantum gravity and gauge interactions leads naturally to string theory. This field of research has received a revival of interest after the discovery of duality symmetries in recent years. We present a self contained account of some non-perturbative aspects of string theory which have been recently understood. The spectrum and interactions of the five consistent superstring theories in ten dimensions are recollected and the fundamental principles underlying this initial stage in the construction of the theory are briefly reviewed. We next discuss some evidences that these apparently different superstrings are just different aspects of one unique theory. The key to this development is given by the non-perturbative duality symmetries which have modified and improved our understanding of string dynamics in many ways. In particular, by relating the fundamental objects of one theory to solitons of another theory, they have unraveled the presence of extended objects in the theory which stand on an equal footing with strings. We introduce these higher dimensional objects, named D-branes, and discuss applications of D-brane physics.
Introduction to Electroweak Symmetry Breaking
Dawson,S.
2008-10-02
The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.
Discreteness effects in population dynamics
NASA Astrophysics Data System (ADS)
Guevara Hidalgo, Esteban; Lecomte, Vivien
2016-05-01
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of additive observables for stochastic processes. A method commonly used in order to determine such functions is the so-called cloning algorithm which in its non-constant population version essentially reduces to the determination of the growth rate of a population, averaged over many realizations of the dynamics. However, the averaging of populations is highly dependent not only on the number of realizations of the population dynamics, and on the initial population size but also on the cut-off time (or population) considered to stop their numerical evolution. This may result in an over-influence of discreteness effects at initial times, caused by small population size. We overcome these effects by introducing a (realization-dependent) time delay in the evolution of populations, additional to the discarding of the initial transient regime of the population growth where these discreteness effects are strong. We show that the improvement in the estimation of the large deviation function comes precisely from these two main contributions.
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.
Emergence of symmetry breaking in fucoid zygotes.
Homblé, Fabrice; Léonetti, Marc
2007-06-01
Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents. PMID:17499009
Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks
Brantley, P S
2001-03-23
An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S{sub N}) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems.
Dragging two-dimensional discrete solitons by moving linear defects
Brazhnyi, Valeriy A.; Malomed, Boris A.
2011-07-15
We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schroedinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.
Numerical solution of Boltzmann equation using discrete velocity grids
NASA Astrophysics Data System (ADS)
Vedula, Prakash
2015-11-01
An importance sampling based approach for numerical solution of the (single species) Boltzmann equation using discrete velocity grids is proposed. This approach involves a stochastic method for evaluation of the collision integral based on sampling of depleting/replenishing collisions and is designed to preserve important symmetries of the collision operator, including collision invariants. The underlying particle distribution function is represented as a collection of delta functions with associated weights that are non-negative. A key feature in the construction of the proposed method is that it ensures that the weights associated with the distribution function remain non-negative during collisional relaxation, thereby satisfying an important realizability condition. Performance of the proposed approach will be studied using test problems involving spatially homogeneous collisional relaxation flow and microchannel flows. Results obtained from the proposed method will be compared with those obtained from the (deterministic) collisional Lattice Boltzmann Method (cLBM) and the traditional direct simulation Monte Carlo (DSMC) method for solution of Boltzmann equation. Extension of the proposed method using discrete velocity grids for multicomponent mixtures will also be discussed.
Spontaneous symmetry breaking in Schroedinger lattices with two nonlinear sites
Brazhnyi, Valeriy A.; Malomed, Boris A.
2011-05-15
We introduce discrete systems in the form of straight (infinite) and ring-shaped chains, with two symmetrically placed nonlinear sites. The systems can be implemented in nonlinear optics (as waveguiding arrays) and Bose-Einstein condensates (by means of an optical lattice). A full set of exact analytical solutions for symmetric, asymmetric, and antisymmetric localized modes is found, and their stability is investigated in a numerical form. The symmetry-breaking bifurcation, through which the asymmetric modes emerge from the symmetric ones, is found to be of the subcritical type. It is transformed into a supercritical bifurcation if the nonlinearity is localized in relatively broad domains around two central sites, and also in the ring of a small size, i.e., in effectively nonlocal settings. The family of antisymmetric modes does not undergo bifurcations and features both stable and unstable portions. The evolution of unstable localized modes is investigated by means of direct simulations. In particular, unstable asymmetric states, which exist in the case of the subcritical bifurcation, give rise to breathers oscillating between the nonlinear sites, thus restoring an effective dynamical symmetry between them.
NASA Astrophysics Data System (ADS)
Sharkey, Amanda J. C.
2007-09-01
Swarm Robotics (SR) is closely related to Swarm Intelligence, and both were initially inspired by studies of social insects. Their guiding principles are based on their biological inspiration and take the form of an emphasis on decentralized local control and communication. Earlier studies went a step further in emphasizing the use of simple reactive robots that only communicate indirectly through the environment. More recently SR studies have moved beyond these constraints to explore the use of non-reactive robots that communicate directly, and that can learn and represent their environment. There is no clear agreement in the literature about how far such extensions of the original principles could go. Should there be any limitations on the individual abilities of the robots used in SR studies? Should knowledge of the capabilities of social insects lead to constraints on the capabilities of individual robots in SR studies? There is a lack of explicit discussion of such questions, and researchers have adopted a variety of constraints for a variety of reasons. A simple taxonomy of swarm robotics is presented here with the aim of addressing and clarifying these questions. The taxonomy distinguishes subareas of SR based on the emphases and justifications for minimalism and individual simplicity.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. PMID:25354765
Scars of symmetries in quantum chaos
Delande, D.; Gay, J.C.
1987-10-19
The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
Search for primordial symmetry breakings in CMB
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke
2016-06-01
There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Evidence for tetrahedral symmetry in (16)O.
Bijker, R; Iachello, F
2014-04-18
We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band. PMID:24785032
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Issues in standard model symmetry breaking
Golden, M.
1988-04-01
This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.
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.
Neutrino mixing and masses in SO(10) GUTs with hidden sector and flavor symmetries
NASA Astrophysics Data System (ADS)
Chu, Xiaoyong; Smirnov, Alexei Yu.
2016-05-01
We consider the neutrino masses and mixing in the framework of SO(10) GUTs with hidden sector consisting of fermionic and bosonic SO(10) singlets and flavor symmetries. The framework allows to disentangle the CKM physics responsible for the CKM mixing and different mass hierarchies of quarks and leptons and the neutrino new physics which produces smallness of neutrino masses and large lepton mixing. The framework leads naturally to the relation U PMNS ˜ V CKM † U 0, where structure of U 0 is determined by the flavor symmetry. The key feature of the framework is that apart from the Dirac mass matrices m D , the portal mass matrix M D and the mass matrix of singlets M S are also involved in generation of the lepton mixing. This opens up new possibilities to realize the flavor symmetries and explain the data. Using A 4 × Z 4 as the flavor group, we systematically explore the flavor structures which can be obtained in this framework depending on field content and symmetry assignments. We formulate additional conditions which lead to U 0 ˜ U TBM or U BM. They include (i) equality (in general, proportionality) of the singlet flavons couplings, (ii) equality of their VEVs; (iii) correlation between VEVs of singlets and triplet, (iv) certain VEV alignment of flavon triplet(s). These features can follow from additional symmetries or be remnants of further unification. Phenomenologically viable schemes with minimal flavon content and minimal number of couplings are constructed.
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
NASA Astrophysics Data System (ADS)
Hamada, Yuta; Kawai, Hikaru; Oda, Kin-ya
2014-02-01
We consider a possibility that the Higgs field in the Standard Model (SM) serves as an inflaton when its value is around the Planck scale. We assume that the SM is valid up to an ultraviolet cutoff scale Λ , which is slightly below the Planck scale, and that the Higgs potential becomes almost flat above Λ . Contrary to the ordinary Higgs inflation scenario, we do not assume the huge non-minimal coupling, of O(10^4), of the Higgs field to the Ricci scalar. We find that Λ must be less than 5× 10^{17} {GeV} in order to explain the observed fluctuation of the cosmic microwave background, no matter how we extrapolate the Higgs potential above Λ . The scale 10^{17} {GeV} coincides with the perturbative string scale, which suggests that the SM is directly connected with string theory. For this to be true, the top quark mass is restricted to around 171 GeV, with which Λ can exceed 10^{17} {GeV}. As a concrete example of the potential above Λ , we propose a simple log-type potential. The predictions of this specific model for the e-foldings N_*=50-60 are consistent with the current observation, namely, the scalar spectral index is n_s=0.977hbox {-}0.983 and the tensor to scalar ratio 0
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Minimal sufficient positive-operator valued measure on a separable Hilbert space
Kuramochi, Yui
2015-10-15
We introduce a concept of a minimal sufficient positive-operator valued measure (POVM), which is the least redundant POVM among the POVMs that have the equivalent information about the measured quantum system. Assuming the system Hilbert space to be separable, we show that for a given POVM, a sufficient statistic called a Lehmann-Scheffé-Bahadur statistic induces a minimal sufficient POVM. We also show that every POVM has an equivalent minimal sufficient POVM and that such a minimal sufficient POVM is unique up to relabeling neglecting null sets. We apply these results to discrete POVMs and information conservation conditions proposed by the author.
Voit, E O
1992-04-01
An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems. PMID:1591448
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.