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.