Duality Diagrams Research Articles

FTMP-based Simulation and Evaluation of Apparent Reduction in Elastic Modulus

This study attempts to quantitatively evaluate the apparent reduction in elastic moduli, generally observed in metallic materials during unloading and/or cyclic elasto-plastic deformation, based on Field Theory of Multiscale Plasticity (FTMP). Two typical arrangements of bowing-out dislocation segments that yield mutually-distinct trends are examined by utilizing the FTMP-based duality diagram representation scheme. It is demonstrated that not only the scheme allows us to visualize the associated energy flow but also to correlate the resultant apparent shear modulus reduction rate in a unified manner by the duality coefficient measured on the duality diagrams. The scheme is demonstrated to be effective also for more complex cases accompanied by pinning/unpinning and the following relaxation processes.

Selection index for meat and milk traits of buffaloes in Colombia

Genetic parameters and breeding values from unitrait, multitrait, and reduced principal component models for weaning weight, yearling weight, weight at 18 months, weight at two years, age at first calving, milk yield, and maternal genetic effects for weaning weight and yearling weight were estimated for dual purpose buffaloes in Colombia. With those values we constructed selection indices (SI) and estimated genetic progress obtained through mating-modeling under various selection criteria and weighted values for each trait. Comparison of SI was performed using duality diagrams in principal components of breeding values obtained by pseudo-simulation of mating with animals selected with the constructed SIs. The index constructed with the first principal component of the reduced range model led to improved meat, milk yield, and age at first calving.

Metalogical Decorations of Logical Diagrams

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams (viz. Aristotelian and duality diagrams) and four kinds of metalogical decorations (viz. those based on the opposition, implication, Aristotelian and duality relations).

On the N = 1 ∗ $$ \mathcal{N}={1}^{\ast } $$ gauge theory on a circle and elliptic integrable systems

We continue our study of the N=1* supersymmetric gauge theory and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the classification of nilpotent orbits, as well as on the conjugacy classes of the component group of their centralizer. We demonstrate that semi-classically massless vacua can be lifted by Wilson lines in unbroken discrete gauge groups. The pseudo-Levi subalgebras that play a classifying role in the nilpotent orbit theory are also key in defining generalized Inozemtsev limits of (twisted) elliptic integrable systems. We illustrate our analysis in the N=1* theories with gauge algebras su(3), su(4), so(5) and for the exceptional gauge algebra G2. We map out modular duality diagrams of the massive and massless vacua. Moreover, we provide an analytic description of the branches of massless vacua in the case of the su(3) and the so(5) theory. The description of these branches in terms of the complexified Wilson lines on the circle invokes the Eichler-Zagier technique for inverting the elliptic Weierstrass function. After fine-tuning the coupling to elliptic points of order three, we identify the Argyres-Douglas singularities of the su(3) theory.

Quarks in the bootstrap era

The quark model emerged from the Gell-Mann–Ne'eman flavor SU(3) symmetry. Its development, in the context of strong interactions, took place in a heuristic theoretical framework, referred to as the Bootstrap Era. Setting the background for the dominant ideas in strong interaction of the early 1960s, we outline some aspects of the constituent quark model. An independent theoretical development was the emergence of hadron duality in 1967, leading to a realization of the Bootstrap idea by relating hadron resonances (in the s-channel) with Regge pole trajectories (in t- and u-channels). The synthesis of duality with the quark-model has been achieved by duality diagrams, serving as a conceptual framework for discussing many aspects of hadron dynamics toward the end of the 1960s.

FTMP-BASED SIMULATION OF TWIN NUCLEATION AND SUBSTRUCTURE EVOLUTION UNDER HYPERVELOCITY IMPACT

The deformation twinning model based on Field Theory of Multiscale Plasticity (FTMP) represents the twin degrees of freedom with the incompatibility tensor, which is incorporated into the hardening law of the FTMP-based crystalline plasticity framework. The model is further implemented into a finite element code. In the present study, the model is adapted to a single slip-oriented FCC single crystal sample, and preliminary simulations are conducted under static conditions to confirm the model's basic capabilities. The simulation results exhibit nucleation and growth of twinned regions, accompanied by serrated stress response and overall softening. Simulations under hypervelocity impact conditions are also conducted to investigate the model's descriptive capabilities of induced complex substructures composing of both twins and dislocations. The simulated nucleation of twins is examined in detail by using duality diagrams in terms of the flow-evolutionary hypothesis.

Duality, crossing and MacLane’s coherence

It is shown that MacLane’ rectangle, pentagon and hexagon identities in category theory, when applied in particle physics to duality diagrams or to rational conformal field theories in two dimensions, yield the necessary physical algebraic constraints.

A note about linear inequality systems and duality

The optimization of a linear function on a closed convex set,F, can be stated as a linear semi-infinite program, sinceF is the solution set of (usually) infinite linear inequality systems, the so-called linear representations ofF. The duality properties of these programs are analyzed when the linear representation ofF ranges in some well known classes of linear inequality systems. This paper provides propositions on the duality diagrams of Farkas-Minkowski, canonically closed, compact and closed systems. Converse statements are also given.

Multiple production of η-mesons and pomeron-gluonium duality

Multiple production of η-mesons is considered in the framework of approach based on the topological 1/N expansion. As the low energy resonance ηη-amplitudes are governed by the instanton induced interaction in theJ P =0−,0+-channels, the high energyt-channel ηη-amplitudes are assumed to decouple from secondary reggeons, and to be connected via duality with the gluonium resonance amplitudes in thes-channel. The relevant duality diagrams are essentially nonplanar ones. We demonstrate that this fact combined with increase of the mass scale 1/α R ′ ≃1 GeV2, typical of “classical” resonance, to 1/α P ′ ≃3-5 GeV2, the mass scale for gluonium physics, explains the observed hindrance of the η-mesons production at moderate, ∼102GeV, energies and the onset of a copious production in the\(Sp\bar pS\)-collider energy range.

Preon Composites and Their Interactions in a Unified Preon Model

Hypercolor-singlet preon composites (or postons) and their interactions are studied in a unified preon model with the gauge group of SU(7) ⊗SU(7). The preonic structure of postons is combined with duality diagrams to examine features of a few condensations required by the model. Dual amplitudes for the scattering of two massless postons are also discussed. A switch-over phenomenon for two fermion trajectories crossing each other at s=0 and J=1/2 is considered to understand à la Regge how massless postons acquire masses.

Study of antiproton-proton annihilations using the topological-cross-section differences betweenp¯pandppinteractions at 48.9 GeV/c

The multiplicity-cross-section differences $\ensuremath{\Delta}{\ensuremath{\sigma}}_{n}$ between $\overline{p}p$ and $\mathrm{pp}$ interactions are determined and are compared with measured annihilations and $\ensuremath{\Delta}{\ensuremath{\sigma}}_{n}$ at other energies. To the extent that these cross-section differences measure the values of ${\ensuremath{\sigma}}_{n}^{A}$, the topological cross sections for annihilations, we present evidence for a decided break from a single-cluster-model prediction for the parameter ${f}_{2}^{{A}_{\ensuremath{-}\ensuremath{-}}}$. Alternatively, a picture of precocious Koba-Nielsen-Olesen scaling in $\overline{p}p$ annihilations leads to a reasonably good representation of ${f}_{2}^{{A}_{\ensuremath{-}\ensuremath{-}}}$ vs $〈{n}_{\ensuremath{-}}^{A}〉$ over the whole measured range. We find $〈{n}^{A}〉=7.57\ifmmode\pm\else\textpm\fi{}0.31$, ${D}^{A}=2.77\ifmmode\pm\else\textpm\fi{}0.10$, ${f}_{2}^{{A}_{\ensuremath{-}\ensuremath{-}}}=\ensuremath{-}1.86\ifmmode\pm\else\textpm\fi{}0.20$, and $\frac{〈{n}^{A}〉}{D}=2.73\ifmmode\pm\else\textpm\fi{}0.15$. Finally we observe a remarkable agreement with theoretical prediction for ${R}_{n}^{*}=\frac{\ensuremath{\Delta}{\ensuremath{\sigma}}_{n}}{{\ensuremath{\sigma}}_{n+2}(\mathrm{pp})}$, an experimental ratio based on a strict application of the counting rules for quark duality diagrams, and we thereby find evidence that in the topological-cross-section difference $\ensuremath{\Delta}{\ensuremath{\sigma}}_{n}$ the small nonannihilation contribution becomes progressively more negligible as $n$ increases.

How quarks that are strange build their Regge exchange

The scattering of strange mesons can produce resonance states both with and without hidden strangeness. Making use of the very recent analyses of K −p data at 4.2 GeV, we conduct a definitive test of the hypothesis, suggested by duality diagrams, that resonances made of non-strange quarks build the f′-ϕ exchange in the crossed channel. For this, in fact to succeed, the η′ is determined to be close to an SU(3) singlet and have an equal amount of strange and non-strange quarks just as required by the quadratic version of the Gell-Mann-Okubo mass formula.

Dual unitarization approach to current-induced reactions

We establish an ansatz which incorporates the photon into the structure of duality diagrams. This then allows us to apply the Mueller-Regge formalism to deep-inelastic electron scattering. We derive Bjorken scaling, in particular the behavior (1 - x)/sup ..beta../ near x = 1 for the structure function, with ..beta.. compatible with the value deduced from the data. We also give results on the relative sizes of sea and valence quark distributions.

Asymptotic-freedom phenomenology and the Zweig-rule-violating decays of ψ and ψ′

We discuss the Zweig-Iizuka-rule-violating decays of ψ and ψ′ from a phenomenological field theory point of view with effective quark-gluon couplings satisfying asymptotic freedom. This leads to a satisfactory qualitative and quantitative description of those decays. It provides, moreover, an alternative and equivalent approach to the usual strong-interaction approach, based on quark duality diagrams, with which we compare it.

Violation of the ozi rule in central production of the φ meson

The suppression mechanism of the OZI forbidden production in the central region is pointed out to be different from that in the fragmentation region. The cancellation in the unitarity due to twists in duality diagrams does not work for the central vertex of φ multiperipheral production. Relatively copious production of φ mesons is expected in the central region.

A possible description of baryon dynamics in dual and gauge theories

We present an attempt to generalize to baryons a framework recently proposed in order to unify gauge, dual and Regge-Gribov theories of mesons. We find it necessary to depart from the 1 N colour expansion of quantum chromodynamics (QCD) and to replace it by a more general definition of a “dual” approximation of QCD, based on the zero-width limit. Theoretical and phenomenological consequences of the scheme are derived. For N colour = 3, the baryon resembles a Y shaped string; three families of new “baryonium” bound states are predicted and rough estimates of intercepts and slopes of the associated Regge trajectories are given. A new type of Zweig-like selection rule is found to hold in leading order and its violations through higher-order topologies are discussed. Duality diagrams for baryons are ambiguous unless implemented with extra lines indicating the flow of certain colour indices. Duality between scattering and annihilation channels is found in B B scattering and its consequences are discussed. Some justification is given for the quark counting rule for total cross sections. Finally, implications of our scheme for the Regge-Gribov calculus in processes involving baryons are discussed.

Incorporation of baryons into the topological expansion

Veneziano's topological expansion is extended to duality diagrams involving mesons and baryons.

Dynamical thresholds in the dual unitarization scheme

Mass differences of particles produced in high-energy collisions lead to dynamical thresholds in unitarity integrals for two-body scattering. These thresholds are understood as being responsible for the rapid energy dependence of exotic-exchange and Zweig-rule-violating amplitudes. Processes involving twisted intermediate states, and consequently cancellations, in the unitarity sum are expected to be particularly sensitive to these thresholds. In the J-plane, the corresponding amplitudes are characterized by a weak leading singularity accompanied by strong non-leading effective singularities associated with threshold effects. The requirement that states of even and odd C-conjugation be produced with equal strength in order to keep exotic amplitudes small at high energies can also be relaxed as a consequence of the said threshold phenomena. The SU(3) structure of exotic states generated by multiperipheral duality diagrams is also discussed.

Total widths of resonances: A criterion for the formulation of hadronic interactions

The structure of relativistic hadron couplings in the harmonic-oscillator model is studied in terms of a criterion which demands aless-than-exponential increase of total widths of resonances with theirexcitation quantum numbers. The implementation of this program in turn requires a model for the evaluation of total widths which is formulated within the framework of the harmonic-oscillator model with the help of a physically plausible inclusiveness ansatz. For the coupling structures, two available alternatives are examined:A) the unsymmetrical radiation quantum (RQ) hypothesis for one of the mesons andB) the more symmetrical quark pair creation (QPC) hypothesis consistent with duality diagrams. For their relativistic formulations, a comparison is made betweena) the 4-dimensional covariant theory of the Lipes-Kim-Noz type andb) a 3-dimensional noncovariant approach due to Licht and Pagnamenta. Model calculations are performed mostly for M→MM transitions, by involving radial and orbital excitations, but by ignoring the spin andSU3 degrees of freedom. It is found that the 4-dimensional covariant formulation, with either of the RQ and QPC hypotheses, gives rise toexponentially increasing total widths, and hence is incompatible with the stated criterion. The noncovariant relativistic version, on the other hand, satisfies the criterion only under QPC, but not under RQ. It is therefore concluded that, of the four alternatives studied, only one, the 3-dimensional relativistic formulation with the QPC hypothesis, is favoured by the chosen criterion which is defended on other grounds as well.

Amplitude analysis for the process K − p → (π + π −) s-wave ϵ 0 (1385)

Transversity amplitudes and spin density matrix elements are determined for the process K − p → (π + π −) s-wave ϵ 0(1385). Predictions of the additive quark model and of duality diagrams are tested and found consistent with the data; this is the first information about the applicability of these models to processes where a scalar object is produced at the mesonic vertex.