Spectral duality in integrable systems from AGT conjecture

We describe relationships between integrable systems with N degrees of freedom arising from the Alday-Gaiotto-Tachikawa conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl _N Gaudin model both at classical and quantum level. The former one appears on the gauge theory side of the Alday-Gaiotto-Tachikawa relation in the Nekrasov-Shatashvili (and further the Seiberg-Witten) limit while the latter one is natural on the CFT side. At the classical level, the duality transformation relates the Seiberg-Witten differentials and spectral curves via a bispectral involution. The quantum duality extends this to the equivalence of the corresponding Baxter-Schrödinger equations (quantum spectral curves). This equivalence generalizes both the spectral self-duality between the 2 × 2 and N × N representations of the Toda chain and the famous Adams-Harnad-Hurtubise duality.     

Chiral rings,singularity theory and electric-magnetic duality

We study in detail the space of perturbations of a pair of dual N = 1 supersymmetric theories based on an SU(N_c) gauge theory with an adjoint X and fundamentals with a superpotential which is polynomial in X. The equivalence between them depends on non-trivial facts about polynomial equations, i.e. singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges “trivial” classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

The dipole picture of high energy scattering,the BFKL equation and many gluon compound states

The relationship and equivalence between the BFKL and dipole equation kernels are investigated by means of explicit calculations in light-cone perturbation theory. A dipole equation, equivalent to the usual equation, for interactions between four reggeized gluons is given in the large N_c limit. The leading trajectory of the four-gluon system is bounded by 2αp − 1 with αp the BFKL pomeron intercept.     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

Ignition limit and shock-to-detonation transition mode of n-heptane/air mixture in high-speed wedge flows

In this work, oblique detonation of n-heptane/air mixture in high-speed wedge flows is simulated by solving the reactive Euler equations with a two-dimensional (2D) configuration. This is a first attempt to model complicated hydrocarbon fuel oblique detonation waves (ODWs) with a detailed chemistry (44 species and 112 reactions). Effects of freestream equivalence ratios and velocities are considered, and the abrupt and smooth transition from oblique shock to detonation are predicted. Ignition limit, ODW characteristics, and predictability of the transition mode are discussed. Firstly, homogeneous constant-volume ignition calculations are performed for both fuel-lean and stoichiometric mixtures. The results show that the ignition delay generally increases with the wedge angle. However, a negative wedge angle dependence is observed, due to the negative temperature coefficient effects. The wedge angle range for successful ignition of n-heptane/air mixtures decreases when the wedge length is reduced. From two-dimensional simulations of stationary ODWs, the initiation length generally decreases with the freestream equivalence ratio, but the transition length exhibits weakly non-monotonic dependence. Smooth ODW typically occurs for lean conditions (equivalence ratio < 0.4). The interactions between shock/compression waves and chemical reaction inside the induction zone are also studied with the chemical explosive mode analysis. Moreover, the predictability of the shock-to-detonation transition mode is explored through quantifying the relation between ignition delay and chemical excitation time. It is demonstrated that the ignition delay (the elapsed time of the heat release rate, HRR, reaches the maximum) increases, but the excitation time (the time duration from the instant of 5% maximum HRR to that of the maximum) decreases with the freestream equivalence ratio for the three studied oncoming flow velocities. Smaller excitation time corresponds to stronger pressure waves from the ignition location behind the oblique shock. When the ratio of excitation time to ignition delay is high (e.g., > 0.5 for n-C₇H₁₆, > 0.3 for C₂H₂ and > 0.2 for H₂, based on the existing data compilation in this work), smooth transition is more likely to occur.     

Intermittency and scaling relations

We show that to a very good approximation there exists in general an equivalence between intermittency and the assumption that the first factorial correlatorF ₁₁ is independent of bin size. We further show that strict bin size independence imposes for the possible values of the intermittency index?, ?=0, or?=1.     

The effects of burner stabilization on Fenimore NO formation in low-pressure, fuel-rich premixed CH4/O2/N2 flames

We investigate the effects of varying the degree of burner stabilization on Fenimore NO formation in fuel-rich low-pressure flat CH₄/O₂/N₂ flames. Towards this end, axial profiles of flame temperature and OH, NO and CH mole fractions are measured using laser-induced fluorescence (LIF). The experiments are performed at equivalence ratios between 1.3 and 1.5. The flame temperature is seen to decrease by 200-300 K, with a concomitant decrease in OH mole fraction, upon reducing the total flow rate from 5 to 3 L/min, thus increasing stabilization. At equivalence ratios between 1.3 and 1.5, this decrease in flow rate lowers the maximum CH mole fraction by a factor of 2, and the NO mole fraction by ∼40% in all flames studied. Integrating the reaction rate for CH + N₂ to estimate Fenimore NO formation, using the rate coefficient in GRI-Mech 3.0, and the measured temperatures and CH profiles show very good agreement with the measured NO mole fraction for ? = 1.3 and 1.4, supporting the current choice for this rate. This agreement also shows that the increase in residence time caused by increased stabilization is an important factor in the ultimate impact of the changes in CH mole fraction on NO formation. The results at ? = 1.5 suggest that substantial quantities of fixed nitrogen species, e.g., HCN, are only slowly oxidized in the post-flame zone under these conditions, leading to a significant discrepancy between the measured NO mole fraction and that obtained by integrating over the CH profile. Detailed calculations using GRI-Mech 3.0 predict the experimental results at ? = 1.3 nearly quantitatively, but show increasing differences with the measurements for both CH and NO profiles with increasing equivalence ratio.     

The FN solution of the time-dependent neutron transport equation for a sphere with forward scattering

The one-speed time-dependent and stationary neutron transport equation in spherical geometry with forward scattering is considered. A formal equivalence between the transport equations for a critical and for a decaying system is established. By considering the pseudo-slab problem the scaled transport equation is solved using the F_N method. Numerical values of radii for a critical and time-dependent systems are tabulated as a function of the scattering parameters and the fundamental decay constant. Some of the results are discussed and compared with others obtained using various methods. The results agree for four or five significant figures with the published results. It is shown that the F_N method yields good numerical results for the problem considered. Finally, a few remarks about the effect of the forward anisotropy on the radius is also given.     

A chemical kinetic study of n-butanol oxidation at elevated pressure in a jet stirred reactor

Biofuels are attractive alternatives to petroleum derived transportation fuels. n-Butanol, or biobutanol, is one alternative biofuel that can replace gasoline and diesel in transportation applications. Similar to ethanol, n-butanol can be produced via the fermentation of sugars, starches, and lignocelluloses obtained from agricultural feedstocks. n-Butanol has several advantages over ethanol, but the detailed combustion characteristics are not well understood. This paper studies the oxidation of n-butanol in a jet stirred reactor at 10 atm and a range of equivalence ratios. The profiles for CO, CO₂, H₂O, H₂, C₁-C₄ hydrocarbons, and C₁-C₄ oxygenated compounds are presented herein. High levels of carbon monoxide, carbon dioxide, water, hydrogen, methane, formaldehyde, ethylene, and propene are detected. The experimental data are used to validate a novel detailed chemical kinetic mechanism for n-butanol oxidation. The proposed mechanism well predicts the concentration of major product species at all temperatures and equivalence ratios studied. Insights into the prediction of other species are presented herein. The proposed mechanism indicates that n-butanol consumption is dominated by H-atom abstraction from the α, β, and γ carbon atoms. A sensitivity analysis is also presented to show the effects of reaction kinetics on the concentration of several poorly predicted species.     

Classification of two-shell nanotubes with commensurate structures of shells

A classification of two-shell carbon nanotubes with commensurate structures of shells is proposed. The classification is based on the concept of equivalence classes as a set of shells with chiral indices of the (kf, kg) type, where f and g are the chiral indices of the equivalence class and k is the index of the shell diameter. All two-shell nanotubes with commensurate shells that are characterized by the chiral indices (k₁f₁, k₁g₁) and (k₂f₂, k₂g₂), where k₁ and k₂ are integral numbers, make up a family of nanotubes of different radii but with equal geometric parameters (such as the intershell distance, the unit cell length of the nanotube, and the difference between the chiral angles of the shells). The geometric parameters of nanotubes are calculated for a number of families, the distribution of different types of two-shell nanotubes with commensurate shells over the outer-shell radii is determined, and the threshold forces required to induce relative motion of nanotube shells are evaluated. The possible use of two-shell nanotubes with commensurate shells in nanostructures is discussed.     

Computational study on lean and rich combustion of flame ball,counterflow flame and planar flame: Their limits and stoichiometries

To investigate (fuel-)lean/rich limits and essential stoichiometries, i.e., the borders of lean/rich combustion, one-dimensional steady computations with detailed chemistry for flame balls, counterflow flames, and stretch-free planar flames were conducted using a CH₄/O₂/Xe mixture that has been used in microgravity experiments. As continuous converged solutions were obtained under lean/rich conditions, it was suggested that the existence of flame ball not only under lean but also under rich condition. Flame radii and temperatures of flame balls decreased and increased toward the lean/rich limits from their maximum and minimum values, respectively. The lean limits were wider in the order of the flame ball, counterflow flame, and stretch-free planar flame. Therefore, the lean flammability limit corresponded to the lean limit of the flame ball in the mixture. Conversely, the rich limits were wider in the order of the counterflow flame, stretch-free planar flame, and flame ball. Thus, the rich flammability limit corresponded to the rich limit of the counterflow flame in the mixture. Essential stoichiometry, which represents the actual stoichiometry depending on the dominant transport in near-flame front, was not uniquely determined as conventional stoichiometry (ϕ = 1); it was located between the equivalence ratio of ϕ = 1 and ϕ_c, where ϕ _c denotes the critical equivalence ratio is evaluated using the fuel and oxidizer Lewis number of a target mixture. The results indicated that the essential stoichiometry of the stretch-free planar flame corresponded to ϕ = 1, that of the flame ball corresponded to ϕ = ϕ _c, and that of the stretched flame was located between ϕ = 1 and ϕ _c depending on the stretch rate.     

Microcanonical ensemble study of a gas column under gravity

The study of a classical ideal gas column of finite height H in a uniform gravitational field g is made by the microcanonical ensemble at energy E. The primary functions of this ensemble, the phase volume and the density of states, are derived. Related statistical quantities, such as the entropy, the temperature and the heat capacity, are also reported. The equivalence in the thermodynamic limit between the calculated microcanonical expressions and those obtained from the canonical ensemble is shown numerically. The expression for the temperature is used to analyze the temperature change when the gas is permitted to expand into an evacuated region increasing the height of the column from H ₁ to H ₂. The microcanonical single-particle momentum and height distributions are also reported.     

QCD corrections to b→sγγ and exclusive Bs→γγ decay

The short distance QCD corrections to b→sγγ are calculated in the leading logarithmic approximation. The equivalence of operator basis reduction for S-matrix elements by using the equations of motion or by proving a low energy theorem is discussed. We apply the above results to the exclusive B_s→γγ decay. The branching ratio of this decay is found to be 5×10⁻⁷ in the Standard Model. We also found that QCD corrections modify considerably the ratio between CP-even and CP-odd two-photon amplitudes.     

A computational analysis of strained laminar flame propagation in a stratified CH4/H2/air mixture

Propagation of a H₂-added strained laminar CH₄/air flame in a rich-to-lean stratified mixture is numerically studied. The back-support effect, which is known to enhance the consumption speed of a flame propagating into a leaner mixture compared to that into a homogeneous mixture, is evaluated. A new method is devised to characterize unsteady reactant-to-reactant counterflow flames under transiently decreasing equivalence ratio, in order to elucidate the influence of flow strain on the back-support effect. In contrast to the conventional reactant-to-product configurations, the current configuration is more relevant to unsteady stratified flames back-supported by their own combustion products. Moreover, since H₂ distribution downstream of the flame is known to play a crucial role in back-supported CH₄/air flames, the influence of H₂ addition in the upstream mixture is examined. The results suggest that a larger strain rate leads to a larger equivalence ratio gradient at the reaction zone through increased flow divergence, which amplifies the back-support. Meanwhile, since H₂ addition in the upstream mixture does not affect the downstream H₂ content, the relative increase in the consumption speed, i.e. the back-support, is suppressed with larger H₂ addition. Especially, when the upstream H₂ content decreases with the equivalence ratio, the H₂ preferentially diffuses toward the unburned gas, which mitigates H₂ accumulation in the preheat zone and further weakens the back-support.     

CCAP for Universal Discrete Quantum Groups

We show that the discrete duals of the free orthogonal quantum groups have the Haagerup property and the completely contractive approximation property. Analogous results hold for the free unitary quantum groups and the quantum automorphism groups of finite-dimensional C^*-algebras. The proof relies on the monoidal equivalence between free orthogonal quantum groups and SU _q (2) quantum groups, on the construction of a sufficient supply of bounded central functionals for SU _q (2) quantum groups, and on the free product techniques of Ricard and Xu. Our results generalize previous work in the Kac setting due to Brannan on the Haagerup property, and due to the second author on the CCAP.     

Experimental behaviour of noise indices as a function of averaging time

The behaviour of noise indices as a function of averaging time has been investigated. Measurements were made on 13 noise samples selected as representative of noises of industrial origin which are rapidly varying in time.It was found that log χ² distributions well represent the SPL distributions of the noises; moreover an equivalence between the integration time (T) and the time constant (τ) was achieved when T = 2τ. For noises of rapid time variation the choice of the averaging time is of some importance, while for traffic noise it is fairly uncritical. As regards fluctuation measurements the indices L_DI and σ_L show a similar behaviour for high time constants and slowly varying noises. On the contrary, for short time constants and rapidly varying noises they have a somewhat different trend.     

Higher Hochschild Homology,Topological Chiral Homology and Factorization Algebras

We study the higher Hochschild functor, factorization algebras and their relationship with topological chiral homology. To this end, we emphasize that the higher Hochschild complex is a functor sSet _∞ × CDGA _∞ where sSet and CDGA _∞ are the (∞,1)-categories of simplicial sets and commutative differential graded algebras, and give an axiomatic characterization of this functor. From the axioms, we deduce several properties and computational tools for this functor. We study the relationship between the higher Hochschild functor and factorization algebras by showing that, in good cases, the Hochschild functor determines a constant commutative factorization algebra. Conversely, every constant commutative factorization algebra is naturally equivalent to a Hochschild chain factorization algebra. Similarly, we study the relationship between the above concepts and topological chiral homology. In particular, we show that on their common domains of definition, the higher Hochschild functor is naturally equivalent to topological chiral homology. Finally, we prove that topological chiral homology determines a locally constant factorization algebra and, further, that this functor induces an equivalence between locally constant factorization algebras on a manifold and (local system of) E _n -algebras.     

Understanding the effect of inhomogeneous fuel–air mixing on knocking characteristics of various ethanol reference fuels with RON 100 using rapid compression machine

We investigated the effect of inhomogeneous mixing of a fuel–air mixture in a spark-ignition engine on knocking characteristics and the dependency of the effect on the fuel, especially for various ethanol reference fuels with a fixed RON of 100. We assumed that a locally lean spot and rich spots exist in the end gas owing to inhomogeneous mixing and calculated their thermodynamic states with a multizone spark-ignition engine simulation. Subsequently, the ignition delay around the state was measured using a rapid compression machine at varying temperatures and equivalence ratios. The obtained results were processed to calculate ξ, which is the ratio of sound speed to auto-ignition propagation speed, and $?$, defined as the time required for acoustic front to exit the hot spot divided by the excitation time. Then, we analyzed the knocking occurrence and intensity from the locally lean spot and rich spots based on Zel'dovich and Bradley's ξ–$?$ theory. Our results show that the lean spot has a shorter ignition delay than the stoichiometric mixture (ξ?>?0) regardless of the ethanol content, whereas the rich spot does not (ξ?<?0), implying that only the lean spot can initiate knocking. This is because the temperature of the lean spot is higher than the surrounding mixture owing to its higher specific heat ratio and less charge cooling effect. In addition, the knocking intensity from the lean spot is found to be maximized with ERF0, showing the largest ${\xi }^{?2}$ value. Further analysis was conducted by dividing ξ into the effect of the temperature gradient, ξ_T, and that of the equivalence ratio gradient, ξ_?. Consequently, we found that the magnitude of ξ_T is related to the activation energy of the fuel, while that of ξ_? is determined by the dependency of the pre-heat release characteristics of the fuel on the equivalence ratio.     

The blow-off and transient characteristics of co-firing ammonia/methane fuels in a swirl combustor

Recent studies have demonstrated that ammonia could be one of the most promising hydrogen carrier candidates which can be used in large-scale power plants. However, it is challenging to burn ammonia in gas turbines due to its narrow flame stabilization limits. This study investigates the blow-off characteristics and flame macrostructure transition behavior of ammonia/air flame (i.e. NH₃ flame) and ammonia/methane/air flame (i.e. 50%NH₃ flame) in a swirl combustor. Methane/air flame (i.e. CH₄ flame) is also demonstrated for comparative purposes. The flow field and instantaneous OH profile are measured with PIV and OH-PLIF technique, respectively. Large eddy simulation (LES) is conducted to extend understandings of the experimental findings. The results show that the NH₃ flame possesses a poor lean flame stability limit which can be largely extended by adding CH₄ in the fuel. Moreover, changing swirl number (S) shows no apparent effect on the lean blow-off limit (?_b) for the NH₃ flame. On the contrary, a clear extension on ?_b is found for the 50%NH₃ flame when increasing S. Four flame macrostructure modes can be identified when decreasing equivalence ratio (?). The transition from flame II to flame III (?_t describes the transition equivalence ratio) can be considered as the early warning of blow-off for a swirl stabilized flame. It is found that for the NH₃ flame, there is no clear flame macrostructure transition at small inlet velocities (U < 3.8 m/s), i.e., ?_b ≈ ?_t, while the difference between ?_b and ?_t will be observed as the inlet velocity increases. However, for the 50%NH₃ and CH₄ flames, a clear flame macrostructure transition from flame II to flame III is observed even for a lower inlet velocity. The LES results show that the NH₃ flame has a faster blow-off process compared to the CH₄ flame, which is mainly attributed to the excessive stretch causing local extinction during the blow-off process.