Quantum Numbers Research Articles

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Fourier-transform spectroscopy and global deperturbation treatment of the A1Σu+ and b3Πu states of K2 in the entire bound energy range.

Rotationally resolved Fourier-transform spectra of laser-induced fluorescence A1Σu+∼b3Πu→X1Σg+ of K2 molecules were recorded and analyzed, yielding 4053 term values of the spin-orbit (SO) coupled A ∼ b complex of the 39K2 isotopologue with ∼0.01 cm-1 accuracy. Their compilation with 1739 term values from previously published sources allowed them to cover the energy range [9955, 17 436] cm-1 from the bottom of the lower-lying b3Πu state up to the vicinity of the atomic asymptote 4s2S12 + 4p2P12, with a rotational quantum number J ∈ [0, 149]. The experimental data were processed by a direct 6 × 6 coupled-channel (CC) deperturbation treatment, which accounted explicitly for both SO and electronic-rotational interactions between all six e-symmetry states: A1Σu+(0u+), b3Πu(0u+,1u,2u), c3Σu(1u), and B1Πu(1u). The initial parameters of the global deperturbation model have been estimated in the framework of abinitio electronic structure calculations applying multi-reference configuration-interaction and coupled-clusters methods. The interatomic potentials analytically defined for A and b states, as well as SO-splitting of the triplet b state and A ∼ b SO-coupling functions, have been particularly refined to fit the 5792 term values of the 39K2 isotopologue, whereas the rest parameters were fixed on their abinitio values. The resulting mass-invariant parameters of the 6 × 6 CC model reproduced the overall rovibronic term energies of the A ∼ b complex of 39K2 with accuracy, which is well within the experimental errors. The quality of the deperturbation analysis was independently confirmed by comparison with the present obtained 705 and 14 term values of respective 39K41K and 41K2 isotopologues, as well as by agreement between measured and predicted relative intensity distributions in long A ∼ b → X(vX) band progressions. This deperturbation analysis provided the refined dissociation energy Tdis = 17 474.569(5) cm-1 and the long-range coefficient C3Σ = 5.501(4) × 105 cm-1 Å3 relevant to the non-relativistic atomic limit 4s + 4p. The derived Tdis yielded the accurate well depth De = 4450.910(5) cm-1 for the ground X1Σg+ state, whereas the new C3Σ value yielded the improved estimates for atomic K(4p2P12;32) radiative lifetimes, τ12 = 26.67(3) and τ32 = 26.32(3) ns.

The noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field

In this work, we investigate the noncommutative Dirac oscillator (NCDO) with a permanent electric dipole moment (EDM) in the presence of an electromagnetic field. We consider a radial magnetic field generated by anti-Helmholtz coils and the uniform electric field of the Stark effect. Next, we determine the exact solutions of the system, given by the Dirac spinor and by the relativistic energy spectrum. We note that such a spinor is written in terms of the generalized Laguerre polynomials, and such a spectrum is a linear function on the potential energy U and depends on the quantum numbers n and m, spin parameter s, and of four angular frequencies: ω, ω¯ , ω θ , and ω η , where ω is the frequency of the DO, ω¯ is a type of ‘cyclotron frequency’, and ω θ and ω η are the NC frequencies of position and momentum. We graphically analyze the behavior of the spectrum as a function of these frequencies for three different values of n, with and without the influence of U. Besides, as an interesting result, another interpretation can be given for the origin of the nonminimal coupling of the DO, which would be through a neutral fermion with EDM in a radial magnetic field. Finally, we also analyze the nonrelativistic limit of our results, and comparing our problem with other works, we verified that our results generalize some particular cases in the literature.

An updated fluorescence emission model of CO+ for cometary science

ABSTRACT A new CO$^+$ fluorescence emission model for analysing cometary spectra is presented herein. Accurate line lists are produced using the PGOPHER software for all transitions between the three electronic states (X $^2\Sigma$, A $^2\Pi$, B $^2\Sigma$) with vibrational states up to $v_\textrm {max} = 9, 8, 6$, respectively, and maximum rotational states with rotational quantum numbers $N\le 20$. As a result of improved molecular constants and theoretical transition rates, an expansion of the utilized solar spectrum into the infrared, and the substantial expansion of the included rovibronic states, the model provides an update of the fluorescence efficiencies of the CO$^+$ cation. The dependencies on heliocentric velocity and distance are explicitly included. We report, for the first time, quantification of the fluorescence efficiencies for the ground state rovibrational transitions of CO$^+$ and predict the positions and relative intensities of CO$^+$ lines in windows accessible to both ground- and space-based observatories. The computed fluorescence efficiencies show excellent agreement with UV/optical observations of both C/2016 R2 (PanSTARRS) and 29P/Schwassmann-Wachmann 1. The updated fluorescence efficiencies allow for revised N$_2$/CO abundances for comets 1P/Halley, C/1987 P1 (Bradfield), and C/2016 R2 (PanSTARRS), which can change by up to 30 per cent when accounting for recent improvements to CO$^+$ and N$_2^+$ fluorescence efficiencies. The model code, input files, and fluorescence efficiencies are publicly available and distributed on permanent archives for future uses in cometary analyses.

Interacting topological quantum chemistry in 2D with many-body real space invariants

The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

Interface fluctuations associated with split Fermi seas

We consider the asymptotic behaviour of a family of unidimensional lattice fermion models, which are in exact correspondence with certain probability laws on partitions and on unitary matrices. These models exhibit limit shapes, and in the case where the bulk of these shapes are described by analytic functions, the fluctuations around their interfaces have been shown to follow a universal Tracy–Widom distribution or its higher-order analogue. Non-differentiable bulk limit shape functions arise when a gap appears in some quantum numbers of the model, in other words when the Fermi sea is split. We show that split Fermi seas give rise to new interface fluctuations, governed by integer powers of universal distributions. This breakdown in universality is analogous to the behaviour of a random Hermitian matrix when the support of its limiting eigenvalue distribution has multiple cuts, with oscillations appearing in the limit of the two-point correlation function. We show that when the Fermi sea is split in the lattice fermion model, there are multiple cuts in the eigenvalue support of the corresponding unitary matrix model.

Nonlinear Rydberg exciton-polaritons in Cu2O microcavities

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon–photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu2O-filled microresonator. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as ∝ n4.4±1.8 for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly correlated photonic (polaritonic) states in a solid state system.

Constructional modeling in the formalism of cognitive-quantitative construction grammar

This paper discusses the findings of constructional modeling in the formalism of cognitive quantitative construction grammar, a newly developed research framework within a cognitive-quantitative grammar approach. Triangulating theoretical tenets, methodological principles and research tools of cognitivesemiotic frameworks with quantitative corpus studies, cognitive quantitative construction grammar provides a comprehensive qualitative-quantitative approach to examining cognitive foundations, general and idiosyncratic linguistic features, usage patterns and distribution of linguistic constructions. In this context, constructional modeling entails applying a computerized linguoquantitative procedure for a construction profile parametrization. This procedure yields operationalized and statistically verified data on the essential parameters that determine a construction’s linguistic behavior. The modeling uses the boxbracket notation, which integrates the box notation to represent holistic construction-level information and construction’s constituent-level information, and the bracket notation to detail specific linguistic properties and constructional constraints.The constructional modeling in the integrated box-bracket notational system applied to English ꞌdetached nonfinite/nonverbal with explicit subjectꞌ-constructions allows for a comprehensive representation of their external and internal linguistic properties and captures inheritance links betweenthe constructions at macro-, meso- and micro-levels of the constructional network. The research findings demonstrate the feasibility of applying the cognitive quantitative construction grammar formalism to model the linguistic properties and constraints of complex clause-level constructions and how these constructions are likely to be represented in the mental grammar of speakers.

Machine-learning and CFD based optimization and comprehensive experimental study on diagonal flow fan for energy conservation and efficiency enhancement

The diagonal flow fan, known for its innovative airflow guiding technique, presents a dual advantage of heightened efficiency and reduced noise levels. Despite garnering attention in energy production systems, research on optimizing outlet guide vanes for diagonal flow fan performance remains limited. This study introduces a novel machine learning approach, utilizing Opt LHD sampling instead of traditional simulations and experiments to accumulate ample sample data. The fusion of LS-SVM and improved GA-PSO is employed for multi-objective optimization of outlet guide vanes, aiming to simultaneously enhance fan performance and reduce energy consumption. Experimental assessments reveal the optimized fan's significant improvements, including a 106 Pa increase in total pressure, a 3.6 dB reduction in noise levels, and a remarkable 16.3% enhancement in total pressure efficiency. These results highlight the robustness of the machine learning approach in optimizing diagonal flow fan exit guide vanes, effectively addressing the research gap in this area. Additionally, numerical analysis of internal flow dynamics and acoustic properties pre and post-optimization uncovers the intrinsic mechanisms influencing the overall performance of the diagonal flow fan.

Performance enhancement of 3D‐printed carbon fiber‐reinforced nylon 6 composites

AbstractThe inherent defects of the layer‐by‐layer manufacturing process limit the mechanical performance of 3D‐printed composite parts. This paper explores a process optimization method for continuous fiber composites 3D printing to improve the mechanical performance of 3D‐printed CF/PA6 (Carbon Fiber/Nylon 6) parts. First, the effects of printing temperature, printing speed, layer thickness, and side step on the mechanical performance of 3D‐printed CF/PA6 were studied by conducting variable parameter printing experiments. All optimal printing parameters for CF/PA6 were obtained, and their impact mechanisms were analyzed. Second, the coupling effect of temperature and pressure of post‐processing reduced the internal voids of 3D‐printed CF/PA6 and improved its mechanical properties. The influence mechanism of the coupling effect of temperature and pressure was summarized, and the optimal post‐processing parameters applicable to CF/PA6 were obtained. Based on the above process optimization, the fiber volume content of the printed CF/PA6 reached 41.05%, and the bending strength and elastic modulus reached 651.54 MPa and 79.08 GPa, which were 209.05% and 179.53% higher than those before optimization. Moreover, the tensile strength and elastic modulus reached 730 MPa and 29.23GPa, which were 98.10% and 81.10% higher than those before optimization. The experimental results give a positive validation of the effectiveness and feasibility of the proposed methodology.Highlights The effects of printing temperature, printing speed, layer thickness, and side step on the mechanical properties of 3D‐printed CF/PA6 were investigated. The optimal printing parameters applicable to CF/PA6 were obtained and their influence mechanisms were analyzed. The effects of the heat press processing method on the internal voids and mechanical properties of 3D‐printed CF/PA6 were investigated, and the optimal post‐processing parameters applicable to CF/PA6 were obtained. The study resulted in optimal printing parameters and post‐processing parameters for 3D printing CF/PA6, which greatly enhanced its tensile and flexural strength and modulus.

Pseudospin symmetry in resonant states in deformed nucleus 154Dy

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus [Formula: see text]Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection [Formula: see text] and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei.

Betelgeuse as a Merger of a Massive Star with a Companion

We investigate the merger between a 16M ⊙ star, on its way to becoming a red supergiant (RSG), and a 4M ⊙ main-sequence companion. Our study employs three-dimensional hydrodynamic simulations using the state-of-the-art adaptive mesh refinement code Octo-Tiger. The initially corotating binary undergoes interaction and mass transfer, resulting in the accumulation of mass around the companion and its subsequent loss through the second Lagrangian point (L2). The companion eventually plunges into the envelope of the primary, leading to its spin-up and subsequent merger with the helium core. We examine the internal structural properties of the post-merger star, as well as the merger environment and the outflow driven by the merger. Our findings reveal the ejection of approximately ∼0.6 M ⊙ of material in an asymmetric and somewhat bipolar outflow. We import the post-merger stellar structure into the MESA stellar evolution code to model its long-term nuclear evolution. In certain cases, the post-merger star exhibits persistent rapid equatorial surface rotation as it evolves in the H–R diagram toward the observed location of Betelgeuse. These cases demonstrate surface rotation velocities of a similar magnitude to those observed in Betelgeuse, along with a chemical composition resembling that of Betelgeuse. In other cases, efficient rotationally induced mixing leads to slower surface rotation. This pioneering study aims to model stellar mergers across critical timescales, encompassing dynamical, thermal, and nuclear evolutionary stages.

Transformations for non-destructive evaluation of brix in mango by reflectance spectroscopy and machine learning

Mango is a very popular climacteric fruit in America and Europe. Among the internal properties of the mango, total soluble solids (TSS) are an adequate indicator to estimate the quality of mango, however, the measurement of this indicator requires destructive tests. Several research have addressed similar issues; they have made use of pre-processing transformations without making it clear which of them is statistically better. Here, we created a new spectral database to build machine learning (ML) models. We analyzed a total of 18 principal component regression (PCR) models and 18 partial least squared regression (PLSR) models, where 4 types of transformations, 3 different feature extractors, and 3 different pre-processing techniques are combined. The research proposes a double cross validation (CV) both to determine the optimal number of components and to obtain the final metrics. The best model had a root mean square error (RMSE) of 1.1382 °Brix and a RMSE on the transformed scale of 0.5140. The best model used 4 components, used y<sup>2</sup> transformation, reflectance R as the independent variable and MSC as a pre-processing technique.

Two-Pole Nature of the Λ(1405) Resonance from Lattice QCD.

This Letter presents the first lattice QCD computation of the coupled channel πΣ-K[over ¯]N scattering amplitudes at energies near 1405MeV. These amplitudes contain the resonance Λ(1405) with strangeness S=-1 and isospin, spin, and parity quantum numbers I(J^{P})=0(1/2^{-}). However, whether there is a single resonance or two nearby resonance poles in this region is controversial theoretically and experimentally. Using single-baryon and meson-baryon operators to extract the finite-volume stationary-state energies to obtain the scattering amplitudes at slightly unphysical quark masses corresponding to m_{π}≈200 MeV and m_{K}≈487 MeV, this study finds the amplitudes exhibit a virtual bound state below the πΣ threshold in addition to the established resonance pole just below the K[over ¯]N threshold. Several parametrizations of the two-channel K matrix are employed to fit the lattice QCD results, all of which support the two-pole picture suggested by SU(3) chiral symmetry and unitarity.

Galactic cosmic-ray scattering due to intermittent structures

ABSTRACT Cosmic rays (CRs) with energies ≪ TeV comprise a significant component of the interstellar medium (ISM). Major uncertainties in CR behaviour on observable scales (much larger than CR gyroradii) stem from how magnetic fluctuations scatter CRs in pitch angle. Traditional first-principles models, which assume these magnetic fluctuations are weak and uniformly scatter CRs in a homogeneous ISM, struggle to reproduce basic observables such as the dependence of CR residence times and scattering rates on rigidity. We therefore explore a new category of ‘patchy’ CR scattering models, wherein CRs are pre-dominantly scattered by intermittent strong scattering structures with small volume-filling factors. These models produce the observed rigidity dependence with a simple size distribution constraint, such that larger scattering structures are rarer but can scatter a wider range of CR energies. To reproduce the empirically inferred CR scattering rates, the mean free path between scattering structures must be $\ell _{\rm mfp}\sim 10\, {\rm pc}$ at GeV energies. We derive constraints on the sizes, internal properties, mass/volume-filling factors, and the number density any such structures would need to be both physically and observationally consistent. We consider a range of candidate structures, both large scale (e.g. H ii regions) and small scale (e.g. intermittent turbulent structures, perhaps even associated with radio plasma scattering) and show that while many macroscopic candidates can be immediately ruled out as the primary CR scattering sites, many smaller structures remain viable and merit further theoretical study. We discuss future observational constraints that could test these models.

Perplexing EPR Signals from 5f36d1 U(II) Complexes.

Metal complexes with unpaired electrons in orbitals of different angular momentum quantum numbers (e.g., f and d orbitals) are unusual and opportunities to study the interactions among these electrons are rare. X-band electron paramagnetic resonance (EPR) data were collected at <10 and 77 K on 10 U(II) complexes with 5f36d1 electron configurations and on some analogous Ce(II), Pr(II), and Nd(II) complexes with 4fn5d1 electron configurations. The U(II) compounds unexpectedly display similar two-line axial signals with g|| = 2.04 and g⊥ = 2.00 at 77 K. In contrast, U(II) complexes with 5f4 configurations are EPR-silent. Unlike U(II), the congenic 4f35d1 Nd(II) complex is EPR-silent. The Ce(II) complex with a 4f15d1 configuration is also EPR-silent, but a signal is observed for the Pr(II) complex, which has a 4f25d1 configuration. Whether or not an EPR signal is expected for these complexes depends on the coupling between f and d electrons. Since the coupling in U(II) systems is expected to be sufficiently strong to preclude an EPR signal from compounds with a 5f36d1 configuration, the results are viewed as unexplained phenomena. However, they do show that 5f36d1 U(II) samples can be differentiated from 5f4 U(II) complexes by EPR spectroscopy.

Two-Dimensional Spectroscopy Isolates Infrared Rovibrational Patterns.

The rovibrational spectra of freely rotating gas phase molecules are often plagued by spectral congestion due to the high density of rotational peaks. The congestion is especially severe at higher infrared frequencies due to the large numbers of overlapping overtones and combination bands that form polyads. As a result, rovibrational peaks in the near-infrared region of the spectrum are seldom assigned. This work describes how two-dimensional (2D) rovibrational spectroscopy can use the coupling between vibrational modes to isolate rovibrational bands that would otherwise remain overlapped and congested. Multidimensional spectroscopic techniques that make use of the large number of cross-peaks that form rich 2D rovibrational patterns are explored. Propyne is used to demonstrate 2D methods for identifying the frequencies and symmetries of coupled vibrations and for assigning rotational quantum numbers, even in regions that are heavily congested.

Energies and radiative properties of 1s22l2l′ and 1s(2l)22l′ levels in tungsten ion, W70+

Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations of energy levels, oscillator strengths and transition rates of open K-shell transitions in beryllium-like tungsten ion, W[Formula: see text], are performed using the fully relativistic GRASP2018 code. For only principal quantum number [Formula: see text], energy levels of 1[Formula: see text] 2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2p, 1[Formula: see text] and 1[Formula: see text] at different angular momenta and parity ([Formula: see text] are presented. Excitations of up to four electrons from the ground level, 1[Formula: see text] 2[Formula: see text], to excited levels are allowed. Correlations up to 5l orbitals are included in the configuration state function (CSF), [Formula: see text], p, d, f and g. The fine-structure calculations of E1, E2, M1 and M2 oscillator strengths and radiative rates between intercombination transitions in W[Formula: see text] ions are evaluated. The accuracy of these results is estimated using different ways, such as the comparison with previously published results and calculating the uncertainty of the transition data. The uncertainty of the transition probabilities showed low values for most of transitions.

Superradiance of ultracold cesium Rydberg |65D5/2〉 → |66P3/2〉

We investigate Rydberg |65D5/2〉 → |66P3/2〉 superradiance in dense ultracold cesium atoms, where the ground atoms are excited to |65D5/2〉 Rydberg states via two-photon excitation in a standard magneto-optical trap. The superradiant spectrum of |65D5/2〉 → |66P3/2〉 is obtained using the state-selective field ionization technique. We observe its dynamic evolution process by varying the delay time of ionization field t d. The results show that the evolution process of |65D5/2〉 → |66P3/2〉 is much shorter than its radiation lifetime at room temperature, which verifies the superradiance effect. The dependence of the superradiance process on Rydberg atoms number N e and principal quantum number n is investigated. The results show that the superradiance becomes faster with increasing N e, while it is suppressed for stronger van der Waals (vdW) interactions. Superradiance has potential applications in quantum technologies, and the Rydberg atom is an ideal medium for superradiance. Our system is effective for studying the strong two-body interaction between Rydberg atoms.

Empirical rovibrational energy levels for nitrous oxide

A survey of the huge number of measured rovibrational transitions of the 14N216O isotopologue of nitrous oxide is performed which either confirms the positions, the assignments, and the uncertainties of the measurements or refutes at least one of them. Data from 95 literature sources are analyzed and their assignments adjusted to a uniform set of polyads and associated counting numbers. This is an important result of the present study and this canonical set of vibrational state assignments is recommended for future studies. The adjusted list of 67930 transitions (43246 unique ones) then underwent a thorough Marvel (Measured Active Rotational–Vibrational Energy Levels) analysis, yielding 17561 empirical rovibrational energy levels. Uncertainties for these levels are determined using a newly implemented bootstrap approach. The bootstrap uncertainties indicate that the uncertainties for about 1.5% of the energy levels had to be increased significantly, often by more than 10 times compared to previous level uncertainty estimates. This study yields empirical values for 78 band origins of 14N216O for states with ℓ=0, where ℓ is the vibrational angular momentum quantum number. The measured transitions and the empirical energy levels are compared to the SISAM and the recent NOSL-296 line lists with the result that while the overall agreement is good, there are still a number of issues requiring further careful experimental and modeling studies.