Dispersive Corrections Research Articles

Energy-energy correlation in the back-to-back region at N3LL+NNLO in QCD

We consider the energy-energy correlation (EEC) function in high-energy electron-positron annihilation to hadrons. In the back-to-back (two-jet) region, we perform the all-order resummation of the logarithmically enhanced contributions in QCD perturbation theory up to next-to-next-to-next-to-leading logarithmic (N3LL) accuracy. Away from the back-to-back region, we consistently combine resummed predictions with the known fixed-order results up to next-to-next-to-leading order (NNLO), and we are able to obtain an accurate fit of the O(αS3) remainder function from the numerical QCD computation of the full spectrum. All perturbative terms up to order αS3 are included in our calculation, and a nontrivial cross-check in the back-to-back region is obtained by comparing the soft collinear effective theory analytic calculation against the corresponding numerical QCD computation. In particular, the values of the O(αS3) resummation coefficients have been numerically verified. We regularize the Landau singularity of the QCD coupling within the so-called minimal prescription, and we discuss the reduction of the perturbative scale dependence of distributions at higher orders, as a means to estimate the corresponding residual perturbative uncertainty. Finally, after introducing within a dispersive approach nonperturbative power corrections, we are able to obtain an accurate description of experimental data at the LEP and SLC accelerators. Published by the American Physical Society 2024

Ab Initio Theoretical Study of DyScO3 at High Pressure

DyScO3 is a member of a family of compounds (the rare-earth scandates) with exceptional properties and prospective applications in key technological areas. In this paper, we study theoretically the behavior of DyScO3 perovskite under pressures up to about 65 GPa, including its structural and vibrational properties (with an analysis of the Raman and infrared activity), elastic response, and stability. We have worked within the ab initio framework of the density functional theory, using projector-augmented wave potentials and a generalized gradient approximation form to the exchange-correlation functional, including dispersive corrections. We compare our results with existing theoretical and experimental published data and extend the range of previous studies. We also propose a candidate high-pressure phase for this material.

Low dispersion finite volume/element discretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes

We study a hybrid approach combining a finite volume (FV) and a finite element (FE) method to solve a fully-nonlinear and weakly-dispersive depth averaged wave propagation model. The FV method is used to solve the underlying hyperbolic shallow water system, while a standard P1 finite element method is used to solve the elliptic system associated to the dispersive correction. We study the impact of several numerical aspects: the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the well-posedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H1. We show, based on both heuristic and strong numerical evidence, that numerical dissipation plays a major role in stabilizing the coupled method, and not only providing convergent results, but also providing the expected convergence rates. Finally, the full mode, coupling a wave breaking closure previously developed by the authors, is thoroughly tested on standard benchmarks using unstructured grids with sizes comparable or coarser than those usually proposed in literature.

Mechanical and Electronic Properties of a Carbon-Composite 3D Nanomaterial with an Island-Type Topology

An atomistic model of a carbon-composite 3D nanomaterial with an island-type topology based on fullerene and graphene fragments as well as chiral/achiral single-walled carbon nanotubes (SWCNTs) with a subnanometer diameter is constructed. The island type refers to the presence of inhomogeneously distributed local regions with increased density of the nanomaterial in the structure of the composite. The effect of the concentration of nanotubes in the composite on the volume compressibility and electronic properties is investigated. It is found that an increase in the mass fraction of SWCNTs in the composite leads to a decrease in the coefficient of volume compressibility and, at the same time, improvement in the conductive properties. Classical molecular dynamics and the density functional based tight binding (DFTB) method with the use of dispersive energy correction are used for the physically correct description of individual fragments of the composite which are not covalently bound.

Reflectivity spectra as absorption resonant spectra: is it correct?

Approximate expressions for X-ray resonant and Mössbauer reflectivity in the total external reflection region are developed for the limiting cases of a semi-infinite mirror with a small resonant addition to the total susceptibility and for the case of an ultrathin resonant layer. It is shown that in this region the reflectivity can depend linearly on the imaginary part of the refraction index; therefore in these cases the consideration of reflectivity spectra (R-spectra) as absorption resonant spectra, taken up in several experimental studies, can be justified. However, several effects producing dispersive distortions of the R-spectrum shape, even for very small grazing angles, have been found. It has been shown that dispersive corrections to the R-spectrum shape are mostly necessary if the non-resonant absorption is relatively large. Model calculations demonstrate that the quantitative spectroscopic information extracted from R-spectra using the software developed for absorption spectra can be inaccurate.

High-Throughput Computational Exploration of MOFs with Open Cu Sites for Adsorptive Separation of Hydrogen Isotopes.

Effective separation of hydrogen isotopes still remains one of the extremely challenging tasks in industry. Compared to the present methods that are energy- and cost-intensive, quantum sieving technology based on nanostructured materials offers a more efficient alternative approach, where metal-organic frameworks (MOFs) featuring open metal sites (OMS) can serve as an ideal platform. Herein, a combination of periodic density functional theory (DFT) with dispersive correction and high-throughput molecular simulation was employed from thermodynamic viewpoints to explore the D2/H2 separation properties of 929 experimental MOFs bearing a copper-paddlewheel unit. The DFT calculations showed that there is a negligible rotational energy barrier for the molecule adsorbed at the OMS, and the movement of the Cu atoms along the Cu-Cu axis vector almost has no influence on the interaction energy. On the basis of the DFT results, a new force field with a proposed cutoff scheme was developed to accurately describe the strong isotope-OMS interaction. Under practical conditions (40 K and 1.0 bar), large-scale computational material screening demonstrated that the OMS interaction plays a more important role in highly selective materials and ignoring such interactions can lead to completely wrong identification of the most promising materials. Using the adsorption selectivity and adsorbent performance score as evaluation metrics, this work demonstrated that the materials with sql topology notably outperform many benchmark adsorbents reported so far.

Electrostatic electron plasma wave envelope with nonlinear Landau damping in nonthermal plasmas

The characteristics of nonlinear electrostatic electron plasma wave modulation are investigated in collisionless plasmas in the context of the Cairns and Kappa (generalized Lorentzian distribution with spectral index κ) nonthermal electron distribution, with particular attention to the nonlinear Landau damping process with resonance effect at the group velocity of the modulated wave. A modified nonlinear Schrödinger equation (mNLSE) with a nonlocal nonlinear Landau damping term governs the dynamics of the wave modulations. The results predict a far equilibrium region () where the Kappa distributed electrons lead to new dispersive corrections, an overall reduction of the carrier wave frequency () and the phase velocity and the existence of parameter regions where . On the contrary, the results in the near equilibrium region () are qualitatively similar to that of Cairns distributed electrons. The carrier waves always become damped by transferring energy to the side band waves due to nonlinear Landau damping and nonthermal particles enhance the energy transfer rate. The mNLSE is simulated extensively by a 2nd order split-step Fourier method with various initial pulses in different parameter regions.

Improving modeling of low-altitude particulate matter emission and dispersion: A cotton gin case study

Monitoring and modeling of airborne particulate matter (PM) from low-altitude sources is becoming an important regulatory target as the adverse health consequences of PM become better understood. However, application of models not specifically designed for simulation of PM from low-altitude emissions may bias predictions. To address this problem, we describe the modification and validation of an air dispersion model for the simulation of low-altitude PM dispersion from a typical cotton ginning facility. We found that the regulatory recommended model (AERMOD) overestimated pollutant concentrations by factors of 64.7, 6.97 and 7.44 on average for PM2.5, PM10, and TSP, respectively. Pollutant concentrations were negatively correlated with height (p < 0.05), distance from source (p < 0.05) and standard deviation of wind direction (p < 0.001), and positively correlated with average wind speed (p < 0.001). Based on these results, we developed dispersion correction factors for AERMOD and cross-validated the revised model against independent observations, reducing overestimation factors to 3.75, 1.52 and 1.44 for PM2.5, PM10 and TSP, respectively. Further reductions in model error may be obtained from use of additional observations and refinement of dispersive correction factors. More generally, the correction permits the validated adjustment and application of pre-existing models for risk assessment and development of remediation techniques. The same approach may also be applied to improve simulations of other air pollutants and environmental conditions of concern.

ESTIMATION OF GPS DISPERSIVE AND NON-DISPERSIVE NETWORK CORRECTION FOR ISKANDARnet NETWORK-BASED REAL-TIME KINEMATIC (N-RTK) POSITIONING SYSTEM

The concept of N-RTK positioning has been extensively developed in order to better model the distance-dependent errors of GPS carrier-phase measurements. These errors can be separated into a frequency-dependent or dispersive component (i.e., the ionospheric delay) and a non-dispersive component (i.e., the tropospheric delay and orbit biases) to express the network correction in order to attain better modelling of GPS distance dependent errors. However, the N-RTK performance may degrades due to severe atmospheric irregularities that would seriously affect the modelling of the GPS distance-dependent errors, thus affecting the quality of network correction generation. The development of integrity monitoring for network correction would be great idea to identify the quality and reliability of network correction data dissemination. Therefore, this paper aims to estimates the trend of GPS dispersive and non-dispersive network correction to supports future development of integrity monitoring for network correction of ISKANDARnet N-RTK positioning system. The first part of this paper is to extract the GPS dispersive and non-dispersive network residual components. This part includes the double-differencing technique, ambiguity resolution and carrier-phased linear combination in the process. The LIM then are applied for user network coefficient value computation purpose in the second part. Finally, the GPS dispersive and non-dispersive network correction can be generated with GF and IF network correction algorithm respectively. The trend of GPS dispersive and non-dispersive network correction is expected to aid the estimation and realization of threshold limit value for development of integrity monitoring for network correction of ISKANDARnet N-RTK positioning system.

Unraveling the Relationship between Zeolite Structure and MTO Product Distribution by Theoretical Study of the Reaction Mechanism

Determination of the relative contributions of aromatic-based and alkene-based cycles in the MTO process is essential for understanding the reaction mechanism and estimating the product selectivity over various zeolites. However, it is a great challenge due to the high complexity of the reaction network. Thus, the olefin formation mechanisms are systematically investigated here by the density functional theory with van der Waals dispersive corrections over structurally different zeolites. It is shown that the aromatic-based cycle dominates the MTO process over H-SAPO-34 with a side-chain route as the major reaction pathway, while the alkene-based cycle plays a major role on H-BEA and H-ZSM-5. Over H-ZSM-22, the alkene-based cycle is the main route with C5+ alkenes as primary products. The energy barriers of the aromatic-based cycle are similar over the above four types of zeolites. A linear relationship is found between the ethene/propene molar ratios and the free energy barriers of alkene-based cycles over these zeolites, indicating that the ethene and propene selectivities are mainly determined by the propagation of the alkene-based cycle. This suggests that the ultimate free energy barrier of the alkene-based cycle can be used as a measure to predict the C2=/C3= molar ratios obtained on topologically different zeolites.

CP-violating transport theory for electroweak baryogenesis with thermal corrections

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences.We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.

Dispersive correction for the second- and the third-order nonlinear terms of the electrical energy density for a light-dielectric system

The classical energy of a light-dielectric system plays a key role in presenting a quantum theory for the system as the Hamiltonian resulted from the Lagrangian of the system should be equal to it. It is normally, assumed that the second- and the third-order nonlinear terms of the electrical energy are not frequency dependent. However, for some conditions (including the real case) their frequency dependence should be taken into account. Here, we consider the pulse propagation through a lossless, isotropic and inhomogeneous dielectric. Considering the properties of the second- and the third-order susceptibility tensors of the isotropic dielectric, we obtain the dispersive correction for the second and the third-order nonlinear terms of the electromagnetic energy density for this medium as in all practical cases the susceptibility tensors of the dielectrics are frequency dependent.

A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part I: Derivation, implementation and model verification

Numerical and physical modeling are the two main tools available for predicting the influence of water waves on coastal or offshore structures. Both models have their strengths and weaknesses. An integrated use of numerical and physical modeling which exploits their advantages can provide an optimal description of full-scale, realistic engineering problems. In this series of two papers, we report on a generalized three-dimensional (3D) deterministic coupling theory for multidirectional nonlinear wave propagation from a numerical model to a physical model up to second order. In this work, the second-order coupling theory developed by [Z. Yang, S. Liu, H.B. Bingham and J. Li, 2014a. Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part I Formulation, implementation and numerical properties. Coast. Eng. 92, 48–60] and the ad hoc unified wave generation theory developed by [H. Zhang, H.A., Schäffer, K.P., Jakobsen, 2007. Deterministic combination of numerical and physical coastal wave models. Coast. Eng. 54, 171–186.] have been extended to include the coupling between multidirectional nonlinear waves. In part I of this article series, the full second-order 3D coupling theory for multidirectional nonlinear waves is been described in detail. A novel generalized fully-nonlinear motion boundary equation has been derived, which allows the interface between the numerical and physical wave domains to be a 3D arbitrarily shaped wavemaker system. The corresponding 3D wave coupling equation is given for I-, L-, and O-shaped wavemaker layouts. The new formulation is presented in a unified form for an arbitrarily shaped layout of planar wavemakers, and covers both hinged and piston wavemaker types. For the second-order dispersive correction of the paddle stroke, the super-harmonic and sub-harmonic wave-wave interactions have been taken into account. For practical implementation, a typical discretization method for the 3D coupling equations is derived by considering the case of the I-shaped piston wavemaker. The new 3D coupling equations are solved by a combined five-point Lagrange interpolation and the fourth-order Runge–Kutta scheme. Numerical evaluations of the implementation have been conducted by considering a theoretical second-order unidirectional wave field over a range of spatial and time resolutions. The results thus obtained indicate that the proposed discretization scheme is accurate and effective. In addition, the precision of the discrete scheme is observed to be closely related to the spatial and temporal resolution. A separate experimental validation of the theory is presented in Part II.

A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part II: Experimental validation using an I-shaped segmented wavemaker

This paper provides the experimental validation of the generalized second-order three-dimensional (3D) coupling theory outlined by Yang et al. [Z. Yang, S. Liu, X. Ji, and H.B. Bingham, 2020. A generalized second-order 3D theory for coupling multidirectional nonlinear wave propagation from a numerical model to a physical model. Part I: Derivation, implementation and model verification, submitted for publication] using multidirectional nonlinear 3D irregular waves. Based on the second-order theory for two-dimensional (2D) irregular waves described by Yang et al. (2014a), this work provides a second-order dispersive correction for the physical wavemaker signal which improves the nonlinear 3D wave information transfer between the numerical and physical models compared to the first-order method of Zhang et al. (2007). The important coupling equation and its discretization schemes were presented in detail in Part I. For further validating the performance of the second-order 3D coupling model under complex waves and bathymetry conditions, in this Part II, a careful experimental validation has been carried out by establishing a flat coupling basin and a concave-convex coupling basin. In addition, a sequence of progressively more complex numerical target waves has been used and an I-shaped segmented piston-type wavemaker system has been considered for verification of the theory. The effectiveness, adaptability, and precision of the second-order 3D coupling model have been discussed in detail. The effects of the wave parameters and its nonlinearity on the coupling simulation have also been evaluated from the discrepancy error and a wave harmonic analysis. By defining a space synchronization error, the overall error of the spatial wave field has been analyzed. Coupling simulation experiments using oblique regular and irregular waves, unidirectional irregular waves, and multidirectional irregular waves show that the traditional first-order coupling model has limitations when coupling complex waves with strong nonlinearity. When controlling the waves using the second-order 3D coupling signal, the higher harmonics underlying the numerical waves are accurately captured and transferred into the physical model, and the unwanted second-order spurious free waves are substantially reduced. Results obtained from the experimental verification described in this paper demonstrate the strengths of the second-order 3D coupling theory, which are more evident with increased wave nonlinearity.

Discontinuous Galerkin methods for a dispersive wave hydro-sediment-morphodynamic model

A dispersive wave hydro-sediment-morphodynamic model developed by complementing the shallow water hydro-sediment-morphodynamic (SHSM) equations with the dispersive term from the Green–Naghdi equations is presented. A numerical solution algorithm for the model based on the second-order Strang operator splitting is presented. The model is partitioned into two parts, (1) the SHSM equations and (2) the dispersive correction part, which are discretized using discontinuous Galerkin finite element methods. This splitting technique provides a facility to select dynamically regions of a problem domain where the dispersive term is not applied, e.g. wave breaking regions where the dispersive wave model is no longer valid. Algorithms that can handle wetting–drying and detect wave breaking are provided and a number of numerical examples are presented to validate the developed numerical solution algorithm. The results of the simulations indicate that the model is capable of predicting sediment transport and bed morphodynamic processes correctly provided that the empirical models for the suspended and bed load transport are properly calibrated. Moreover, the developed model is able to accurately capture hydrodynamics and wave dispersion effects up to swash zones, and its application is justified for simulations where dispersive wave effects are prevalent.

Crime pays; homogenized wave equations for long times

This article examines the accuracy for large times of asymptotic expansions from periodic homogenization of wave equations. As usual, ϵ denotes the small period of the coefficients in the wave equation. We first prove that the standard two scale asymptotic expansion provides an accurate approximation of the exact solution for times t of order ϵ − 2 + δ for any δ &gt; 0. Second, for longer times, we show that a different algorithm, that is called criminal because it mixes different powers of ϵ, yields an approximation of the exact solution with error O ( ϵ N ) for times ϵ − N with N as large as one likes. The criminal algorithm involves high order homogenized equations that, in the context of the wave equation, were first proposed by Santosa and Symes and analyzed by Lamacz. The high order homogenized equations yield dispersive corrections for moderate wave numbers. We give a systematic analysis for all time scales and all high order corrective terms.

Erratum to: Dispersive corrections in elastic electron-nucleus scattering: an investigation in the intermediate energy regime and their impact on the nuclear matter

In the original PDF online version of this article, the references 22–26 were missing.These are the missing references.

Dispersive corrections in elastic electron-nucleus scattering: an investigation in the intermediate energy regime and their impact on the nuclear matter

Measurements of elastic electron scattering data within the past decade have highlighted two-photon exchange contributions as a necessary ingredient in theoretical calculations to precisely evaluate hydrogen elastic scattering cross sections. This correction can modify the cross section at the few percent level. In contrast, dispersive effects can cause significantly larger changes from the Born approximation. The purpose of this experiment is to extract the carbon-12 elastic cross section around the first diffraction minimum, where the Born term contributions to the cross section are small to maximize the sensitivity to dispersive effects. The analysis uses the LEDEX data from the high resolution Jefferson Lab Hall A spectrometers to extract the cross sections near the first diffraction minimum of 12C at beam energies of 362 MeV and 685 MeV. The results are in very good agreement with previous world data, although with less precision. The average deviation from a static nuclear charge distribution expected from linear and quadratic fits indicate a 30.6% contribution of dispersive effects to the cross section at 1 GeV. The magnitude of the dispersive effects near the first diffraction minimum of 12C has been confirmed to be large with a strong energy dependence and could account for a large fraction of the magnitude for the observed quenching of the longitudinal nuclear response. These effects could also be important for nuclei radii extracted from parity-violating asymmetries measured near a diffraction minimum.

Optical Kerr effect in vacuum

From an effective field theory of electromagnetism in vacuum including all lowest-order nonlinear terms consistent with Lorentz invariance and locality of photon-photon interactions, we derive an effective-medium description of strong background fields as regards their influence on a weak probe. We mainly consider as background a pump beam with well-defined wave vector and polarization. This leads us to define a nonlinear index of vacuum which, in the Euler-Heisenberg model derived from QED, has an optimal value of $1.555\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}33}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{2}/\mathrm{W}$ for a linearly polarized pump as seen by a counterpropagating, orthogonally polarized probe. We further generalize the model to include coupling to an axion field. In the limit where the axion mass is much smaller than the typical photon energy, this yields dispersive corrections, and the axionic signature is found to be greatly enhanced for a circularly polarized pump as compared to a linearly polarized one. The formalism here presented points to a simplification of the DeLLight experiment [Sarazin et al., Eur. Phys. J. D 70, 13 (2016)] aiming to measure the deflection of a probe by a tightly focused laser pulse.

Exploring the Reliability of DFT Calculations of the Infrared and Terahertz Spectra of Sodium Peroxodisulfate

A number of DFT programs with various combinations of pseudo-potentials and van der Waals’ dispersive corrections have been used to optimize the structure of sodium peroxodisulfate, Na2(SO4)2, and to calculate the infrared, attenuated total reflectance and terahertz absorption spectra of the powdered crystal. Comparison of the results from the different methods highlights the problems of calculating the absorption spectrum reliably. In particular the low frequency phonon modes are especially sensitive to the choice of grids to represent the wavefunction or the charge distribution, k-point integration grid and the energy cutoff. A comparison is made between the Maxwell-Garnett (MG) and Bruggeman effective medium methods used to account for the effect of crystal shape on the predicted spectrum. Possible scattering of light by air inclusions in the sample and by larger particles of Na2(SO4)2 is also considered using the Mie method. The results of the calculations are compared with experimental measurements of the transmission and attenuated total reflection spectra.