Using Covariant Polarisation Sums in QCD

Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, $$\sum _{\lambda } \varepsilon _\mu ^{(\lambda )}\varepsilon _\nu ^{(\lambda )*} = -\eta _{\mu \nu }$$ ∑ λ ε μ ( λ ) ε ν ( λ ) ∗ = - η μ ν , is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev–Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms $$\mathcal {A}(c_1,\bar{c}_1;\ldots )\mathcal {A}(\bar{c}_1,c_1;\ldots )^*$$ A ( c 1 , c ¯ 1 ; … ) A ( c ¯ 1 , c 1 ; … ) ∗ between ghost amplitudes cannot be transformed into $$(-1)^{n/2}|\mathcal {A}(c_1,\bar{c}_1;\ldots )|^2$$ ( - 1 ) n / 2 | A ( c 1 , c ¯ 1 ; … ) | 2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.

Short Term Load Forecasting for Electric Power Utilities: A Generalized Regression Approach Using Polynomials and Cross-Terms

With the emergence of advanced computational technologies, the capacity to process data for developing machine learning-based predictive models has increased multifold. However, reliance on the model’s mere accuracy has swiftly shifted attention away from its interpretability. Resultantly, a need has emerged amongst forecasters and academics to have predictive models that are not only accurate but also interpretable as well. Therefore, to facilitate energy forecasters, this paper advances the knowledge of short-term load forecasting through generalized regression analysis using high degree polynomials and cross terms. To predict the irregularly changing energy demand at the consumer level, the proposed model uses a time series of an hourly load of three years of an electricity distribution company in Pakistan. Two variants of regression analysis are used: (a) generalized linear regression model (GLRM), and (b) generalized linear regression model with polynomials and cross-terms (GLRM-PCT) for comparative reasons. Experiments revealed that GLRM-PCT showed higher forecasting accuracy across a variety of performance metrics such as mean absolute percentage error (MAPE), mean absolute error (MAE), root mean squared error (RMSE), and r-squared values. Moreover, the enhanced interpretability of GLRM-PCT also explained a wide range of combinations of weather variables, public holidays, as well as lagged load and climatic variables.

On the Validity of CFD for Simulating a Shallow Water CALM Buoy in Extreme Waves

The Catenary Anchor-Leg Mooring (CALM) is the most popular and widely-used type of offshore loading terminal. A CALM buoy consists of a floating buoy anchored to the seabed by catenary chain legs which are secured to anchors or piles. Due to the small inertia of CALM buoys, the mooring line responses are very sensitive to waves and considerable fatigue risk is introduced to the mooring lines. Extreme waves may even lead to mooring line failure. Therefore it is highly relevant to study the motions of the CALM buoy in (extreme) wave conditions. This paper presents a validation study of a coupled CFD – dynamic mooring model for simulating the response of a shallow water CALM buoy in extreme waves (Figure 1). Simulations of an interactively moving CALM buoy in a horizontal mooring system were performed by coupling a Navier-Stokes based finite-volume, VoF CFD solver with a dynamic mooring model. The CFD results are validated against model tests performed in MARIN’s shallow-water basin during the ComFLOW-2 joint industry project. The validation study concentrates on the correct prediction of the coupled responses of the CALM buoy in extreme, regular shallow-water waves. As an alternative to simulations with a fully coupled dynamic mooring set-up, also CFD simulations are presented in which the mooring system is represented by a linearly equivalent spring matrix, including cross terms. The importance of correctly modelling these cross terms is presented in the paper, and the results obtained with- and without these off-diagonal spring terms are compared.

A new response surface method based on the adaptive bivariate cut-HDMR

Purpose The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness. Design/methodology/approach By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state. Findings The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points. Originality/value This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

The bispectrum and 21-cm foregrounds during the Epoch of Reionization

ABSTRACT Numerous studies have established the theoretical potential of the 21-cm bispectrum to boost our understanding of the Epoch of Reionization (EoR). We take a first look at the impact of foregrounds (FGs) and instrumental effects on the 21-cm bispectrum and our ability to measure it. Unlike the power spectrum for which (in the absence of instrumental effects) there is a window clear of smooth-spectrum FGs in which it may be detectable, there is no such ‘EoR window’ for the bispectrum. For the triangle configurations and scales we consider, the EoR structures are completely swamped by those of the FGs, and the EoR + FG bispectrum is entirely dominated by that of the FGs. By applying a rectangular window function on the sky combined with a Blackman–Nuttall filter along the frequency axis, we find that spectral, or in our case scale, leakage (caused by FFTing non-periodic data) suppresses the FG contribution so that cross-terms of the EoR and FGs dominate. While difficult to interpret, these findings motivate future studies to investigate whether filtering can be used to extract information about the EoR from the 21-cm bispectrum. We also find that there is potential for instrumental effects to seriously corrupt the bispectrum. FG removal using GMCA (generalized morphological component analysis) is found to recover the EoR bispectrum to a reasonable level of accuracy for many configurations. Further studies are necessary to understand the error and/or bias associated with FG removal before the 21-cm bispectrum can be practically applied in analysis of future data.

Buckley–Leverett Theory for Two-Phase Immiscible Fluids Flow Model with Explicit Phase-Coupling Terms

The theory of two-phase immiscible flow in porous media is based on the extension of single phase models through the concept of relative permeabilities. It mimics Darcy’s law for a fixed average saturation through the introduction of saturation-based permeabilities to model the momentum exchange between the phases. In this paper, we present a model of two-phase flow, based on the extension of Darcy’s law including the effect of capillary pressure, but considering in addition the coupling between the phases modeled through flow cross-terms. In this work, we extend the Buckley–Leverett theory to the subsequent model, and provide numerical experiments shading the light on the effect of the coupling cross-terms in comparison to the classical Darcy’s approach.