Mahikeng, the seat of the Ngaka Modiri Molema District and capital of South Africa’s North West province, has identified tourism as an economic driver based on cultural heritage related to Batswana, ...Boer, and British contestation. However, the colonial heritage is underutilised as visitors come to Mahikeng (formerly Mafeking) in search of experiences relating to the siege of Mafeking, the Anglo–Boer War, and the origins of the Boy Scouts movement but leave disappointed. This heritage has been downgraded in democratic post-apartheid South Africa as there is an agenda that seeks to highlight African cultural heritage, particularly relating to the anti-apartheid struggle. This formerly suppressed cultural heritage needs to be promoted as it is crucial to South Africa’s history, identity, and social cohesion. However, other heritages that are also important are falling by the wayside with the result that the country’s diversity as the ‘rainbow nation’ is being eroded, and heritage tourism opportunities, which could prompt Local Economic Development (LED), are missed. A more critical engagement with the colonial heritage by including African perspectives, critiques, interactions, and roles within the narrative is needed.
A
bstract
We exploit the recently described property of cluster adjacency for scattering amplitudes in planar
N
=
4
super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon ...amplitude. We use a manifestly cluster adjacent ansatz and describe how the parameters of this ansatz are determined using simple physical consistency requirements. We then specialise our answer for the amplitude to the multi-Regge limit, finding agreement with previously available results up to the next-to-leading logarithm, and obtaining new predictions up to (next-to)
3
-leading-logarithmic accuracy.
Cluster adjacency beyond MHV Drummond, James; Foster, Jack; Gürdoğan, Ömer
The journal of high energy physics,
03/2019, Letnik:
2019, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A
bstract
We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls ...the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the
Q
¯
-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.
A
bstract
We present the three-loop remainder function, which describes the scattering of six gluons in the maximally-helicity-violating configuration in planar
= 4 super-Yang-Mills theory, as a ...function of the three dual conformal cross ratios. The result can be expressed in terms of multiple Goncharov polylogarithms. We also employ a more restricted class of
hexagon functions
which have the correct branch cuts and certain other restrictions on their symbols. We classify all the hexagon functions through transcendental weight five, using the coproduct for their Hopf algebra iteratively, which amounts to a set of first-order differential equations. The three-loop remainder function is a particular weight-six hexagon function, whose symbol was determined previously. The differential equations can be integrated numerically for generic values of the cross ratios, or analytically in certain kinematic limits, including the near-collinear and multi-Regge limits. These limits allow us to impose constraints from the operator product expansion and multi-Regge factorization directly at the function level, and thereby to fix uniquely a set of Riemann
ζ
valued constants that could not be fixed at the level of the symbol. The near-collinear limits agree precisely with recent predictions by Basso, Sever and Vieira based on integrability. The multi-Regge limits agree with the factorization formula of Fadin and Lipatov, and determine three constants entering the impact factor at this order. We plot the three-loop remainder function for various slices of the Euclidean region of positive cross ratios, and compare it to the two-loop one. For large ranges of the cross ratios, the ratio of the three-loop to the two-loop remainder function is relatively constant, and close to −7.
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Abstract We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar ... ...= 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N^sup 3^LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.
A
bstract
We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar
N
= 4 super Yang-Mills theory. We argue that connections ...between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.
A
bstract
We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr(
k, n
). A finite cluster algebra ...provides a natural triangulation for the tropical Grassmannian whose volume computes the scattering amplitudes. Using this method one can construct the entire colour-ordered amplitude via mutations starting from a single term.
A
bstract
We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each ...fan associated to the Grassmannian Gr(
k, n
) there is a notion of a generalised
ϕ
3
amplitude and an associated set of scattering equations which further generalise the Gr(
k, n
) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4
, n
) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar
N
= 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.
Following past studies to quantify decadal trends in global carbon monoxide (CO) using satellite observations, we update estimates and find a CO trend in column amounts of about −0.50 % per year ...between 2002 to 2018, which is a deceleration compared to analyses performed on shorter records that found −1 % per year. Aerosols are co-emitted with CO from both fires and anthropogenic sources but with a shorter lifetime than CO. A combined trend analysis of CO and aerosol optical depth (AOD) measurements from space helps to diagnose the drivers of regional differences in the CO trend. We use the long-term records of CO from the Measurements of Pollution in the Troposphere (MOPITT) and AOD from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. Other satellite instruments measuring CO in the thermal infrared, AIRS, TES, IASI, and CrIS, show consistent hemispheric CO variability and corroborate results from the trend analysis performed with MOPITT CO. Trends are examined by hemisphere and in regions for 2002 to 2018, with uncertainties quantified. The CO and AOD records are split into two sub-periods (2002 to 2010 and 2010 to 2018) in order to assess trend changes over the 16 years. We focus on four major population centers: Northeast China, North India, Europe, and Eastern USA, as well as fire-prone regions in both hemispheres. In general, CO declines faster in the first half of the record compared to the second half, while AOD trends show more variability across regions. We find evidence of the atmospheric impact of air quality management policies. The large decline in CO found over Northeast China is initially associated with an improvement in combustion efficiency, with subsequent additional air quality improvements from 2010 onwards. Industrial regions with minimal emission control measures such as North India become more globally relevant as the global CO trend weakens. We also examine the CO trends in monthly percentile values to understand seasonal implications and find that local changes in biomass burning are sufficiently strong to counteract the global downward trend in atmospheric CO, particularly in late summer.
•The global decreasing trend in CO has shown a recent slowdown.•Fire emissions in NH boreal regions counteract decreasing CO in late summer.•AOD helps interpret CO trends and variability.•Trends in four industrial regions show impact from varying air quality controls.
Understanding the fundamental properties of materials is crucial for expanding their potential applications. Chiral nematic cellulose nanocrystal (CNC) gels and aerogels have been explored in various ...areas, yet there are significant knowledge gaps in their assembly, structure and properties. In order to fulfill different practical applications, such as in insulation, the thermal conductivity and mechanical strength of CNC aerogels should be studied. Here, we report the directional thermal and mechanical properties of chiral nematic CNC aerogels that originate from their unique anisotropic structure. Unexpected differences of thermal conductivities between the top (0.036 ± 0.001 W m
−1
K
−1
) and bottom surface (0.042 ± 0.002 W m
−1
K
−1
) of chiral nematic CNC aerogel monoliths prepared in vials have been discovered. A time lapse study of the sol-gel preparation process indicated that disturbances to the chiral nematic aligned CNCs during solvent addition are the primary reason for the anisotropy. This conclusion was supported by a comparison between the thermal conductivities of the chiral nematic CNC aerogels obtained from containers with different hydrophobicity, together with the analysis of their microstructures by scanning electron microscopy. The chiral nematic CNC aerogels also showed unprecedented high mechanical strengths
via
compression tests. The Young's moduli of the samples were determined to be 43.0 ± 2.0 MPa and 8.8 ± 0.3 MPa in the directions parallel and perpendicular to the CNC chiral nematic alignment, respectively. These impressive and directional mechanical properties arise from the highly ordered and anisotropic chiral nematic structure within the aerogels, and were further probed by X-ray microtomography (XMT) analysis under different strains ranging from 0 to 15% applied in directions parallel and perpendicular to the CNC lamellae. The results of the mechanical and thermal studies, combined with structural analysis, have helped to understand the nature of chiral nematic aerogels and will expand their potential applications.
Cellulose nanocrystal (CNC) aerogels with chiral nematic organization show surface-dependent thermal conductivities and directional mechanical properties.
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