An assessment of road-verge grass as a feedstock for farm-fed anaerobic digestion plants

Cuttings from road-verge grass could provide biomass for energy generation, but currently this potential is not exploited. This research assessed the technical, practical and financial feasibility of using grass harvested from road verges as a feedstock in farm-fed anaerobic digestion (AD) plants. The methane potential (191 mL CH4 gDM−1) and digestion characteristics of verge grass were similar to those of current farm feedstocks; indicating suitability for AD. Ensiling had no significant impact on the biomethane generated. Testing co-digestions of verge grass with current farm feedstocks showed enhanced methane yields, suggesting that verge grass could be a valuable addition to AD feedstock mixes. In a case study of the UK county of Lincolnshire, potential volumes and locations of verge grass biomass were estimated, with capacities and locations of existing AD plants, to assess the potential to supply practical grass volumes. Grass harvesting costs were modelled and compared with other feedstock costs. Finally, the attitudes of AD operators to using verge grass were investigated to understand whether a market for verge grass exists. In a small survey all operators were willing to use it as a feedstock and most were prepared to pay over the estimated harvesting cost. If verge grass was legally recognised as a waste product it could be attractive to AD operators especially where financial incentives to use waste feedstocks are in place. In rural areas, verge grass could be harvested and co-digested by existing farm-fed AD plants, potentially reducing the cost of road verge maintenance and increasing biodiversity

Mellin Amplitudes for Dual Conformal Integrals

Motivated by recent work on the utility of Mellin space for representing conformal correlators in $AdS$/CFT, we study its suitability for representing dual conformal integrals of the type which appear in perturbative scattering amplitudes in super-Yang-Mills theory. We discuss Feynman-like rules for writing Mellin amplitudes for a large class of integrals in any dimension, and find explicit representations for several familiar toy integrals. However we show that the power of Mellin space is that it provides simple representations even for fully massive integrals, which except for the single case of the 4-mass box have not yet been computed by any available technology. Mellin space is also useful for exhibiting differential relations between various multi-loop integrals, and we show that certain higher-loop integrals may be written as integral operators acting on the fully massive scalar $n$-gon in $n$ dimensions, whose Mellin amplitude is exactly 1. Our chief example is a very simple formula expressing the 6-mass double box as a single integral of the 6-mass scalar hexagon in 6 dimensions.Comment: 29+7 page

New differential equations for on-shell loop integrals

We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N=4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N=4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.Comment: 39 pages, 8 figures; v2: typos corrected, definition of harmonic polylogarithms adde

Collinear and Soft Limits of Multi-Loop Integrands in N=4 Yang-Mills

It has been argued in arXiv:1112.6432 that the planar four-point integrand in N=4 super Yang-Mills theory is uniquely determined by dual conformal invariance together with the absence of a double pole in the integrand of the logarithm in the limit as a loop integration variable becomes collinear with an external momentum. In this paper we reformulate this condition in a simple way in terms of the amplitude itself, rather than its logarithm, and verify that it holds for two- and three-loop MHV integrands for n>4. We investigate the extent to which this collinear constraint and a constraint on the soft behavior of integrands can be used to determine integrands. We find an interesting complementarity whereby the soft constraint becomes stronger while the collinear constraint becomes weaker at larger n. For certain reasonable choices of basis at two and three loops the two constraints in unison appear strong enough to determine MHV integrands uniquely for all n.Comment: 27 pages, 14 figures; v2: very minor change

Theoretical Study of High Frequency Ultrasonic Wave Attenuation in Polycrystalline Materials

Three different regimes for scattering of ultrasonic waves in poly-crystalline materials exist, depending on the ratio of the mean grain size to the wavelength: (i) the low frequency (Rayleigh) region with scattering-induced attenuation proportional to the fourth power of the frequency and to the cube of the mean grain diameter, (ii) the medium frequency (stochastic) region with scattering proportional to the square of the frequency and to the mean grain diameter, and (iii) the high-frequency (geometric) region with scattering independent of frequency

Some analytic results for two-loop scattering amplitudes

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum) twistors and focus on a restricted kinematics in which the answer depends only on two independent cross-ratios. The theory of motives can be used to vastly simplify the results, which can be expressed as simple combinations of classical polylogarithms.Comment: 18 page

Wilson Loops @ 3-Loops in Special Kinematics

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit. We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof). We also describe the uplift of this result to 10 points.Comment: 26 pages. Typos correcte

The low pKa value of iron-binding ligand Tyr188 and its implication in iron release and anion binding of human transferrin

2D NMR-pH titrations were used to determine pKa values for four conserved tyrosine residues, Tyr45, Tyr85, Tyr96 and Tyr188, in human transferrin. The low pKa of Tyr188 is due to the fact that the iron-binding ligand interacts with Lys206 in open-form and with Lys296 in the closed-form of the protein. Our current results also confirm the anion binding of sulfate and arsenate to transferrin and further suggest that Tyr188 is the actual binding site for the anions in solution. These data indicate that Tyr188 is a critical residue not only for iron binding but also for chelator binding and iron release in transferrin. © 2004 Published by Elsevier B.V. on behalf of the Federation of European Biochemical Societies.postprin

Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills

Scattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $\mathcal{N}=4$ Yang-Mills, we consider a generalization of scattering amplitudes which depends on twice as many Grassmann variables. We conjecture that it restores at least half of the superconformal symmetries, and all of the dual superconformal symmetries. The object arises naturally as the dual of a null polygonal Wilson loop in an $(x,\theta,\bar\theta)$ superspace. We support the conjecture by using it to obtain the total differential of all $n$-point two-loop MHV amplitudes, and showing that the result passes consistency checks. Potential all-loop constraints are also discussed.Comment: 25 pages, 2 figures and 1 noteboo

Yangian symmetry of light-like Wilson loops

We show that a certain class of light-like Wilson loops exhibits a Yangian symmetry at one loop, or equivalently, in an Abelian theory. The Wilson loops we discuss are equivalent to one-loop MHV amplitudes in N=4 super Yang-Mills theory in a certain kinematical regime. The fact that we find a Yangian symmetry constraining their functional form can be thought of as the effect of the original conformal symmetry associated to the scattering amplitudes in the N=4 theory.Comment: 15 pages, 5 figure