An Overview of Maximal Unitarity at Two Loops

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.Comment: 7 pages, presented at Loops & Legs 2012, Wernigerode, German

Performance of interFoam on the simulation of progressive waves

The performance of interFoam (a widely-used solver within the popular open source CFD package OpenFOAM) in simulating the propagation of a nonlinear (stream function solution) regular wave is investigated in this work, with the aim of systematically documenting its accuracy. It is demonstrated that over time there is a tendency for surface elevations to increase, wiggles to appear in the free surface, and crest velocities to become (severely) overestimated. It is shown that increasing the temporal and spatial resolution can mitigate these undesirable effects, but that a relatively small Courant number is required. It is further demonstrated that the choice of discretization schemes and solver settings (often treated as a "black box" by users) can have a major impact on the results. This impact is documented, and it is shown that obtaining a "diffusive balance" is crucial to accurately propagate a surface wave over long distances without requiring exceedingly high temporal and spatial resolutions. Finally, the new code isoAdvector is compared to interFoam, which is demonstrated to produce comparably accurate results, while maintaining a sharper surface. It is hoped that the systematic documentation of the performance of the interFoam solver will enable its more accurate and optimal use, as well as increase awareness of potential shortcomings, by CFD researchers interested in the general CFD simulation of free surface waves.Comment: 18 pages and 23 figure

Two-Loop Maximal Unitarity with External Masses

We extend the maximal unitarity method at two loops to double-box basis integrals with up to three external massive legs. We use consistency equations based on the requirement that integrals of total derivatives vanish. We obtain unique formulae for the coefficients of the master double-box integrals. These formulae can be used either analytically or numerically.Comment: 41 pages, 7 figures; small corrections, final journal versio

Maximal Unitarity for the Four-Mass Double Box

We extend the maximal-unitarity formalism at two loops to double-box integrals with four massive external legs. These are relevant for higher-point processes, as well as for heavy vector rescattering, VV -> VV. In this formalism, the two-loop amplitude is expanded over a basis of integrals. We obtain formulas for the coefficients of the double-box integrals, expressing them as products of tree-level amplitudes integrated over specific complex multidimensional contours. The contours are subject to the consistency condition that integrals over them annihilate any integrand whose integral over real Minkowski space vanishes. These include integrals over parity-odd integrands and total derivatives arising from integration-by-parts (IBP) identities. We find that, unlike the zero- through three-mass cases, the IBP identities impose no constraints on the contours in the four-mass case. We also discuss the algebraic varieties connected with various double-box integrals, and show how discrete symmetries of these varieties largely determine the constraints.Comment: 25 pages, 3 figures; final journal versio

COLLECTIONS AND MARKETS: PITFALLS AND POSSIBILITIES

Many archives have special collections that experience or could experience consistent use by publishers and broadcasters to illustrate a particular historical period or subject field. Archives and archives professionals, however, often find themselves uncertain about how to deal with what they see as “commercial” interests. How does one protect the integrity of a collection and even the principle of open access against such interests; when are such interests valid and when are they illegitimate? What is the role of publishers and broadcasters in society and where does this overlap with the mandate of archives to preserve, research, educate and inform? And where do the roles diverge? What is the difference between editorial and commercial publishing? This paper seeks to explore such questions, moving toward the formulation of clear policies and strategies for interacting with editorial markets. Insight will be provided from a decade of working on the interface between public archives and publishing and broadcast markets. The paper seeks to facilitate understanding and give insights that empower wise choices that protect the long-term integrity of archival collections. Building on the concept of appropriate access, the paper will argue that there is a significant difference between commercial markets for archival content, and editorial markets. Commercial markets in the business of promoting products or services are almost never appropriate channels for the publishing of archival content. Editorial markets, on the other hand, when operating with the mandate that society has given them, should be seen as an extension of the mandate that archives have to educate and inform. In this regard they should be seen as strategic partners.This paper will also argue for layers of appropriate access and rights to use a collection, indicating appropriate models for interacting with various users and granting usage rights

The Tannakian Formalism and the Langlands Conjectures

Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let G be an abstract group. In this note we show that every homomorphism from the Grothendieck semiring of H to that of G which maps irreducible representations to irreducibles, comes from a group homomorphism from G to H. We also connect this result with the Langlands conjectures.Comment: 15 page

Cross-Order Integral Relations from Maximal Cuts

We study the ABDK relation using maximal cuts of one- and two-loop integrals with up to five external legs. We show how to find a special combination of integrals that allows the relation to exist, and how to reconstruct the terms with one-loop integrals squared. The reconstruction relies on the observation that integrals across different loop orders can have support on the same generalized unitarity cuts and can share global poles. We discuss the appearance of nonhomologous integration contours in multivariate residues. Their origin can be understood in simple terms, and their existence enables us to distinguish contributions from different integrals. Our analysis suggests that maximal and near-maximal cuts can be used to infer the existence of integral identities more generally.Comment: 58 pages, 19 figures; v2 references adde