Global Poles of the Two-Loop Six-Point N=4 SYM integrand

Recently, a recursion relation has been developed, generating the four-dimensional integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory for any number of loops and legs. In this paper, I provide a comparison of the prediction for the two-loop six-point maximally helicity-violating (MHV) integrand against the result obtained by use of the leading singularity method. The comparison is performed numerically for a large number of randomly selected momenta and in all cases finds agreement between the two results to high numerical accuracy.Comment: 32+34 pages, 16 figures, 1 notebook; minor typos corrected, ref. added; version accepted by Phys. Rev.

Graphical method for predicting life of a rocket thrust chamber with half-hard zirconium-copper liner and electroformed nickel closeout

A method for estimating the life of a regeneratively cooled rocket thrust chamber was developed and is based on the hot-gas wall temperature and the temperature difference between the hot-gas wall and the outside surface of the closeout. This method permits a quick estimate of the life of a thrust chamber when design changes or test-cycle variations are considered. Strain range and life are presented graphically as functions of these temperature parameters for a typical high-performance rocket thrust chamber with a half-hard zirconium-copper liner and an electroformed nickel closeout

Integration-by-parts reductions from unitarity cuts and algebraic geometry

We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.Comment: 5 pages, 1 figure; a Mathematica package implementing the algorithm is attached as an ancillary file; v3: minor change

MultivariateResidues - a Mathematica package for computing multivariate residues

We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of scattering amplitude computations. Examples include applications to the extraction of master integral coefficients from maximal unitarity cuts, the construction of canonical bases of loop integrals and the construction of tree amplitudes from scattering equations.Comment: 7 pages, 2 figures, contribution to the proceedings of the 13th International Symposium on Radiative Corrections (RADCOR 2017

Experimental combustor study program

Advanced combustor concepts are evaluated as a means of accommodating possible future broad specification fuels. The three advanced double annular combustor concepts consisted of (1) a concept employing high pressure drop fuel nozzles for improved atomization, (2) a concept with premixing tubes in the main stage, and (3) a concept with the pilot stage on the inside and the main stage on the sideout, which is the reverse of the other two concepts. All of the advanced concepts show promise for reduced sensitivity to fuel hydrogen content. Some hardware problems were encountered, but these problems could be quickly resolved if refinement tests were conducted. The design with the premixing main stage was selected for a parametric test because of its low NOx emissions level, carbon free dome, and very low dome temperatures which were essentially independent of fuel type. The other advanced designs also had low done temperatures. The premixing dome design liner temperatures exhibited less sensitivity to fuel type than did the base-line combustor, although more sensitivity than observed for concept 1. The inner liner hot spot and the observed smoke results for the premixing design suggest that the fuel-air mixture was not as uniform as desired

Effect of low-stiffness closeout overwrap on rocket thrust-chamber life

Three rocket thrust chambers with copper liners and a thrust level of 20.9 kN were cyclically test fired to failure. Two of the liners were made from oxygen free, high conductivity (OFHC) copper and from annealed Amzirc. The milled coolant channels were closed out with a thin copper closeout over which a fiberglass composite was wrapped to provide hoop strength only. Experimental data are presented, along with the results of a preliminary analysis that was performed before fabrication to evaluate the life extending potential of a thin copper closeout with a fiberglass overwrap

Position-space cuts for Wilson line correlators

We further develop the formalism for taking position-space cuts of eikonal diagrams introduced in [Phys.Rev.Lett. 114 (2015), no. 18 181602, arXiv:1410.5681]. These cuts are applied directly to the position-space representation of any such diagram and compute its discontinuity to the leading order in the dimensional regulator. We provide algorithms for computing the position-space cuts and apply them to several two- and three-loop eikonal diagrams, finding agreement with results previously obtained in the literature. We discuss a non-trivial interplay between the cutting prescription and non-Abelian exponentiation. We furthermore discuss the relation of the imaginary part of the cusp anomalous dimension to the static interquark potential.Comment: 39+18 pages, 16 figures; elaborated the discussion of the comparison of numerical and analytic results for the three-gluon vertex diagram in the caption of fig. 16; version to be published in JHE

Imaginary parts and discontinuities of Wilson line correlators

We introduce a notion of position-space cuts of eikonal diagrams, the set of diagrams appearing in the perturbative expansion of the correlator of a set of straight semi-infinite Wilson lines. The cuts are applied directly to the position-space representation of any such diagram and compute its imaginary part to the leading order in the dimensional regulator. Our cutting prescription thus defines a position-space analog of the standard momentum-space Cutkosky rules. Unlike momentum-space cuts which put internal lines on shell, position-space cuts constrain a number of the gauge bosons exchanged between the energetic partons to be lightlike, leading to a vanishing and a non-vanishing imaginary part for space- and timelike kinematics, respectively.Comment: 5 pages, 2 figures; minor changes; version published in PR