Preprints aus dem Institut für Mathematikhttp://edoc.hu-berlin.de/18452/682019-07-22T10:19:04Z2019-07-22T10:19:04ZOperator-Splitting Methods Respecting Eigenvalue Problems For Shallow Shelf Equations With Basal DragCalov, ReinhardGeiser, Jürgenhttp://edoc.hu-berlin.de/18452/34932019-03-19T13:19:29Z2013-09-12T00:00:00ZOperator-Splitting Methods Respecting Eigenvalue Problems For Shallow Shelf Equations With Basal Drag
Calov, Reinhard; Geiser, Jürgen
We discuss different numerical methods for solving the shallow shelf equations with basal drag. The coupled equations are decomposed into operators for membranes stresses, basal shear stress and driving stress. Applying reasonable parameter values, we demonstrate that the operator of the membrane stresses is much stiffer than operator of the basal shear stress. Therefore, we propose a new splitting method, which alternates between the iteration on the membrane-stress operator and the basal-shear operator, with a stronger iteration on the operator of the membrane stress. We show that this splitting improves the computational performance of the numerical method, although the choice of the (standard) method to solve for all operators in one step speeds up the scheme too. (Based on the delicate and coupled equation we propose a new decomposition method to decouple into simpler solvable sub-equations. After a number of approximations we consider the error of the method and proposed a choice of the operators.)
2013-09-12T00:00:00ZReview of AdS/CFT Integrability, Chapter I.2Sieg, Christophhttp://edoc.hu-berlin.de/18452/34922019-03-19T13:25:12Z2011-10-20T00:00:00ZReview of AdS/CFT Integrability, Chapter I.2
Sieg, Christoph
We review the constructions and tests of the dilatation operator and of the spectrum of composite operators in the flavour SU(2) subsector of N=4 SYM in the planar limit by explicit Feynman graph calculations with emphasis on analyses beyond one loop. From four loops on, the dilatation operator determines the spectrum only in the asymptotic regime, i.e. to a loop order which is strictly smaller than the number of elementary fields of the composite operators. We review also the calculations which take a first step beyond this limitation by including the leading wrapping corrections.
2011-10-20T00:00:00ZReview of AdS/CFT IntegrabilityBeisert, NiklasAhn, ChangrimAlday, Luis F.Bajnok, ZoltánDrummond, James M.Freyhult, LisaGromov, NikolayJanik, Romuald A.Kazakov, VladimirKlose, ThomasKorchemsky, Gregory P.Kristjansen, Charlottehttp://edoc.hu-berlin.de/18452/34912019-03-19T13:25:11Z2011-10-20T00:00:00ZReview of AdS/CFT Integrability
Beisert, Niklas; Ahn, Changrim; Alday, Luis F.; Bajnok, Zoltán; Drummond, James M.; Freyhult, Lisa; Gromov, Nikolay; Janik, Romuald A.; Kazakov, Vladimir; Klose, Thomas; Korchemsky, Gregory P.; Kristjansen, Charlotte
This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.
2011-10-20T00:00:00ZTwist operators in N=4 beta-deformed theoryLeeuw, Marius deLukowski, Tomaszhttp://edoc.hu-berlin.de/18452/34902019-03-19T13:25:10Z2011-09-27T00:00:00ZTwist operators in N=4 beta-deformed theory
Leeuw, Marius de; Lukowski, Tomasz
In this paper we derive both the leading order finite size corrections for twist-2 and twist-3 operators and the next-to-leading order finite-size correction for twist-2 operators in beta-deformed SYM theory. The obtained results respect the principle of maximum transcendentality as well as reciprocity. We also find that both wrapping corrections go to zero in the large spin limit. Moreover, for twist-2 operators we studied the pole structure and compared it against leading BFKL predictions.
2011-09-27T00:00:00Z