607 research outputs found
Hexagon OPE Resummation and Multi-Regge Kinematics
We analyse the OPE contribution of gluon bound states in the double scaling
limit of the hexagonal Wilson loop in planar N=4 super Yang-Mills theory. We
provide a systematic procedure for perturbatively resumming the contributions
from single-particle bound states of gluons and expressing the result order by
order in terms of two-variable polylogarithms. We also analyse certain
contributions from two-particle gluon bound states and find that, after
analytic continuation to the Mandelstam region and passing to
multi-Regge kinematics (MRK), only the single-particle gluon bound states
contribute. From this double-scaled version of MRK we are able to reconstruct
the full hexagon remainder function in MRK up to five loops by invoking
single-valuedness of the results.Comment: 29 pages, 3 figures, 4 ancillary file
An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds
For an absolutely continuous (integer-valued) r.v. of the Pearson (Ord)
family, we show that, under natural moment conditions, a Stein-type covariance
identity of order holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18
(2005) 237--260]). This identity is closely related to the corresponding
sequence of orthogonal polynomials, obtained by a Rodrigues-type formula, and
provides convenient expressions for the Fourier coefficients of an arbitrary
function. Application of the covariance identity yields some novel expressions
for the corresponding lower variance bounds for a function of the r.v. ,
expressions that seem to be known only in particular cases (for the Normal, see
[Houdr\'{e} and Kagan, J. Theoret. Probab. 8 (1995) 23--30]; see also
[Houdr\'{e} and P\'{e}rez-Abreu, Ann. Probab. 23 (1995) 400--419] for
corresponding results related to the Wiener and Poisson processes). Some
applications are also given.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ282 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A Hybrid Boundary Element Method for Elliptic Problems with Singularities
The singularities that arise in elliptic boundary value problems are treated
locally by a singular function boundary integral method. This method extracts
the leading singular coefficients from a series expansion that describes the
local behavior of the singularity. The method is fitted into the framework of
the widely used boundary element method (BEM), forming a hybrid technique, with
the BEM computing the solution away from the singularity. Results of the hybrid
technique are reported for the Motz problem and compared with the results of
the standalone BEM and Galerkin/finite element method (GFEM). The comparison is
made in terms of the total flux (i.e. the capacitance in the case of
electrostatic problems) on the Dirichlet boundary adjacent to the singularity,
which is essentially the integral of the normal derivative of the solution. The
hybrid method manages to reduce the error in the computed capacitance by a
factor of 10, with respect to the BEM and GFEM
Optimization of Patterned Surfaces for Improved Superhydrophobicity Through Cost-Effective Large-Scale Computations
The growing need for creating surfaces with specific wetting properties, such
as superhyrdophobic behavior, asks for novel methods for their efficient
design. In this work, a fast computational method for the evaluation of
patterned superhyrdophobic surfaces is introduced. The hydrophobicity of a
surface is quantified in energy terms through an objective function. The
increased computational cost led to the parallelization of the method with the
Message Passing Interface (MPI) communication protocol that enables
calculations on distributed memory systems allowing for parametric
investigations at acceptable time frames. The method is demonstrated for a
surface consisting of an array of pillars with inverted conical (frustum)
geometry. The parallel speedup achieved allows for low cost parametric
investigations on the effect of the fine features (curvature and slopes) of the
pillars on the superhydophobicity of the surface and consequently for the
optimization of superhyrdophobic surfaces.Comment: 18 pages, 18 figure
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