12,131 research outputs found
Star Integrals, Convolutions and Simplices
We explore single and multi-loop conformal integrals, such as the ones
appearing in dual conformal theories in flat space. Using Mellin amplitudes, a
large class of higher loop integrals can be written as simple
integro-differential operators on star integrals: one-loop -gon integrals in
dimensions. These are known to be given by volumes of hyperbolic simplices.
We explicitly compute the five-dimensional pentagon integral in full generality
using Schl\"afli's formula. Then, as a first step to understanding higher
loops, we use spline technology to construct explicitly the hexagon and
octagon integrals in two-dimensional kinematics. The fully massive hexagon
and octagon integrals are then related to the double box and triple box
integrals respectively. We comment on the classes of functions needed to
express these integrals in general kinematics, involving elliptic functions and
beyond.Comment: 23 page
A Framework for Modeling Subgrid Effects for Two-Phase Flows in Porous Media
In this paper, we study upscaling for two-phase flows in strongly heterogeneous porous media. Upscaling a hyperbolic convection equation is known to be very difficult due to the presence of nonlocal memory effects. Even for a linear hyperbolic equation with a shear velocity field, the upscaled equation involves a nonlocal history dependent diffusion term, which is not amenable to computation. By performing a systematic multiscale analysis, we derive coupled equations for the average and the fluctuations for the two-phase flow. The homogenized equations for the coupled system are obtained by projecting the fluctuations onto a suitable subspace. This projection corresponds exactly to averaging along streamlines of the flow. Convergence of the multiscale analysis is verified numerically. Moreover, we show how to apply this multiscale analysis to upscale two-phase flows in practical applications
Integrable lattice spin models from supersymmetric dualities
Recently, there has been observed an interesting correspondence between
supersymmetric quiver gauge theories with four supercharges and integrable
lattice models of statistical mechanics such that the two-dimensional spin
lattice is the quiver diagram, the partition function of the lattice model is
the partition function of the gauge theory and the Yang-Baxter equation
expresses the identity of partition functions for dual pairs. This
correspondence is a powerful tool which enables us to generate new integrable
models. The aim of the present paper is to give a short account on a progress
in integrable lattice models which has been made due to the relationship with
supersymmetric gauge theories.Comment: 35 pages, preliminary versio
Determinant and Weyl anomaly of Dirac operator: a holographic derivation
We present a holographic formula relating functional determinants: the
fermion determinant in the one-loop effective action of bulk spinors in an
asymptotically locally AdS background, and the determinant of the two-point
function of the dual operator at the conformal boundary. The formula originates
from AdS/CFT heuristics that map a quantum contribution in the bulk partition
function to a subleading large-N contribution in the boundary partition
function. We use this holographic picture to address questions in spectral
theory and conformal geometry. As an instance, we compute the type-A Weyl
anomaly and the determinant of the iterated Dirac operator on round spheres,
express the latter in terms of Barnes' multiple gamma function and gain insight
into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte
An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak
The penalization method is used to take account of obstacles, such as the
limiter, in a tokamak. Because of the magnetic confinement of the plasma in a
tokamak, the transport occurs essentially in the direction parallel to the
magnetic field lines. We study a 1D nonlinear hyperbolic system as a simplified
model of the plasma transport in the area close to the wall. A penalization
which cuts the flux term of the momentum is studied. We show numerically that
this penalization creates a Dirac measure at the plasma-limiter interface which
prevents us from defining the transport term in the usual distribution sense.
Hence, a new penalty method is proposed for this hyperbolic system. For this
penalty method, an asymptotic expansion and numerical tests give an optimal
rate of convergence without spurious boundary layer. Another two-fields
penalization has also been implemented and the numerical convergence analysis
when the penalization parameter tends to reveals the presence of a boundary
layer
Gravitational waves from compact binaries in post-Newtonian accurate hyperbolic orbits
We derive from first principles third post-Newtonian (3PN) accurate
Keplerian-type parametric solution to describe PN-accurate dynamics of
non-spinning compact binaries in hyperbolic orbits. Orbital elements and
functions of the parametric solution are obtained in terms of the conserved
orbital energy and angular momentum in both Arnowitt-Deser-Misner type and
modified harmonic coordinates. Elegant checks are provided that include a
modified analytic continuation prescription to obtain our independent
hyperbolic parametric solution from its eccentric version. A prescription to
model gravitational wave polarization states for hyperbolic compact binaries
experiencing 3.5PN-accurate orbital motion is presented that employs our
3PN-accurate parametric solution
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