4,788 research outputs found
Quiescent cosmological singularities
The most detailed existing proposal for the structure of spacetime
singularities originates in the work of Belinskii, Khalatnikov and Lifshitz. We
show rigorously the correctness of this proposal in the case of analytic
solutions of the Einstein equations coupled to a scalar field or stiff fluid.
More specifically, we prove the existence of a family of spacetimes depending
on the same number of free functions as the general solution which have the
asymptotics suggested by the Belinskii-Khalatnikov-Lifshitz proposal near their
singularities. In these spacetimes a neighbourhood of the singularity can be
covered by a Gaussian coordinate system in which the singularity is
simultaneous and the evolution at different spatial points decouples.Comment: 38 page
Hamiltonian Relaxation
Due to the complexity of the required numerical codes, many of the new
formulations for the evolution of the gravitational fields in numerical
relativity are not tested on binary evolutions. We introduce in this paper a
new testing ground for numerical methods based on the simulation of binary
neutron stars. This numerical setup is used to develop a new technique, the
Hamiltonian relaxation (HR), that is benchmarked against the currently most
stable simulations based on the BSSN method. We show that, while the length of
the HR run is somewhat shorter than the equivalent BSSN simulation, the HR
technique improves the overall quality of the simulation, not only regarding
the satisfaction of the Hamiltonian constraint, but also the behavior of the
total angular momentum of the binary. The latest quantity agrees well with
post-Newtonian estimations for point-mass binaries in circular orbits.Comment: More detailed description of the numerical implementation added and
some typos corrected. Version accepted for publication in Class. and Quantum
Gravit
F-theory and AdS_3/CFT_2
We construct supersymmetric AdS_3 solutions in F-theory, that is Type IIB
supergravity with varying axio-dilaton, which are holographically dual to 2d
N=(0,4) superconformal field theories with small superconformal algebra. In
F-theory these arise from D3-branes wrapped on curves in the base of an
elliptically fibered Calabi-Yau threefold Y_3 and correspond to strings in the
6d N=(1,0) theory obtained from F-theory on Y_3. The non-trivial fibration over
the wrapped curves implies a varying coupling of the N=4 Super-Yang-Mills
theory on the D3-branes. We compute the holographic central charges and show
that these agree with the field theory and with the anomalies of self-dual
strings in 6d. We complement our analysis with a discussion of the dual
M-theory solutions and a comparison of the central charges.Comment: 83 pages, v2: references added, typos correcte
Feynman Integrals and Intersection Theory
We introduce the tools of intersection theory to the study of Feynman
integrals, which allows for a new way of projecting integrals onto a basis. In
order to illustrate this technique, we consider the Baikov representation of
maximal cuts in arbitrary space-time dimension. We introduce a minimal basis of
differential forms with logarithmic singularities on the boundaries of the
corresponding integration cycles. We give an algorithm for computing a basis
decomposition of an arbitrary maximal cut using so-called intersection numbers
and describe two alternative ways of computing them. Furthermore, we show how
to obtain Pfaffian systems of differential equations for the basis integrals
using the same technique. All the steps are illustrated on the example of a
two-loop non-planar triangle diagram with a massive loop.Comment: 13 pages, published versio
A numerical method for computing unsteady 2-D boundary layer flows
A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results
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