4,493 research outputs found
AdS boundary conditions and the Topologically Massive Gravity/CFT correspondence
The AdS/CFT correspondence provides a new perspective on recurrent questions
in General Relativity such as the allowed boundary conditions at infinity and
the definition of gravitational conserved charges. Here we review the main
insights obtained in this direction over the last decade and apply the new
techniques to Topologically Massive Gravity. We show that this theory is dual
to a non-unitary CFT for any value of its parameter mu and becomes a
Logarithmic CFT at mu = 1.Comment: 10 pages, proceedings for XXV Max Born Symposium, talks given at
Johns Hopkins workshop and Holographic Cosmology workshop at Perimeter
Institute; v2: added reference
MURPHY -- A scalable multiresolution framework for scientific computing on 3D block-structured collocated grids
We present the derivation, implementation, and analysis of a multiresolution
adaptive grid framework for numerical simulations on octree-based 3D
block-structured collocated grids with distributed computational architectures.
Our approach provides a consistent handling of non-lifted and lifted
interpolating wavelets of arbitrary order demonstrated using second, fourth,
and sixth order wavelets, combined with standard finite-difference based
discretization operators. We first validate that the wavelet family used
provides strict and explicit error control when coarsening the grid, and show
that lifting wavelets increase the grid compression rate while conserving
discrete moments across levels. Further, we demonstrate that high-order PDE
discretization schemes combined with sufficiently high order wavelets retain
the expected convergence order even at resolution jumps. We then simulate the
advection of a scalar to analyze convergence for the temporal evolution of a
PDE. The results shows that our wavelet-based refinement criterion is
successful at controlling the overall error while the coarsening criterion is
effective at retaining the relevant information on a compressed grid. Our
software exploits a block-structured grid data structure for efficient
multi-level operations, combined with a parallelization strategy that relies on
a one-sided MPI-RMA communication approach with active PSCW synchronization.
Using performance tests up to 16,384 cores, we demonstrate that this leads to a
highly scalable performance. The associated code is available under a BSD-3
license at https://github.com/vanreeslab/murphy.Comment: submitted to SIAM Journal of Scientific Computing (SISC) on Dec 1
Lattice Green's Functions for High Order Finite Difference Stencils
Lattice Green's Functions (LGFs) are fundamental solutions to discretized
linear operators, and as such they are a useful tool for solving discretized
elliptic PDEs on domains that are unbounded in one or more directions. The
majority of existing numerical solvers that make use of LGFs rely on a
second-order discretization and operate on domains with free-space boundary
conditions in all directions. Under these conditions, fast expansion methods
are available that enable precomputation of 2D or 3D LGFs in linear time,
avoiding the need for brute-force multi-dimensional quadrature of numerically
unstable integrals. Here we focus on higher-order discretizations of the
Laplace operator on domains with more general boundary conditions, by (1)
providing an algorithm for fast and accurate evaluation of the LGFs associated
with high-order dimension-split centered finite differences on unbounded
domains, and (2) deriving closed-form expressions for the LGFs associated with
both dimension-split and Mehrstellen discretizations on domains with one
unbounded dimension. Through numerical experiments we demonstrate that these
techniques provide LGF evaluations with near machine-precision accuracy, and
that the resulting LGFs allow for numerically consistent solutions to
high-order discretizations of the Poisson's equation on fully or partially
unbounded 3D domains
Cosmological Origin of the Stellar Velocity Dispersions in Massive Early-Type Galaxies
We show that the observed upper bound on the line-of-sight velocity
dispersion of the stars in an early-type galaxy, sigma<400km/s, may have a
simple dynamical origin within the LCDM cosmological model, under two main
hypotheses. The first is that most of the stars now in the luminous parts of a
giant elliptical formed at redshift z>6. Subsequently, the stars behaved
dynamically just as an additional component of the dark matter. The second
hypothesis is that the mass distribution characteristic of a newly formed dark
matter halo forgets such details of the initial conditions as the stellar
"collisionless matter" that was added to the dense parts of earlier generations
of halos. We also assume that the stellar velocity dispersion does not evolve
much at z<6, because a massive host halo grows mainly by the addition of
material at large radii well away from the stellar core of the galaxy. These
assumptions lead to a predicted number density of ellipticals as a function of
stellar velocity dispersion that is in promising agreement with the Sloan
Digital Sky Survey data.Comment: ApJ, in press (2003); matches published versio
Topological regluing of rational functions
Regluing is a topological operation that helps to construct topological
models for rational functions on the boundaries of certain hyperbolic
components. It also has a holomorphic interpretation, with the flavor of
infinite dimensional Thurston--Teichm\"uller theory. We will discuss a
topological theory of regluing, and trace a direction in which a holomorphic
theory can develop.Comment: 38 page
C-start: optimal start of larval fish
We investigate the C-start escape response of larval fish by combining flow simulations using remeshed vortex methods with an evolutionary optimization. We test the hypothesis of the optimality of C-start of larval fish by simulations of larval-shaped, two- and three-dimensional self-propelled swimmers. We optimize for the distance travelled by the swimmer during its initial bout, bounding the shape deformation based on the larval mid-line curvature values observed experimentally. The best motions identified within these bounds are in good agreement with in vivo experiments and show that C-starts do indeed maximize escape distances. Furthermore we found that motions with curvatures beyond the ones experimentally observed for larval fish may result in even larger escape distances. We analyse the flow field and find that the effectiveness of the C-start escape relies on the ability of pronounced C-bent body configurations to trap and accelerate large volumes of fluid, which in turn correlates with large accelerations of the swimme
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