3,236 research outputs found
Delaunay triangulation and computational fluid dynamics meshes
In aerospace computational fluid dynamics (CFD) calculations, the Delaunay triangulation of suitable quadrilateral meshes can lead to unsuitable triangulated meshes. Here, we present case studies which illustrate the limitations of using structured grid generation methods which produce points in a curvilinear coordinate system for subsequent triangulations for CFD applications. We discuss conditions under which meshes of quadrilateral elements may not produce a Delaunay triangulation suitable for CFD calculations, particularly with regard to high aspect ratio, skewed quadrilateral elements
A non-perturbative Lorentzian path integral for gravity
A well-defined regularized path integral for Lorentzian quantum gravity in
three and four dimensions is constructed, given in terms of a sum over
dynamically triangulated causal space-times. Each Lorentzian geometry and its
associated action have a unique Wick rotation to the Euclidean sector. All
space-time histories possess a distinguished notion of a discrete proper time.
For finite lattice volume, the associated transfer matrix is self-adjoint and
bounded. The reflection positivity of the model ensures the existence of a
well-defined Hamiltonian. The degenerate geometric phases found previously in
dynamically triangulated Euclidean gravity are not present. The phase structure
of the new Lorentzian quantum gravity model can be readily investigated by both
analytic and numerical methods.Comment: 11 pages, LaTeX, improved discussion of reflection positivity,
conclusions unchanged, references update
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and
geometric-based approaches to sampling are investigated. Some aspects of coding
and communication through a Gaussian channel are considered. In particular, a
constructive method to determine the quantizing dimension in Zador's theorem is
provided. A geometric version of Shannon's Second Theorem is introduced.
Applications to Pulse Code Modulation and Vector Quantization of Images are
addressed.Comment: 19 pages, submitted for publicatio
Quantum Gravity via Causal Dynamical Triangulations
"Causal Dynamical Triangulations" (CDT) represent a lattice regularization of
the sum over spacetime histories, providing us with a non-perturbative
formulation of quantum gravity. The ultraviolet fixed points of the lattice
theory can be used to define a continuum quantum field theory, potentially
making contact with quantum gravity defined via asymptotic safety. We describe
the formalism of CDT, its phase diagram, and the quantum geometries emerging
from it. We also argue that the formalism should be able to describe a more
general class of quantum-gravitational models of Horava-Lifshitz type.Comment: To appear in "Handbook of Spacetime", Springer Verlag. 31 page
Unstructured and adaptive mesh generation for high Reynolds number viscous flows
A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes
Conforming restricted Delaunay mesh generation for piecewise smooth complexes
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise
smooth domains is described. Built using a restricted Delaunay framework, this
new algorithm combines a number of novel features, including: (i) an
unweighted, conforming restricted Delaunay representation for domains specified
as a (non-manifold) collection of piecewise smooth surface patches and curve
segments, (ii) a protection strategy for domains containing curve segments that
subtend sharply acute angles, and (iii) a new class of off-centre refinement
rules designed to achieve high-quality point-placement along embedded curve
features. Experimental comparisons show that the new Frontal-Delaunay algorithm
outperforms a classical (statically weighted) restricted Delaunay-refinement
technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl
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