260 research outputs found
The Generalized Hartle-Hawking Initial State: Quantum Field Theory on Einstein Conifolds
Recent arguments have indicated that the sum over histories formulation of
quantum amplitudes for gravity should include sums over conifolds, a set of
histories with more general topology than that of manifolds. This paper
addresses the consequences of conifold histories in gravitational functional
integrals that also include scalar fields. This study will be carried out
explicitly for the generalized Hartle-Hawking initial state, that is the
Hartle-Hawking initial state generalized to a sum over conifolds. In the
perturbative limit of the semiclassical approximation to the generalized
Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds
is recovered. In particular, the quantum field theory of a scalar field on de
Sitter spacetime with spatial topology is derived from the generalized
Hartle-Hawking initial state in this approximation. This derivation is carried
out for a scalar field of arbitrary mass and scalar curvature coupling.
Additionally, the generalized Hartle-Hawking boundary condition produces a
state that is not identical to but corresponds to the Bunch-Davies vacuum on
de Sitter spacetime. This result cannot be obtained from the original
Hartle-Hawking state formulated as a sum over manifolds as there is no Einstein
manifold with round boundary.Comment: Revtex 3, 31 pages, 4 epsf figure
Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds
This paper proposes to generalize the histories included in Euclidean
functional integrals from manifolds to a more general set of compact
topological spaces. This new set of spaces, called conifolds, includes
nonmanifold stationary points that arise naturally in a semiclasssical
evaluation of such integrals; additionally, it can be proven that sequences of
approximately Einstein manifolds and sequences of approximately Einstein
conifolds both converge to Einstein conifolds. Consequently, generalized
Euclidean functional integrals based on these conifold histories yield
semiclassical amplitudes for sequences of both manifold and conifold histories
that approach a stationary point of the Einstein action. Therefore sums over
conifold histories provide a useful and self-consistent starting point for
further study of topological effects in quantum gravity. Postscript figures
available via anonymous ftp at black-hole.physics.ubc.ca (137.82.43.40) in file
gen1.ps.Comment: 81pp., plain TeX, To appear in Nucl. Phys.
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Particle-Based Sampling and Meshing of Surfaces in Multimaterial Volumes
Methods that faithfully and robustly capture the geometry of complex material interfaces in labeled volume data are important for generating realistic and accurate visualizations and simulations of real-world objects. The generation of such multimaterial models from measured data poses two unique challenges: first, the surfaces must be well-sampled with regular, efficient tessellations that are consistent across material boundaries; and second, the resulting meshes must respect the nonmanifold geometry of the multimaterial interfaces. This paper proposes a strategy for sampling and meshing multimaterial volumes using dynamic particle systems, including a novel, differentiable representation of the material junctions that allows the particle system to explicitly sample corners, edges, and surfaces of material intersections. The distributions of particles are controlled by fundamental sampling constraints, allowing Delaunay-based meshing algorithms to reliably extract watertight meshes of consistently high-quality.Engineering and Applied Science
Automatic CAD-model Repair: Shell-Closure
Shell-closure is critical to the repair of CAD-models described in the .STL file-format,
the de facto solid freeform fabrication industry-standard. Polyhedral CAD-models that
do not exhibit shell-closure, i.e. have cracks, holes, or gaps, do not constitute valid solids
and frequently cause problems during fabrication. This paper describes a solution for
achieving shell-closure of polyhedral CAD-models. The solution accommodates nonmanifold
conditions, and guarantees orientable shells. There are several topologically
ambiguous situations that might arise during the shell-closure process, and the solution
applies intuitively pleasing heuristics in these cases.Mechanical Engineerin
Reconstruction of phase maps from the configuration of phase singularities in two-dimensional manifolds
Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or
biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily
derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase
map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided
that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting
medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane
and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal
wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for
cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology
The Bing-Borsuk and the Busemann Conjectures
We present two classical conjectures concerning the characterization of
manifolds: the Bing Borsuk Conjecture asserts that every -dimensional
homogeneous ANR is a topological -manifold, whereas the Busemann Conjecture
asserts that every -dimensional -space is a topological -manifold. The
key object in both cases are so-called {\it generalized manifolds}, i.e. ENR
homology manifolds. We look at the history, from the early beginnings to the
present day. We also list several open problems and related conjectures.Comment: We have corrected three small typos on pages 8 and
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