211 research outputs found
Physical and chemical test results of electrostatic safe flooring materials
This test program was initiated because a need existed at the Kennedy Space Center (KSC) to have this information readily available to the engineer who must make the choice of which electrostatic safe floor to use in a specific application. The information, however, should be of value throughout both the government and private industry in the selection of a floor covering material. Included are the test results of 18 floor covering materials which by test evaluation at KSC are considered electrostatically safe. Tests were done and/or the data compiled in the following areas: electrostatics, flammability, hypergolic compatibility, outgassing, floor type, material thickness, and available colors. Each section contains the test method used to gather the data and the test results
Localized Exotic Smoothness
Gompf's end-sum techniques are used to establish the existence of an infinity
of non-diffeomorphic manifolds, all having the same trivial
topology, but for which the exotic differentiable structure is confined to a
region which is spatially limited. Thus, the smoothness is standard outside of
a region which is topologically (but not smoothly) ,
where is the compact three ball. The exterior of this region is
diffeomorphic to standard . In a
space-time diagram, the confined exoticness sweeps out a world tube which, it
is conjectured, might act as a source for certain non-standard solutions to the
Einstein equations. It is shown that smooth Lorentz signature metrics can be
globally continued from ones given on appropriately defined regions, including
the exterior (standard) region. Similar constructs are provided for the
topology, of the Kruskal form of the Schwarzschild
solution. This leads to conjectures on the existence of Einstein metrics which
are externally identical to standard black hole ones, but none of which can be
globally diffeomorphic to such standard objects. Certain aspects of the Cauchy
problem are also discussed in terms of \models which are
``half-standard'', say for all but for which cannot be globally
smooth.Comment: 8 pages plus 6 figures, available on request, IASSNS-HEP-94/2
Blow-up of generalized complex 4-manifolds
We introduce blow-up and blow-down operations for generalized complex
4-manifolds. Combining these with a surgery analogous to the logarithmic
transform, we then construct generalized complex structures on nCP2 # m
\bar{CP2} for n odd, a family of 4-manifolds which admit neither complex nor
symplectic structures unless n=1. We also extend the notion of a symplectic
elliptic Lefschetz fibration, so that it expresses a generalized complex
4-manifold as a fibration over a two-dimensional manifold with boundary.Comment: 25 pages, 15 figures. This is the final version, which was published
in J. To
Wilson Line Picture of Levin-Wen Partition Functions
Levin and Wen [Phys. Rev. B 71, 045110 (2005)] have recently given a lattice
Hamiltonian description of doubled Chern-Simons theories. We relate the
partition function of these theories to an expectation of Wilson loops that
form a link in 2+1 dimensional spacetime known in the mathematical literature
as Chain-Mail. This geometric construction gives physical interpretation of the
Levin-Wen Hilbert space and Hamiltonian, its topological invariance, exactness
under coarse-graining, and how two opposite chirality sectors of the doubled
theory arise.Comment: Final published version; Appendix adde
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, , possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.Comment: 13 pages, LaTe
An invariant of smooth 4-manifolds
We define a diffeomorphism invariant of smooth 4-manifolds which we can
estimate for many smoothings of R^4 and other smooth 4-manifolds. Using this
invariant we can show that uncountably many smoothings of R^4 support no Stein
structure. (Gompf has constructed uncountably many smoothings of R^4 which do
support Stein structures.) Other applications of this invariant are given.Comment: 19 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol1/paper6.abs.htm
Topology of multiple log transforms of 4-manifolds
Given a 4-manifold X and an imbedding of T^{2} x B^2 into X, we describe an
algorithm X --> X_{p,q} for drawing the handlebody of the 4-manifold obtained
from X by (p,q)-logarithmic transforms along the parallel tori. By using this
algorithm, we obtain a simple handle picture of the Dolgachev surface
E(1)_{p,q}, from that we deduce that the exotic copy E(1)_{p,q} # 5(-CP^2) of
E(1) # 5(-CP^2) differs from the original one by a codimension zero simply
connected Stein submanifold M_{p,q}, which are therefore examples of infinitely
many Stein manifolds that are exotic copies of each other (rel boundaries).
Furthermore, by a similar method we produce infinitely many simply connected
Stein submanifolds Z_{p} of E(1)_{p,2} # 2(-CP^2)$ with the same boundary and
the second Betti number 2, which are (absolutely) exotic copies of each other;
this provides an alternative proof of a recent theorem of the author and Yasui
[AY4]. Also, by using the description of S^2 x S^2 as a union of two cusps
glued along their boundaries, and by using this algorithm, we show that
multiple log transforms along the tori in these cusps do not change smooth
structure of S^2 x S^2.Comment: Updated, with 17 pages 21 figure
Exotic Smoothness and Quantum Gravity
Since the first work on exotic smoothness in physics, it was folklore to
assume a direct influence of exotic smoothness to quantum gravity. Thus, the
negative result of Duston (arXiv:0911.4068) was a surprise. A closer look into
the semi-classical approach uncovered the implicit assumption of a close
connection between geometry and smoothness structure. But both structures,
geometry and smoothness, are independent of each other. In this paper we
calculate the "smoothness structure" part of the path integral in quantum
gravity assuming that the "sum over geometries" is already given. For that
purpose we use the knot surgery of Fintushel and Stern applied to the class
E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces
E(2). Then we assume that every exotic smoothness structure of the K3 surface
can be generated by knot or link surgery a la Fintushel and Stern. The results
are applied to the calculation of expectation values. Here we discuss the two
observables, volume and Wilson loop, for the construction of an exotic
4-manifold using the knot and the Whitehead link . By using Mostow
rigidity, we obtain a topological contribution to the expectation value of the
volume. Furthermore we obtain a justification of area quantization.Comment: 16 pages, 1 Figure, 1 Table subm. Class. Quant. Grav
A cocycle on the group of symplectic diffeomorphisms
We define a cocycle on the group of symplectic diffeomorphisms of a
symplectic manifold and investigate its properties. The main applications are
concerned with symplectic actions of discrete groups. For example, we give an
alternative proof of the Polterovich theorem about the distortion of cyclic
subgroups in finitely generated groups of Hamiltonian diffeomorphisms.Comment: 19 pages, no figures, corrected versio
Exotic Smooth Structures on Small 4-Manifolds
Let M be either CP^2#3CP^2bar or 3CP^2#5CP^2bar. We construct the first
example of a simply-connected symplectic 4-manifold that is homeomorphic but
not diffeomorphic to M.Comment: 11 page
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