11,926 research outputs found
Rational model of the configuration space of two points in a simply connected closed manifold
Let be a simply connected closed manifold of dimension . We study the
rational homotopy type of the configuration space of 2 points in , .
When is even dimensional, we prove that the rational homotopy type of
depends only on the rational homotopy type of . When the dimension
of is odd, for every , we construct a
commutative differential graded algebra . We prove that for some , encodes completely the rational homotopy type
of . For some class of manifolds, we show that we can take .Comment: 15 page
Simple and Efficient Fully-Functional Succinct Trees
The fully-functional succinct tree representation of Navarro and Sadakane
(ACM Transactions on Algorithms, 2014) supports a large number of operations in
constant time using bits. However, the full idea is hard to
implement. Only a simplified version with operation time has been
implemented and shown to be practical and competitive. We describe a new
variant of the original idea that is much simpler to implement and has
worst-case time for the operations. An implementation based on
this version is experimentally shown to be superior to existing
implementations
Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
We study BPS line defects in N=2 supersymmetric four-dimensional field
theories. We focus on theories of "quiver type," those for which the BPS
particle spectrum can be computed using quiver quantum mechanics. For a wide
class of models, the renormalization group flow between defects defined in the
ultraviolet and in the infrared is bijective. Using this fact, we propose a way
to compute the BPS Hilbert space of a defect defined in the ultraviolet, using
only infrared data. In some cases our proposal reduces to studying
representations of a "framed" quiver, with one extra node representing the
defect. In general, though, it is different. As applications, we derive a
formula for the discontinuities in the defect renormalization group map under
variations of moduli, and show that the operator product algebra of line
defects contains distinguished subalgebras with universal multiplication rules.
We illustrate our results in several explicit examples.Comment: 76 pages, 10 figures; v2: minor revisions, correction to Coulomb
branch calculation for defects in SU(2) SY
Vacuum chamber is remotely sealed by eutectic metal
Vacuum chamber is remotely sealed by a design using metal seal blades which are inserted into a molten eutectic metal by pressurizing an expansion bellows. The process increases allowable manipulations by improving working space and safety factors
Towards a theory of automated elliptic mesh generation
The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented
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