7,594 research outputs found
Deformations of Toric Singularities and Fractional Branes
Fractional branes added to a large stack of D3-branes at the singularity of a
Calabi-Yau cone modify the quiver gauge theory breaking conformal invariance
and leading to different kinds of IR behaviors. For toric singularities
admitting complex deformations we propose a simple method that allows to
compute the anomaly free rank distributions in the gauge theory corresponding
to the fractional deformation branes. This algorithm fits Altmann's rule of
decomposition of the toric diagram into a Minkowski sum of polytopes. More
generally we suggest how different IR behaviors triggered by fractional branes
can be classified by looking at suitable weights associated with the external
legs of the (p,q) web. We check the proposal on many examples and match in some
interesting cases the moduli space of the gauge theory with the deformed
geometry.Comment: 40 pages, 23 figures; typos correcte
Programmable Control of Nucleation for Algorithmic Self-Assembly
Algorithmic self-assembly, a generalization of crystal growth processes, has
been proposed as a mechanism for autonomous DNA computation and for bottom-up
fabrication of complex nanostructures. A `program' for growing a desired
structure consists of a set of molecular `tiles' designed to have specific
binding interactions. A key challenge to making algorithmic self-assembly
practical is designing tile set programs that make assembly robust to errors
that occur during initiation and growth. One method for the controlled
initiation of assembly, often seen in biology, is the use of a seed or catalyst
molecule that reduces an otherwise large kinetic barrier to nucleation. Here we
show how to program algorithmic self-assembly similarly, such that seeded
assembly proceeds quickly but there is an arbitrarily large kinetic barrier to
unseeded growth. We demonstrate this technique by introducing a family of tile
sets for which we rigorously prove that, under the right physical conditions,
linearly increasing the size of the tile set exponentially reduces the rate of
spurious nucleation. Simulations of these `zig-zag' tile sets suggest that
under plausible experimental conditions, it is possible to grow large seeded
crystals in just a few hours such that less than 1 percent of crystals are
spuriously nucleated. Simulation results also suggest that zig-zag tile sets
could be used for detection of single DNA strands. Together with prior work
showing that tile sets can be made robust to errors during properly initiated
growth, this work demonstrates that growth of objects via algorithmic
self-assembly can proceed both efficiently and with an arbitrarily low error
rate, even in a model where local growth rules are probabilistic.Comment: 37 pages, 14 figure
Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media
We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions
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