A proposal for (0,2) mirrors of toric varieties

In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations. Our mirrors are of the form of (B/2-twisted) (0,2) Landau-Ginzburg models, matching Hori-Vafa mirrors on the (2,2) locus. We compare our predictions to (0,2) mirrors obtained by Chen et al for certain examples of toric varieties, and find that they match. We also briefly outline conjectures for analogous results for hypersurfaces in Fano toric varieties. Our methods utilize results from supersymmetric localization, which allows us to incidentally gain occasional further insights into GLSM-based (2,2) mirror constructions. For example, we explicitly verify that closed-string correlation functions of the original A-twisted GLSM match those of the mirror B-twisted Landau-Ginzburg model, as well as (0,2) deformations thereof.Comment: 52 pages, LaTeX; v2: miscellaneous writing updates, typos fixe

Efficient Construction of Probabilistic Tree Embeddings

In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and ${\bf{E}}_{T}[d_T(u,v)]\leq O(\log n)\cdot d_G(u,v)$. Such embeddings have proved highly useful in designing fast approximation algorithms, as many hard problems on graphs are easy to solve on tree instances. For a graph with $n$ vertices and $m$ edges, our algorithm runs in $O(m\log n)$ time with high probability, which improves the previous upper bound of $O(m\log^3 n)$ shown by Mendel et al.\,in 2009. The key component of our algorithm is a new approximate single-source shortest-path algorithm, which implements the priority queue with a new data structure, the "bucket-tree structure". The algorithm has three properties: it only requires linear time in the number of edges in the input graph; the computed distances have a distance preserving property; and when computing the shortest-paths to the $k$-nearest vertices from the source, it only requires to visit these vertices and their edge lists. These properties are essential to guarantee the correctness and the stated time bound. Using this shortest-path algorithm, we show how to generate an intermediate structure, the approximate dominance sequences of the input graph, in $O(m \log n)$ time, and further propose a simple yet efficient algorithm to converted this sequence to a tree embedding in $O(n\log n)$ time, both with high probability. Combining the three subroutines gives the stated time bound of the algorithm. Then we show that this efficient construction can facilitate some applications. We proved that FRT trees (the generated tree embedding) are Ramsey partitions with asymptotically tight bound, so the construction of a series of distance oracles can be accelerated

Dynamics of double emulsion break-up in three phase glass capillary microfluidic devices

Pinch-off of a compound jet in 3D glass capillary microfluidic device, which combines co-flowing and countercurrent flow focusing geometries, was investigated using an incompressible three-phase axisymmetric Volume of Fluid–Continuum Surface Force (VOF–CSF) numerical model. The model showed good agreement with the experimental drop generation and was capable of predicting formation of core/shell droplets in dripping, narrowing jetting and widening jetting regimes. In dripping and widening jetting regimes, the presence of a vortex flow around the upstream end of the necking thread facilitates the jet break-up. No vortex flow was observed in narrowing jetting regime and pinch-off occurred due to higher velocity at the downstream end of the coaxial thread compared to that at the upstream end. In all regimes, the inner jet ruptured before the outer jet, preventing a leakage of the inner drop into the outer fluid. The necking region moves at the maximum speed in the narrowing jetting regime, due to the highest level of shear at the outer surface of the thread. However, in widening jetting regime, the neck travels the longest distance downstream before it breaks

Radiative Neutrino Mass, Dark Matter and Leptogenesis

We propose an extension of the standard model, in which neutrinos are Dirac particles and their tiny masses originate from a one-loop radiative diagram. The new fields required by the neutrino mass-generation also accommodate the explanation for the matter-antimatter asymmetry and dark matter in the universe.Comment: 4 pages, 3 figures. Revised version with improved model. Accepted by PR

Double emulsion production in glass capillary microfluidic device: Parametric investigation of droplet generation behaviour

A three-phase axisymmetric numerical model based on Volume of Fluid–Continuum Surface Force (VOF–CSF) model was developed to perform parametric analysis of compound droplet production in three-phase glass capillary devices that combine co-flow and countercurrent flow focusing. The model predicted successfully generation of core–shell and multi-cored double emulsion droplets in dripping and jetting (narrowing and widening) regime and was used to investigate the effects of phase flow rates, fluid properties, and geometry on the size, morphology, and production rate of droplets. As the outer fluid flow rate increased, the size of compound droplets was reduced until a dripping-to-jetting transition occurred. By increasing the middle fluid flow rate, the size of compound droplets increased, which led to a widening jetting regime. The jetting was supressed by increasing the orifice size in the collection capillary or increasing the interfacial tension at the outer interface up to 0.06 N/m. The experimental and simulation results can be used to encapsulate CO2 solvents within gas-permeable microcapsules

Scattering on two Aharonov-Bohm vortices with opposite fluxes

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations

Baryon Destruction by Asymmetric Dark Matter

We investigate new and unusual signals that arise in theories where dark matter is asymmetric and carries a net antibaryon number, as may occur when the dark matter abundance is linked to the baryon abundance. Antibaryonic dark matter can cause {\it induced nucleon decay} by annihilating visible baryons through inelastic scattering. These processes lead to an effective nucleon lifetime of 10^{29}-10^{32} years in terrestrial nucleon decay experiments, if baryon number transfer between visible and dark sectors arises through new physics at the weak scale. The possibility of induced nucleon decay motivates a novel approach for direct detection of cosmic dark matter in nucleon decay experiments. Monojet searches (and related signatures) at hadron colliders also provide a complementary probe of weak-scale dark-matter--induced baryon number violation. Finally, we discuss the effects of baryon-destroying dark matter on stellar systems and show that it can be consistent with existing observations.Comment: 26 pages, 6 figure