Conifold transitions via affine geometry and mirror symmetry

Mirror symmetry of Calabi-Yau manifolds can be understood via a Legendre duality between a pair of certain affine manifolds with singularities called tropical manifolds. In this article, we study conifold transitions from the point of view of Gross and Siebert. We introduce the notions of tropical nodal singularity, tropical conifolds, tropical resolutions and smoothings. We interpret known global obstructions to the complex smoothing and symplectic small resolution of compact nodal Calabi-Yaus in terms of certain tropical $2$-cycles containing the nodes in their associated tropical conifolds. We prove that the existence of such cycles implies the simultaneous vanishing of the obstruction to smoothing the original Calabi-Yau \emph{and} to resolving its mirror. We formulate a conjecture suggesting that the existence of these cycles should imply that the tropical conifold can be resolved and its mirror can be smoothed, thus showing that the mirror of the resolution is a smoothing. We partially prove the conjecture for certain configurations of nodes and for some interesting examples.Comment: 82 pages, 28 figures. Published version. The main conjecture (Conjecture 8.3) has been reformulated. We added Section 9.5 where we partially prove the conjecture in an example. Improved expositio

Molecular dynamics of nanodroplet impact: The effect of the projectile’s molecular mass on sputtering

The impact of electrosprayed nanodroplets on ceramics at several km/s alters the atomic order of the target, causing sputtering, surface amorphization and cratering. The molecular mass of the projectile is known to have a strong effect on the impact phenomenology, and this article aims to rationalize this dependency using molecular dynamics. To achieve this goal, the article models the impact of four projectiles with molecular masses between 45 and 391 amu, and identical diameters and kinetic energies, 10 nm and 63 keV, striking a silicon target. In agreement with experiments, the simulations show that the number of sputtered atoms strongly increases with molecular mass. This is due to the increasing intensity of collision cascades with molecular mass: when the fixed kinetic energy of the projectile is distributed among fewer, more massive molecules, their collisions with the target produce knock-on atoms with higher energies, which in turn generate more energetic and larger numbers of secondary and tertiary knock-on atoms. The more energetic collision cascades intensify both knock-on sputtering and, upon thermalization, thermal sputtering. Besides enhancing sputtering, heavier molecules also increase the fraction of the projectile’s energy that is transferred to the target, as well as the fraction of this energy that is dissipated