Bootstrapping ADE M-strings

We study elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs from their modularity and explore the relation to topological string partition functions. We find a novel kinematical constraint that elliptic genera should follow, which determines elliptic genera at low base degrees and helps us to conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of related geometries. Using this, we can bootstrap the elliptic genera to arbitrary base degree, including D/E-type theories for which explicit formulas are only partially known. We utilize our results to obtain the 6d Cardy formulas and the superconformal indices for (2,0) theories.

On the Kinematics and Kinetics of Mechanical Seals, Rotors, and Wobbling Bodies

Mechanical seals, rotors, and wobbling bodies are characterized by a kinematical constraint that prevents them from having integral motion with respect to their own frame. A valid kinematical model is a prerequisite to subsequent dynamic analyses. Three previous works have suggested distinctly different kinematical models to the same problem. The analysis herein presents yet another kinematical model that preserves (actually enforces) the proper kinematical constraint. The outcome reaffirms one of the previous models. The equations of motion are derived using Lagrange’s equations to complement results obtained previously by Newton-Euler mechanics.