3 problems

Let $K_+$ and $K_-$ denote the upper and lower fracture thresholds, respectively, for a fixed domain radius $R$. Let $a_1$ and $a_2$ be the model parameters, let $R_*$ denote the r…

The atomistic chain is modeled by a higher-order continuum energy, with the order of the included gradient terms determining the model's accuracy. Higher-order gradient conjecture.…

Common-neighbor conjecture. If $z,z'\in Z$ satisfy \\#N(z)=\\#N(z')=12 and $z\in N(z')$, then