5 problems

A dislocation model describes the evolution of dislocations, including their collision rules, in one, two, or three spatial dimensions. The collision-importance conjecture. Disloca…

Let $A$ be a metric space contained in an ambient metric space $A_{\mathrm{ex}}$. Its metric hull is … An extension of $A$ in $A_{\mathrm{ex}}$ is proper if it is strictly larger t…

Let $\sigma$ be the stress, and consider the region on which $|\sigma|=1$. The characteristic lines there may form boundary fans, exterior fans with apex outside $\overline{\O_p}$,…

Consider a one-dimensional phase-field configuration with one or two interfaces and pinned obstacles located at points of $d_\varepsilon\mathbb Z$, where the interfaces are…

Let $M_0^{\lambda,m,n}$ and $M_1^{\lambda,m,n}$ be the equilibria of the dynamical system, with $W^u(M_0)$ denoting the unstable manifold of $M_0$ and $W^s(M_1)$ denoting the stabl…