4 papers · 1 filter
The double-bubble problem in three dimensions
Manuel Friedrich, Wojciech Górny, Ulisse Stefanelli
We characterize the unique minimizer of the three-dimensional double-bubble problem with respect to the -norm for volume ratios between and .
Nonlocal-to-local limit in linearized viscoelasticity
Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli
We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with re…
Existence of quasi-static crack evolution for atomistic systems
Rufat Badal, Manuel Friedrich, Joscha Seutter
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The inte…
On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime
Manuel Friedrich, Bernd Schmidt
We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith en…