18 citations · 54 across the 5 of their papers we have counts for
5 papers
Hysteresis and phase transitions in a lattice regularization of an ill-posed forward-backward diffusion equation
Michael Helmers, Michael Herrmann
We consider a lattice regularization for an ill-posed diffusion equation with trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit.…
Convergence of an approximation for rotationally symmetric two-phase lipid bilayer membranes
Michael Helmers
We consider a diffuse interface approximation for the lipid phases of rotationally symmetric two-phase bilayer membranes and rigorously derive its -limit. In particular, we prov…
Kinks in two-phase lipid bilayer membranes
Michael Helmers
Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an e…
Snapping elastic curves as a one-dimensional analogue of two-component lipid bilayers
Michael Helmers
In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes we consider planar curves that are made of a material with…
Mathematical analysis of a coarsening model with local interactions
Michael Helmers, Barbara Niethammer, Juan J. L. Velazquez
We consider particles on a one-dimensional lattice whose evolution is governed by nearest-neighbor interactions where particles that have reached size zero are removed from the sys…