In this master’s thesis, we consider a model for the free energy of two amphiphilic polymers in a bulk solvent. We are interested in the minimizers of this model, representing the most...Show moreIn this master’s thesis, we consider a model for the free energy of two amphiphilic polymers in a bulk solvent. We are interested in the minimizers of this model, representing the most energetically favorable configurations, and specifically study the existence of lipid bilayers, which partition the solvent phase as a codimension one subspace. To find such bilayers, we will look for a stationary pulse solution of a system of partial differential equations describing the volume fractions of the polymers over time. We will use geometric singular perturbation theory as posed by Neil Fenichel, and follow techniques used in earlier work on similar systems of differential equations. We will see that the system admits a stationary pulse solution for a flat bilayer, but that introducing a curvature of the bilayer to the system eliminates the possibility of such a solution.Show less
