Molecular dynamics simulations are used in order to study the self-assembly
process and the physical properties of flexible membranes composed of amph
iphilic molecules. On molecular scales, these membranes are observed to be
rather mobile and to have rough surfaces arising from molecular protrusions
, i.e., from the relative displacements of individual molecules. On length
scales that are only somewhat larger than the membrane thickness, on the ot
her hand, the membranes are found to undergo smooth bending undulations. In
this way, our study provides the first explicit connection between compute
r simulations with molecular resolution and elastic membrane models based o
n differential geometry. [S0031-9007(98)08125-3].