7 research outputs found
Effects of a nanoscopic filler on the structure and dynamics of a simulated polymer melt and the relationship to ultra-thin films
We perform molecular dynamics simulations of an idealized polymer melt
surrounding a nanoscopic filler particle to probe the effects of a filler on
the local melt structure and dynamics. We show that the glass transition
temperature of the melt can be shifted to either higher or lower
temperatures by appropriately tuning the interactions between polymer and
filler. A gradual change of the polymer dynamics approaching the filler surface
causes the change in the glass transition. We also find that while the bulk
structure of the polymers changes little, the polymers close to the surface
tend to be elongated and flattened, independent of the type of interaction we
study. Consequently, the dynamics appear strongly influenced by the
interactions, while the melt structure is only altered by the geometric
constraints imposed by the presence of the filler. Our findings show a strong
similarity to those obtained for ultra-thin polymer films (thickness nm) suggesting that both ultra-thin films and filled-polymer systems might
be understood in the same context
A fully discrete local discontinuous Galerkin method for one-dimensional time-fractional Fisher's equation
On the structure of steady solutions for the kinematic model of spiral waves in excitable media
On a free boundary problem for the curvature flow with driving force
[[abstract]]We study a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shrinking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. One of the main tools of this paper is the intersection number principle, however in order to deal with solutions with free boundaries, we introduce what we call “the extended intersection number principle”, which turns out to be exceedingly useful in handling curves with moving endpoints.[[notice]]補正完