Rugs, Carpets and Carpeting - Need Help Finding a Flat Flexible Moulding

I've been trying to find a floor moulding/room divider that can separate tile from carpet in a curved, sort of half-moon shaped entry. It would need to be flat, so no one trips over it, and flexible, as it would need to follow the curve of the carpet on the floor. The carpet is fraying where it meets the tile and I don't want to replace the whole thing. Does anyone have any thoughts or suggestions?

The problem here is that the transition piece should have been installed beneath the edge of the tile. Schluter makes a transition that can be bent to form curves.
Schluter-SCHIENE - Schluter-Systems (http://www.schluter.com/2171.aspx)

http://www.schluter.com/p/content/ss_prod_schiene_r_rdax_290x191_80.jpg
Photo Credit: Schluter

One option is to replace the tile with a square rather than half moon and install the Schluter transition piece when tile is installed. The new tiled area could be enlarged enough to allow for cutting out the damaged edge of the carpet. This would allow for an opportunity to update a dated decorating concept.

Thanks Twelvepole! I will look into that.