I have created this with cycles:
But the edge between the glowing and non glowing materials is very sharp. The material was manually applied to faces in edit mode. Is there any way I can smooth the edge between them in cycles?
Smoothing the transition between materials:
You can use a texture to mix the "materials" (everything is actually in one material) instead.
Use a wave texture as the mix factor of a mix node mixing the two node setups used to make the bright strips and the dark surface of the ball (everything is one one material datablock).
By using the color ramp node to adjust the falloff of the wave texture, you can control the sharpness of the transition.
Some other things which may make the transition a little more natural: