Awake at approximately 3AM every night this week. My internal clock must have some type of silent alarm. I awaken slightly tired, too tired to begin my day for sure yet less tired than I will be at the intended sleep time a few hours hence despite my best non-chemical effort to return to sleep, which I usually do, if only briefly until the second arousal at about 6AM. I try to be productive in a way, having read a NY Times article on insomnia that suggested just going along with what nature dictates. So I have soothing sleep sounds of various types on my Nexus 7 and iPod devices. I can listen to a shiur on yutorah.org or watch a video on Smithsonian channel, using one of the sets of ear buds kept next to the bed. From the iPod I can listen to a symphony at any hour. Sometimes I go downstairs and watch what is on.
I've never been so productive as to engage in things that have no time limit such as blogging or writing. Even for the soothing sleep sounds I set a timer. Eventually I return to snooze land, sometimes slightly more learned than the night before but usually not quite ready to pursue the days activities until the latest possible time.