from the size and name, I think that 'mdmp' would be either Mini, or Memory Dump files. These are probably occurring during crashes...a bit of searching didn't turn up easy results on how to stop them from generating...but if you aren't using them for troubleshooting the crash, I would say you could delete them
WOW! Exactly one year later and we just noticed this issue on our AR Server. They just started two days ago and filled up our app volume. We just turned on Authenticate Unregistered users (which isn't working at the moment CJ Schafer is next to me on the phone with support now) and at the moment I am thinking something about the authentication change is related.
After a little investigation, in our case it was part of the Authenticate Unregistered users changes but not directly to that feature.
Because we are going to start using AD to authenticate non-support people we deleted 10's of thousands of User records. We have two filters from RKM 7.5 that call a Java process on the AR Server to tell the RKM server to refresh it's cache. The RKM binaries are not on this AR Server so the Java process call failed and created dump files. Many of them were 300mb files and in total took over 20gb of space.