The first time I advanced in an audition was back in 2009, for the Chicago Civic Orchestra position. In my previous attempts at that position, the moment after the proctor announced my number, and it was completely silent, really freaked me out. I'd immediately freeze and begin to shake profusely. This was disastrous for my snare drum playing and after I played so poorly, I was discouraged from then on. But this time was a little different. Instead of focusing on the, "What's gonna happen" silence, I decided to count myself off in my head, as loud as I could, and it worked! It distracted me from the supposed "nothingness" that I would begin playing into, and focused my mind to the tasks at hand. The thing is, in between each instrument, the fear and anxiety would rush back to my brain, and I would have to calm myself down and count even louder to compensate. Still, even with the constant back and forth, I managed to play well enough to get through to the final round.
As I went through more auditions I developed a more fool proof way of dealing with the anxieties of auditions, but the first step for me was getting used to the silence before I played. Stepping on stage and realizing that you are about to perform a piece of music for an audience, the silence before becomes more exciting and enticing, building a type of enjoyable tension and an even sweeter release. The opposite of that, however, is feeling like, "Oh, I hope this works," or feeling like your sound is being judged, so you worry about what will come out, what will break the silence. That way of thinking always got me cut. So in the silence before you play, in my opinion you shouldn't be thinking about anything but the music that you are about to play. Play within that music in your head and I believe it will come out great. Figuring out how you can maintain this mental fortitude is a key to having a great round, even a "flawless" round.
While we all practice specific phrasings and sounds, occasionally, what we practiced might not work on the stage that we find ourselves on. Responding to this takes a certain level of awareness, instinct and quick adaptation (improvisation even) that we are not always taught in school or in lessons. Your ears have to be open to hear everything, the mind has to be clear to respond quickly and efficiently, and you have to be relaxed to let the body respond by itself. In these situations where you have to adapt quickly, panicking is not beneficial, but a cool head, and trusting that your brain and body will naturally make the adjustment, is the way to go.
A similar situation is when the panel asks you to play something different. Again, if you were paying attention during the first play through, you should have plenty of information and experience to make a noticeable, balanced and musical change that they ask for. Sometimes, when we try to make an adjustment, the music we played before becomes stilted, unmusical and mechanical, or there is no noticeable difference at all, even though we may think we're doing it. Listening outwardly, not just at your instrument, so that you know what the panel is hearing. This will help your brain figure out what the body has to do to play the new way. It already has enough information after your first play through, so just trust that it knows what to do. Think about what they asked, hear it in your ears, and let it come out freely; just trust.