I'm at the end of a 2 year post-Bacc at Columbia. My goal when I started was quite clear: I wanted to study atmospheric science through the lens of dynamical systems. However, as I've moved along, it's become clear to me that my interest is really in the approach, and that I care relatively little about the particular field to which it is applied. That is: I'm much more interested in the process of modeling with dynamical systems than I am in what I'm modeling (though I would prefer to stay in the physical sciences). This is great in some senses, because it means that I can apply to a wealth of different sorts of programs, but I'm suffering from paralysis of choice; how can I even decide?
Some pertinent background:
-My undergraduate degree is actually in linguistics from Georgetown (it's how I got interested in complexity science in the first place)
-I've been working with a research team in climate science, although it hasn't been very mathematics heavy.
-My first project has begun to conclude, and so I've recently begun working with an physical oceanography research team doing very mathy stuff
-One of the theoretical climate scientists in the department (who started his career with a very theoretical fluid mechanics/dynamical systems approach) told me that the use of dynamical methods in atmospheric science has been largely mined out: there aren't many tractable questions remaining and it will be difficult to find work doing that even if I do get funding for a PhD.
-My quantum mechanics professor recommended looking into either plasma physics or ion transport in batteries. She says these methods are being used there (and I trust her on this; she has her own lab doing work closely related to the later and is generally quite brilliant all the time).
I really need two things
a) Specific advice about how to navigate this choice and to finesse the applications: Are these fields all equally likely to allow me to play with these techniques? Should I be applying to math programs or science programs given my interests? Are there scientific fields I should consider beyond those recommended to me above (p. oceanography, atmospheric science, plasma).
b) General advice about organizing this choice, selling myself as a legit candidate in a diversity of fields (my background is at this point equivalent to a bachelors in Mathematical Physics kinda; more analysis than most physicist undergrads but less calculations.