What is the process?
You could transfer if you are unhappy with your current institution. Other than that, all you can do is study for classes, GRE, etc. and all that fun stuff. Personally, I wouldn't put too much weight on "top" schools. They have good programs, but so do other schools.
It's simple supply and demand. If there are 100 applications for 10 places, there will be 90 rejects.
First question: why do you think a bunch of strangers on the internet will give you better advice than your department chair?
Second question: why do you think your university has very little reputation? Reputation depends strongly on subfield - if you are interested in nuclear physics, for example, Michigan State has a much stronger program than Harvard or Chicago. Also, the rankings of departments correlates strongly with size: a small department can be good at one thing at most, but a large department can be good at many things.
There may be a slight misunderstanding in the process here. Admission to a particular program is not always a case of "if you're good enough, they will take you." Sometimes particular programs simply don't have spots available. So you have outstanding candidates applying for positions that don't exist. Sometimes applicants assume that because a specialization group exists, or a professor is doing a work in a field the student is interested in, that they will be accepting students because the department as a whole is accepting students. Unfortunately this isn't always the case. Groups may have all the students they can handle, professors may be leaving or going on sabattical, or a group's major funding may run out and the members are moving on to other things, or whatever.
So to tackle this, it's well worth yout time to do some research on the schools and programs you're interested in applying to. Find out if they are taking graduate students in the coming year and what those projects might entail.
As you move through your undergraduate years, your juniour and senior years are the time when most students should be thinking about specializations. Explore possible sub-fields through advanced courses and research projects, as well as your own independent reading. Then when it comes time to appy to graduate school, you should as much as possible be aiming to get involved in a project that aligns with your interests and skills rather than blindly applying to programs because of ranking or reputation.
One thing to remember about research is that for most undergrads it's rare that you'll actually be doing much more than acting as a spare set of hands - particularly if you're below the third year level. Some students, for whatever reason, are lucky enough to get involved in research and get their names on papers early - and this does count in their favour - but I wouldn't beat yourself up if this doesn't happen for you.
There's a lot you can learn by simply developing your own projects.
Many times it is out of your hands. The department that I am in had more acceptances than they expected in the past few years and so this year sent out only about half as many letters of acceptance than they normally would. So far as I understand, strong applicants who normally would have been a shoe in were not accepted here this year. Students applying here would have had no way of knowing this unless they had serious inside information.
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