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In my statement of purpose I talked about the papers that I worked on and two of those papers are currently under review.
Is it acceptable to submit such papers as part of my application? And are there any concerns on the intellectual property of the work (since it is yet to be accepted)?
Is it acceptable to submit such papers as part of my application?
Yes, you inform people about your work in progress. I do suggest to add the submission date for the two papers, and if a first review has been performed, its date too.
And are there any concerns on the intellectual property of the work (since it is yet to be accepted)
I would say yes, if you plan to patent some of the ideas, but it might be too late if you have submitted it already.
And yes in general too. I have seen at a conference C2003 two posters side-by-side, on very similar topics, by researchers from country A, and country B. As I new the researcher from country B, s/he told me that s/he submitted to C2002, which took place in country A. His/her paper was rejected, and s/he suspected his/her idea was used by country A reviewers. No proof though. To maintain your legacy, you can put the paper on a free paper archive, like arxiv. Depending on the precisions you give in your applications, this risk is more or less likely. Do not believe in unknown people honesty.
This is probably journal and field dependent.
On the legal side, things are relatively easy: if you had to sign a copyright agreement to submit (uncommon, but an existing practice) then read it and see what kind of communication is forbidden. Usually, you would only ensure beforehand some transfer of intellectual property after acceptance, but I cannot pretend to know every journal's agreement. In particular, I suspect that fashion magazines such as Nature and Science may ask for no disclosure to ensure better buzz if a special press release is planned.
You can also reread the instruction to author, see if there is anything about your situation. Even if you did not sign anything at the point of submission, there usually is an implied agreement in the act of submission, but most usually only ensuring you do not submit to another venue at the same time.
Joining a manuscript to a non-pbulic application would certainly not qualify as a submission or publication in any way (but in certain field, if the application is public or may be made public, you should probably apply the same rules applicable to deposit of manuscript in a web page).
Last, joining unpublished work to an application may be frown upon by some in your field. I have met this attitude once, in French didactic of math, but it is completely acceptable in math (and as far as I know in physics and computer science) to join manuscript along an application. In fact, we are numerous to put all our manuscripts on our web page and on the arXiv, and then simply provide links or references in the application. To know where your field stands, you should ask a senior academic in the field, or at the very least precise your field and hope someone knowledgeable shows up here with official guidelines.
