Read the fine-print on Yale’s webpage. At the discretion of the Admissions Office, a research paper might be forward to the appropriate faculty. Not all submitted research papers get forwarded to faculty. My guess is that few do.
And remember, when you apply to a school like Yale, Harvard or Princeton you are competing with the best-of-the-best applicants in the world. Some applicants have won Intel or Google Science Fairs with their research project. While your research paper may be wonderful at the local level, can it really stand up to something huge like this? My guess – without even reading your paper – is no. If you send your research paper, it’s going to be compared to a student who has achieved something like this. http://www.businessinsider.com/shree-bose-google-science-fair-winner-2016-5