Design research opportunities

I have been exploring a lot of different facets of design and understanding the importance of design education. In that regard, I have started an initiative called Design For India with the help of few friends. We have started the pilot implementation in Mumbai, India. I graduate in November from the Master of Engineering Management program at Dartmouth. I have an engineering education as well, and am keen to pursue research at the intersection of design and science.

All through my readings on design, what excited me weren’t the outcomes, but it was the process and the underlying fabric of math/physics/philosophy/materials that provide support to the product/service. Is this a well-established area of study? I want to understand and document patterns and logic that is inherent in science, as implemented in design (deliberately or intuitively). There is an established area of work relating psychology to design (obviously so!), but I don’t believe there is anything yet to this effect.

I am keen to hear your thoughts on this. Any help on people to contact/resources will be of immense help! I have tried to look for work opportunities at innovation consultancy (design strategy) firms in the past, but haven’t heard back from any of those in the past.