Entering the PhD Arena: from NSF Fellowship to Thesis

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Research passion drives the discussion on entering a PhD program, emphasizing the importance of choosing a specific field. The individual has a solid academic background in physics and mathematics, along with extensive research experience across various disciplines, including biophysics. Goals include publishing multiple papers and securing an NSF Fellowship to support their research interests, particularly in the intersection of physics and neuroscience. The proposed research aims to explore the universality of consciousness through statistical mechanics, though feedback suggests the proposal needs refinement for clarity and focus. Overall, the discussion highlights the significance of research experience, proposal quality, and outreach in the PhD application process.
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I've known for some time now that research is my passion. However, choosing a particular field to obtain a PhD in is a daunting task. This thread will go over in some detail my strategy for entering a PhD program on my terms, which as expected will be critiqued by this forum.

1. Background

I've graduated from Utah State University with a B.S. in Physics (Professional Emphasis) with a minor in Mathematics; GPA 3.32. I have nearly 4 years of research experience. I began my research endeavors at the world's most sensitive Atmospheric LIDAR lab (headed by Dr. Vincent Wickwar) operating the system for data acquisition during graveyard shifts without pay. As a result I have been acknowledged on several posters and a single paper. Realizing atmospheric physics wasn't for me I moved into the mathematical physics of networks with Dr. David Peak as my mentor. In the span of two years I derived what I believe to be a fundamental relationship between networks and Hilbert space. I have a paper in digital commons called "Centrality Measures utilizing Continuous Walks in Hilbert Space." I am in the process of re-writing the paper in a much more concise and elegant manner (the notation is ugly). Realizing I didn't want to do abstract mathematics for my entire life I moved into biophysics.

I completed an REU at the Center for Nanoscale Materials and Biointegration at the University of Alabama at Birmingham. I worked in a cardiobiology optogenetics laboratory with Dr. LuFang Zhou and Dr. Qince Li investigating the mitochondrial membrane potential with a new far-red shifted fluorescent probe. I had an extraordinary experience working in this lab learning as much as I possibly could about fluorescence, confocal microscopy, patch-clamping, etc. I was offered co-authorship of the paper for my contributions and went to the Biophysical Society's 59th Annual Meeting to present our work. At the conference I networked and as a result I have accepted a Post-Bacc Research Fellowship at the University of Iowa's Department of Molecular Physiology and Biophysics. I will be working with Dr. Janice Robertson and her lab investing the kinetics of protein folding in the lipid bilayer.

2. Goals

I want to build an extensive multidisciplinary research repertoire before entering a PhD program. I would like to have at least 3 papers published in medium impact journals with an established h-index prior to PhD program enrollment. Along side of the publications I want to attend several conferences and perhaps even give a talk to build a substantial professional network. Finally, I need to secure an NSF Fellowship or some other Fellowship that will give me the means to do the research that I want to do.

3. NSF Fellowship

I have a rough idea of what I want my proposal to look like. Keeping in mind this will be a year+ long endeavor I have a lot of work to do. First and foremost is the field the proposal is geared towards. I've become insatiably curious with the marriage between physics and neuroscience. That being said, Self-Organized Criticality has caught my eye along with Tononi's Integrated Information Theory. The idea behind this proposal is and attempt to prove that the physical mechanism responsible for Consciousness is universal and thus can be described using the tools of RG transformations with Dynamic Density Functional Theory (DDFT). This would be a crucial step forward in quantifying Consciousness since it would give us a looking-glass into the role noise plays in a DDFT theory of the physical mechanism of Consciousness.

So how would we go about proving Consciousness is Universal? We take a statistical mechanics approach and look at the correlation between 1/f noise generated in the brain and 1/f noise generated in the behavior of groups of people of various sizes in real-time. If the brain is indeed Self-Organized Critical then 1/f noise should be generated at all spatiotemporal scales. This proposal aims to test the mesoscopic statistics of Consciousness by simultaneous EEG-Sociometic studies. Perhaps most importantly we need suitably large data sets to adequately test for 1/f noise. By using wireless EEG caps with Sociometric badges (designed by Alex Pentland's lab at MIT) we can gather vast amounts of data in various sets and settings. Finally, we may preform a partial correlation or dependency network analysis of the critical exponents.

4. After successful completion of my PhD I would love to do Postdocs at DARPA and or IARPA working towards a true AI.
 
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I will give you some advice based on the feedback I received as I am currently supported by the NSF fellowship (it lasts three years).

The committee is looking for things that show you have the potential to become a great researcher. It was obvious from my comments that they really value undergrad research. Not only do they want you to participate in research, they want you to take a very active role as an undergrad. Your research recommendations are incredibly important for that reason. Your proposal is important because even though you are not bound to it, it shows if you have the ability to write a good proposal. Basically you should be knowledge about the field and try to identify new directions you could take. It's good if you have already done research in the field since you can start with this and extend the idea. You should remember, you are in no way bound to this proposal. For this reason you should choose to write the thing you know most about rather than the exact thing you want to do in grad school if you don't have much experience in that area yet. The NSF knows that it's completely normal for people's interests to shift a little (or a lot) during grad school.

If you have a first or second author publication in undergrad, especially in a high impact journal like physical review or nature, I think that strengthens your application tremendously. I know my reviewers mentioned that about three times on my review sheet.

From you proposal, it seems like you have an idea what you want to do, however, it is so verbose and throws in so much technical language that it is unreadable to me. Remember, your reviewers may not be in your exact field so you need to do a better job providing background to motivate what you are doing. Also, I might not be getting the right idea, but this proposal seems incredibly broad. As far as I know, lots of people are doing research involving tensor networks and DMRG like techniques in neuroscience, how do you expect to convince the NSF you will be able to answer this huge question during grad school. I think you should talk to one of your professors to help your proposal to become more focused.

You also need to consider what you want to do for outreach as it is a very important component of the NSF application.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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