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Rough Draft of Statement of Purpose Physics PhD

  1. Aug 24, 2015 #1
    This is a very rough draft of my statement of purpose. The plan is to use this as a base and customize it for different programs to include why those specific programs will help me achieve my purpose. The conclusion is missing because that will be specific to each program I'm applying to. All comments are welcomed please don't hold back.

    "

    My purpose in graduate school is to gain the skills necessary to answer questions about the physical world that have previously been void of an answer and are of profound interest to not just scientists but also to laymen. To accomplish this purpose I plan to take as much physics classes as I can in whichever graduate school I go to. The purpose of this is so that I can understand how different models of reality accurately predict empirical phenomena on a wide range of scales, from low energy to high energy, from massive objects to quantum sized objects etc. By understanding how all of these models work and why they work I want to consolidate all of these successful but distinct theories of physics into a more unified theory. I am not saying I want to specialize in every subfield of physics; rather I want to heavily incorporate many other fields of physics into my specialization so I can further its ability to explain new phenomena. For example using a modified form of General Relativity to describe how gravity behaves on quantum scales. In order to accomplish my purpose besides just learning vast amounts of physics I would like to hone my abilities as a researcher. To do this I plan on reading many papers from peer reviewed journals on whatever I choice to be my specialization and attend as much conferences as possible. Also I’ll extrapolate as much insights on how to do research as I can from my thesis advisor and other faculties members I interact with. Furthermore I would be constant communication with other students who have interests which I believe are in concord with my own and we’ll have weekly discussions of where our research is going.


    As an undergrad I have spent three continuous semesters conducting research with professor David Mugglin of the Polytechnic School of Engineering of New York University on the dynamics of a Physical Double Pendulum (PDP). The experience has prepared me to do research in graduate school because it taught me the methodology of doing original research. Our project started off by trying to construct a model, which accurately represents the PDP when it’s motion is in the quasi-period regime taking into account air resistance and frictions from the bearings. As I did read more papers on the PDP I started asking more profound questions and our research changed focus to describing the route to chaos that the PDP takes. This research combined computational and theoretical elements. I identified a route to chaos for the PDP as a parameter responsible for determining the intergrability of the system is varied from zero (system is fully intergrable) to small but non zero (system is near intergrable). I expanded the Hamiltonian of the PDP to first order in epsilon in terms of this parameters and interpreted my results in terms of the KAM theorem. Computationally I used Mathematica to solve the nonlinear differential equations of the PDP and construct bifurcation and Poincare sections.


    During my research I gained an understanding of Hamiltonian Chaos and of the various mathematical and computational methods that are employed to study that class of system. Despite my wonderful experience in that field of physics as of now I’m not committed to that being my specialization in graduate school. If I had to rank my preferences as of now I would rank unifying General Relativity with Quantum Field Theory as my first choice, with Cosmology being second and nonlinear dynamics being third. I also have a budding interest in the interdisciplinary field of biophysics. Regardless of what I pick as my specialization I plan on becoming very proficient in all of those fields and more because I feel it will make me better researcher and physicists. "
     
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  3. Aug 25, 2015 #2

    micromass

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    Rewrite this completely. You sound very naive, overconfident and unfocused.

    The goal of grad school is to specialize in one very small topic and to discover new results in those topics. You seem to want a very broad education which will get you in contact with various different fields of physics. This is just not what grad school does.

    Unifying GR and QM is all nice, but you need to be specific. Are you interested in string theory? Something else? Just saying "I want to be the one unifying all of physics" makes you sound very naive.

    This is not up to you.

    So which is it? Biophysics? Nonlinear dynamics? Cosmology? GR & QFT? You sound very unfocused here. That is not a good thing.
     
  4. Aug 25, 2015 #3

    Vanadium 50

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    This. And not just a little bit. A lot. You are a student with an average or a little below record at an average or maybe a little below school. You just wrote an essay, like the last, riddled with English errors. In that essay you claim you want to solve a problem that has been open for centuries - and want to organize the research program to your liking (the "weekly discussions"). This, as they say, will not end well.

    I'm also struck by how different this statement is compared to your last one. Why do you want to go to graduate school? Until you have answered this question in your own mind, you are unlikely to be able to express it clearly to others.
     
  5. Aug 25, 2015 #4
    I'll completely overhaul my statement of purpose and have a completely new draft done sometime later today. My interest mostly right now is in Quantum Field Theory and how it can be modified to be compatible with General Relativity and vice versa. I think I understand what the problem is with my statement of purpose. The problem is not that my purpose is bad but rather my purpose is not appropriate for graduate school. Assuming I spend five years in graduate school it is very unlikely I'll gain the expertise to be able to come up with a unified field theory hence I need to come up with a smaller and more realistic goal to accomplish in graduate school. Thanks for the advice.
     
  6. Aug 25, 2015 #5

    micromass

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    Sure, you need something more realistic than "finding a unified field theory". But you also need something more specific, because searching for a unified field theory is a huge field with a lot of directions. You don't need to be extremely specific though, but they need to get an idea of what you will be doing. Will you be doing string theory? Loop Quantum Gravity? Something else?
     
  7. Aug 25, 2015 #6
    Thank you for telling it as it is. The reason this statement of purpose is different then the last is because that one clearly didn't work. I still don't know what was wrong with it. I was very specific about the type of physics I wanted to do in graduate school and was very technical in my explanation of what I know about that type of physics. I have a hard believing the grammar in my last SOP was very bad. I took it to many writing centers for review specifically to correct the grammar. Are you saying that my transcript is below average and the school that I went to was below average as well? I want to go to grad school because I want to gain the skills necessary to become a theoretical physicist. Specifically I would like to do research in quantum field theory in graduate school. In my mind I do have good reason why I would to do research in QFT but the mathematical are too formidable for me right now open a book in QFT and see a problem and talk about in detail why I would want to tackle that specific problem.
     
  8. Aug 25, 2015 #7

    micromass

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    I don't know harmony, but in your last statement of purpose you're very big on chaos theory and wanting to do stuff in that. Now there is hardly a mention of chaos theory, and you go on about unifying GR and QFT. This makes me think that you don't really have an idea of what to do.
     
  9. Aug 25, 2015 #8
    The reasoning for that is simple. I wrote that SOP in the fall of 2014 where I was knee deep in my senior project and was really high on Hamiltonian Chaos. I completed my senior project successfully but I was urged by many of my physics professors to not pigeon hole myself yet into one field of physics. Now I'm not a hundred percent sure that I want to devote all of graduate school to continuing research in chaos theory.
     
  10. Aug 25, 2015 #9

    micromass

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    OK sure, you don't want to pigeonhole yourself into one field of physics. Very good idea. But then why completely change directions and do something that completely different?
     
  11. Aug 25, 2015 #10
    Because I'm young and want change. It was always my intention to go into the ultra theoretical unified field theory type of physics. The only reason I got involved in nonlinear dynamics was because it was the only available physics REU at my school. I did fall in love with it but now that I know what research at a high level in that field is at I want to give QFT and GR a chance because I feel the questions they attempt to answer are just more interesting. The problem is that I spent the majority of my undergrad not reading a thing on QFT or GR and instead only focused on reading papers on applying the KAM theory and Intergrability or canonical perturbation theory. So unlike nonlinear dynamics I cannot give a very technical reason why I want to study QFT or GR. The best I say is that I find the questions they answer very profound, this is what I would like to do with them after graduate school, in graduate school I would like to focus on this small portion of QFT and then use my experience in nonlinear dynamics to back up that I have what it takes to do research in these fields. But I can't talk super technical about QFT or GR or say I read and understood any papers that represent the current frontier of those fields. Another problem I have is that most of the physics departments I'm applying to don't specialize in nonlinear dynamics. Instead there applied math departments do and I have no intention of getting a PhD in applied math just so I can do research in chaos theory. I feel in order to get into a PhD physics program I need to pick something that the programs I'm applying to have a large amount of faculty in.
     
    Last edited: Aug 25, 2015
  12. Aug 25, 2015 #11

    radium

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    I completely agree with the above posters. You need to rewrite this statement starting from scratch. It is riddled with errors, very unfocused, and is verbose to the point of being incomprehensible. These sentences are especially bad

    1. "I plan to take as much physics classes as I can in whichever graduate school I go to." This is not only grammatically incorrect but also shows you have the wrong idea of how grad school works. You should take interesting classes, but the purpose of grad school is not to take classes, it is to do research. Taking too many classes is a distraction.

    2. The use of the words "unified theory" show you have a very romanticized vision of physics. In my statement, I mentioned how I was interested in how many of the same ideas appear in different fields. For example, a lot of the techniques and ideas used in condensed matter are very similar to things in high energy (I didn't mention these, but some examples are confinement, the Higgs mechanism/spontaneous symmetry breaking, and the AdS/CFT correspondence).

    3. "In order to accomplish my purpose besides just learning vast amounts of physics I would like to hone my abilities as a researcher." The purpose of grad school is to become a researcher, you make it sound like it is a secondary thing. Also the things you mention at the end of the first paragraph are just basic expectations of a grad student.

    4. Different advisors have different methods of advising. The person I started working for is very hands off so there are times that it is not necessary for me to meet with them for a few weeks. I'll send a quick email if I have subtle questions, but a lot of the times you should meet with your advisor only after you have become very informed about what you are doing independently and/or have results. It's ok to go to ask conceptual questions if you are stuck, but you should have read/done a lot before the meeting.

    5. "The experience has prepared me to do research in graduate school because it taught me the methodology of doing original research." This is just incredibly vague

    6. Ranking preferences is just not a very good idea. You could say my main interests lie in ... but I am also interested in these other fields.

    Rather than giving you more advice on how to improve your statement, I will give you advice on how to structure a statement of purpose in general.

    1. I started by saying that I have always wanted to develop an understanding of a field such that I could build an intuition that would allow me to identify and explore new unsolved questions(I didn't word it this way but that is the gist) 2. I was very dedicated to my subfield so I described how I had became interested and why by mentioning how I had became interested in several major developments in this field and learned more about them by talking with my professors 3. I described my research experiences in depth and emphasized how they helped me develop as a scientist. For example, I am now a theorist so I mentioned how my summer in experiment helped me gain a perspective on the interplay between the two. I also mentioned my favorite course and how it helped me in my research. 4. I wrote a paragraph tailored to each school which mentioned 2-4 professors I was interested in and other things I liked about the department (for example one school did experiments I found interesting relating to my proposed work in theory).
     
  13. Aug 25, 2015 #12
    What do you think of this series of paragraphs. As of now I'm having difficulty saying exactly what my purpose is because I simply don't know enough about to QFT or GR to pick a highly active sub topic in any of them to pursue right now. But I plan to talk a lot about my undergrad research to show that I have what it takes to learn QFT or GR really quickly in graduate school and be proficient researching those fields. To do this I took parts of my old SOP and updated them slightly. Right now I'm imagining my SOP will be a introductory paragraph about my what I want to do exactly in grad school. These paragraphs will follow and the conclusion will discuss which professor I'm interested in working with and why.

    "

    I received a chance to do research in chaos theory with Professor (Insert name) of the (insert university)and it increased my scientific maturity. I did work in the lab building a physical double pendulum. I then simulated the double pendulum using Mathematica and used tracking software to monitor the motion of the double pendulum. Our goal was to see if initial conditions that give rise to quasiperiodic motion in our Mathematica simulation also gave rise to quasiperiodic motion in the lab. Because I was trying to compare experimental results with theoretical results I had to take into account how the motion of a real physical pendulum differs from the solution of the system of nonlinear differential equations that govern my idealized pendulum. I also constructed Bifurcation diagrams and Poincare sections and independently learned some shocking things about chaos in a double pendulum. For starters, you can have two different initial conditions with the same energy but one initial condition will lead to chaos while the other won't. By studying the motion of the double pendulum I learned just how subtle problems can be in physics. I also understood why people who study something in physics are usually left with more questions than answers despite seemingly being able to explain the system inside and out.


    Doing research also got me into the habit of constantly reading journals on nonlinear dynamics. One of my favorite papers, Double pendulum and θ-divisor by V. Z. Enolskii from the Journal of Nonlinear Science inspired me to use the integrable solution of the double pendulum when g=0 and then use perturbation theory treating g as a small parameter to get an analytical rather than numerical understanding of the motion of a double pendulum. After working out the hypereliptic function which governs the solution of the double pendulum when g=0, I found another set of parameters in which the double pendulum is integrable. By fixing the bottom pendulum through its center of mass, the top pendulum acts as a uncoupled pendulum and the bottom as a free rotor. If this parameter is taken to be small on order of epsilon compared to the length of the bottom pendulum the Hamiltonian of the double pendulum becomes one of an intergrable system with a small-coupled nonlinear perturbation attached to it. This opens up the topological features of the phase space to be interpreted in terms of the KAM theorem.


    My research finally settled on the topic describing the route to chaos the double pendulum exhibits as that small perturbation is increased but still kept to be much smaller then the length of the bottom pendulum. To study how the invariant tori break down as I increase this parameter Bifurcation diagrams and an animation of Poincare sections were made. The results very beautiful to see and very insightful, in the animation I made I witnessed the tori breaking down by collapsing in on themselves and then exploding into a sea of dots. This was confirmed in the Bifurcation diagrams when I witnessed a split occur at the same value of epsilon in which the invariant tori collapse into points which results in period n orbits. What I was observing was Hopf bifurcation and at the time I didn’t know it at the time. After doing more research I found out that the fixed points I discovered were dependent on the value of epsilon and only existed only for a few select value of epsilon. After computationally observing this for many initial conditions I observed a clear route to chaos. Prior to global chaos emerging period n motion takes place at very precise values of epsilon and as epsilon is increased further the invariant tori quickly disintegrate. This was the extent of my undergraduate research and I believe it has armed me with the critical thinking skills and research methodology to pursue graduate work in any field of physics I choose.

    "
     
  14. Aug 25, 2015 #13

    micromass

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    Now you just described your undergrad research. This is fine, but you only talked about it.
    They want to know
    - Why you want to grad school.
    - What makes you a suitable candidate for their school.
    - What you are interested in doing.
     
  15. Aug 25, 2015 #14
    1. I do agree research is first and foremost the most important thing in grad school but I feel that if I want to do research that people will care about once I finish grad school I need to know a lot about most fields of physics. Also once I leave grad school and have to work as a professor I'll have administrative responsibilities. which will make it hard for me to go and learn in great a detail a field of physics I'm utterly unfamiliar with. So I much rather spend all of my time learning in graduate school.

    2. I don't have a romanticized vision of physics rather I just don't know anything technical about quantum field theory of general relativity so I can only describe them on a popular level. I would like to go to grad school committed to doing research in those fields, take some classes in QFT and GR and then I'll have the tools to find a specific problem in either of those fields to work on.

    3. Agreed

    4. That was my undergrad experience I mostly did the work on my own and just contacted my advisor every so often.

    5. Agreed

    6. I will certainly not rank preference in the next full draft.
     
  16. Aug 25, 2015 #15

    micromass

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    Typically nobody will really care about your research in grad school. It is very common that nobody reads your thesis except the jury. This is not true in any case, but it gives you an idea of how important the research in grad school is. Grad school will teach you how to do research and will teach you how to be an expert in a very small part of physics. The actual important research will typically only come after grad school.

    In grad school, you will have to focus on a very narrow part of physics. This will eat up a lot of your time. You will simply not have the time to learn "most fields of physics". It's not to say you shouldn't be learning something unrelated to your research, but you make it seem like that is one of your main goals. It shouldn't be. It should be a hobby at most. You will not have much time for this.

    You will not accomplish this in grad school. Research nowadays is not about learning "most fields of physics". It is about becoming expert in a very narrow part of physics. Typically as a post-doc you will try to broaden your perspective and do something that is not what you did in grad school, sure. But you'll still be doing something very niche.

    OK, and this is the main problem of your application. You have a romanticized view of physics because you don't know any QFT and GR. So how do you even know you like this research or will be good at this research? You sound like a high-school student reading a book by Stephen Hawking. You have no reason that you like these areas other than that it's famous. And grad schools will sense this very easily.

    3. Agreed

    4. That was my undergrad experience I mostly did the work on my own and just contacted my advisor every so often.

    5. Agreed

    6. I will certainly not rank preference in the next full draft.[/QUOTE]
     
  17. Aug 25, 2015 #16
    "
    My purpose in graduate school is to do research in Quantum Field Theory (QFT) with the intent one day becoming a professor of theoretical physics at a university and to continue doing research in physics. Specifically in graduate school I want to research how to incorporate gravity into QFT by the theory of causal fermions systems. This theory appeals to me because it is based on vibrational principles, which have been so successful in classical mechanics and General Relativity to describe systems with a variety of potentials and geometries. Also mathematically this vibrational principle is done in Hilbert Space and made compatible with the algebra associated with QFT. Also I find that the way it expands the definition of space-time from a set of points which form a open set which has a topology and geometric structures to a set of operators acting on Hilbert Space is a very plausible mechanism to reformulate gravity on small scales in which the nature of space time cannot be ignored.
    "
    For a introductory paragraph is this detailed and technical enough?

    "

    My purpose in graduate school is to do research in Quantum Field Theory (QFT) with the intent of becoming a research professor of theoretical physics at a university. Specifically I want to research how quantum fluctuations in QFT can explain the accelerated expansion of space. Quantum fluctuations lead to a non-zero energy density in the vacuum, which requires the cosmological constant in Einstein’s equations. To complicate the matter there is a divergence between the observed value and the theoretical value. In my research I would like to get closer to the answer of whether a reformulation of QFT is needed to match the observed value of vacuum energy density or perhaps there is more to “dark energy” then just quantum fluctuations. "

    This is another possible introductory paragraph. As of now I';m actively doing research into open problems in QFT and attempts to unify gravity with it.
     
    Last edited: Aug 25, 2015
  18. Aug 26, 2015 #17
    "

    My purpose in graduate school is to do research in Quantum Field Theory (QFT) with the intent of becoming a research professor of theoretical physics at a university. Specifically I want to research how quantum fluctuations in QFT can explain the accelerated expansion of space. Quantum fluctuations lead to a non-zero energy density in the vacuum, which requires the cosmological constant in Einstein’s equations. To complicate the matter there is a divergence between the observed value and the theoretical value. In my research I would like to get closer to the answer of whether a reformulation of QFT is needed to match the observed value of vacuum energy density or perhaps there is more to “dark energy” then just quantum fluctuations.

    I did three semesters of research with Professor (Insert name) of the (insert university) and it increased my scientific maturity. In a lab I built a physical double pendulum (PDP). I simulated it’s motion using Mathematica and used tracking software to monitor it. Our goal was to see if initial conditions that give rise to quasiperiodic motion in our Mathematica simulation gave rise to quasiperiodic motion in the lab. Because I was trying to compare experimental results with theory I took into account how the motion of a real PDP differs from the solution of the system of nonlinear differential equations that govern my idealized pendulum. I learned some shocking things about chaos in a PDP. You can have two different initial conditions with the same energy but one initial condition will lead to chaos while the other won't. This taught me how subtle problems can be in physics. I understood why people who study something in physics are usually left with more questions than answers despite seemingly being able to explain the system inside and out.



    Doing research got me into the habit of constantly reading journals on nonlinear dynamics. One of my favorite papers, Double pendulum and θ-divisor by V. Z. Enolskii from the Journal of Nonlinear Science inspired me to use the integrable solution of the double pendulum when g=0 and then use canonical perturbation theory treating g as a small parameter to get an analytical rather than numerical understanding of the motion it. Later I found by fixing the bottom pendulum through its center of mass, the top pendulum acts as an uncoupled pendulum and the bottom as a free rotor. If this parameter is taken to be small on order of epsilon compared to the length of the bottom pendulum the Hamiltonian of the double pendulum becomes one of an intergrable system with a small-coupled nonlinear perturbation attached to it. This opens up the topological features of the phase space to be interpreted in terms of the KAM theorem.

    My research settled on describing the route to chaos the PDP exhibits as that small perturbation is increased but still kept to be much smaller then the length of the bottom pendulum. To study how the invariant tori break down as I increase this parameter Bifurcation diagrams and an animation of Poincare sections were made. The results were very beautiful to see and very insightful, in the animation I witnessed the tori breaking down by collapsing in on themselves and then exploding into a sea of dots. This was confirmed in the Bifurcation diagrams when I witnessed a split occur at the same value of epsilon in which the invariant tori collapse into points that resulted in period n orbits. What I was observing was Hopf bifurcation and at the time I didn’t know it at the time. After doing more research I found out that the fixed points I discovered were dependent on the value of epsilon and only existed for a few select value of epsilon. After observing this for many initial conditions I saw a clear route to chaos. Prior to global chaos emerging period n motion takes place at very precise values of epsilon and as epsilon is increased further the invariant tori disintegrate.

    This work shows I am capable of conducting research in graduate school. I studied a sub sect of a field of physics and came up with a specific problem I wanted to investigate. In my investigation I produced results that neither of my advisors saw before. My work comprised of theoretical, computational and experimental elements, which means I learned skills to engage in a variety of research. I learned for example how to interpret new results in terms of accepted theories and how to build upon them.
    "

    As of now this is the direction I'm going in my SOP. Am I clearly showing that the research I did as an undergrad has prepared me to do research in graduate school?
     
  19. Aug 26, 2015 #18

    radium

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    "This work shows I am capable of conducting research in graduate school." Ok, this is something that is supposed to be implied in your statement, not directly stated. It just sounds bad. Also there are way too many unnecessary details about your undergrad research. Your first paragraph in the second statement about what you want to do in grad school just states the obvious in terms. the first paragraph in your first statement is also not that great.

    I will give you an example how I motivated my research interests. I said that condensed matter ranges from the very applied to the very exotic, and many times they overlap (for example there is some very mathematical work which can be proved experimentally and proposals for quantum computers using the nonabelian statistics between majorana fermions). I said I had spoken a lot with my professors about the field and gave specific reasons how my interests developed (Nobel prize in graphene). This may be much harder for you to do since I already had a lot of background in my subfield that I applied for.
     
  20. Aug 26, 2015 #19
    That's the main problem for me. I don't have single ounce of experience in my what I want to do research in graduate school. Also I don't have a single professor in my department who has worked in anything close to QFT so I cannot go and have a conversation to them about it. However despite having no background in QFT I've always leaned towards that direction. One of the reasons I lean towards QFT is because it is empirically the most successful theory of all time and can explain a wide range of phenomena. Also I find the question that fields associated with QFT try to answer are much more interesting then the questions in nonlinear dynamics. For example as I implied in my SOP the notion of quantum fluctuations causing a non zero energy density in the vacuum can help us understand the future and origin of our universe. Naturally I'm attracted to his field because it can potentially answer such important questions. What do you mean my first paragraph in my second statement states the obvious in terms? Are you saying it is not necessary for me to explain what I already know about my proposed research interest in graduate school? Or are you saying I'm showing that I don't know enough about quantum fluctuations to warrant being interested in researching it? I will change my last paragraph. I will also be less detailed about what I did in my undergraduate research and spent more time highlighting why my undergrad research prepared me to do research in graduate school rather then just describing what I did.
     
    Last edited: Aug 26, 2015
  21. Aug 26, 2015 #20

    "My research experience consists of three consecutive semesters of working with Professor (Insert name) of (Insert university) on a project concerning the dynamics of a physical double pendulum (PDP). Initially we wanted to see how well the motion of a simulated (PDP) compared to a real one. From there we would try to take into account friction from the bearings and air resistance into our simulation to match the observed motion. During this phase I learned how to think about the difference between the equations I’m studying and the actual systems they represent. Also, I had hands on experience building a PDP and measuring the length and mass of the bars taking into account uncertainty in my measurements. Furthermore, I learned numerical skills necessary to solve systems of nonlinear equations and then animate the solutions.


    The next phase of my research was theoretical and was inspired by constantly reading journals in nonlinear dynamics. One of my favorite papers, Double pendulum and θ-divisor by V. Z. Enolskii from the Journal of Nonlinear Science inspired me to use the integrable solution of the double pendulum when g=0 and then use the canonical perturbation theory treating g as a small parameter to get an analytical rather than numerical understanding of the motion it. I learned many mathematical techniques during this phase, which I know will be valuable to me in the research I’m going to do in the future.

    Later I found by fixing the bottom pendulum through its center of mass, the top pendulum acts as an uncoupled pendulum and the bottom as a free rotor. If this parameter is taken to be small in order of epsilon compared to the length of the bottom pendulum the Hamiltonian of the double pendulum becomes one of an integrable system with a small-coupled nonlinear perturbation attached to it. This opens up the topological features of the phase space to be interpreted in terms of the KAM theorem. I then decided that I would try to see if a clear route to chaos existed for the PDP as this parameter was varied. This led me to use computational means to observe the consequence of the KAM theorem. By interpreting computational results in terms of an established theory I was able to observe a route to chaos for the PDP. During my research I studied a sub sect of a field of physics and came up with a specific problem I wanted to investigate. In my investigation, I produced results that neither of my advisors saw before. My work comprised of theoretical, computational and experimental elements, which means I learned skills to engage in a variety of research.

    I condensed my undergraduate research experience and why I'm capable of doing research in graduate school from four paragraphs to three paragraphs. Do you feel that his is a drastic improvement? Specifically I condensed 669 words into 442 words. Am I showing that my experience as an undergrad has prepared me to do research in grad school in these three paragraphs?
     
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