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Learning to be a PhD advisor

Zhigang Suo's picture

We professors usually start our jobs unprepared. In our days as students, we are considered talented if we can solve problems posed by our professors. We might be even considered brilliant if we can solve them quickly and make a few extensions. After solving a few such problems, we write a thesis. We are then entrusted with a job as a professor. We soon realize that the skill of solving problems posed by others only plays a minor role in our jobs. We have to pose new problems, persuade our peers that our problems are worth solving so that someone will fund us, and motivate students to solve them. Each of the three aspects demands a distinct set of skills. On top of these, we have to teach classes and serve on committees. Our days as students do not prepare us for our jobs; we must learn on the jobs. Perhaps there is nothing unusual about this lack of preparation in any profession. Let us just hope that our doctors are better prepared before they learn something while treating us.

Perhaps we can help each other to learn to be professors by recounting our experience. This thought came to me this morning, and I'm writing to tell you about a recent experience of mine.

Xuanhe Zhao  came to Harvard as a PhD student in the fall of 2006, after obtaining a master degree in Materials Engineering from the University of British Columbia, in Canada; and a bachelor degree in Electrical Engineering from Tianjing University, in China. He has just completed his first year at Harvard. By now he has opened an exciting area of research for himself, and has finished 6 papers, with 4 additional papers in advanced stage of preparation. How did he do that?

When Xuanhe arrived on campus, a project of mine was in serious trouble. The postdoc for the project went elsewhere for a faculty position. I was also unhappy with the way the project was going. I did not have anybody else to put on the project, nor did I have a bright idea for Xuanhe to work on. It occurred to me that perhaps putting two problems together was a solution. I put Xuanhe on the project, and start to meet with him weekly. His charge was to define something interesting to work on within the broad object of the project: using electrostatic field to do something to materials. The only constraint was that my group works on theoretical solid mechanics, and this something should be within the area of theoretical solid mechanics.

For months, he and I met each other weekly. He would tell me with great enthusiasm what he learned from the literature, usually about some exotic technology, and how he might use mechanics to do something. I would tell him the technology looked interesting, but did not seem to lead to any deep mechanics. He did not give up on me, and next week he would come to me again, with yet another enthusiastic idea. The cycle seemed to lead us nowhere. I had never tried this process with any other students before, and began to have doubts. Should I just give him a problem, and let him write a competent but not very exciting thesis? After all, he was an Electrical Engineer or a Materials Engineer. Perhaps he did not have the right background to do "serious" mechanics. Or did he?

One day he brought to our weekly meeting a few papers on using electric field to cause large deformation in rubber-like materials. We suddenly clicked. These active polymers are being studied intensely as muscle-like actuators for soft robots. The intriguing applications aside, the papers reminded me of my old interest in piezoelectric ceramics. The ceramics have very small strains, usually less than 1%, but these polymers can undergo strains much beyond 100%. This large deformation also reminded me of a long-standing theoretical difficulty in the field of deformable dielectrics: how to couple electric field to large deformation. I worked on the problem before, but didn't get anywhere. I dug out my old notes, which turned out to be not very useful, except that they reminded me of where I had trouble with the existing theories. I only had complaints about other people's work, but did not have any clue as to how to fix the problem.

Reading my old notes, it also became evident that one barrier had been that I didn't have much intuition about finite deformation. This barrier was just removed because I was teaching the subject for the first time. I had to learn the subject, and at least had to appear intuitive about the subject in class. (My class notes on finite deformation has been posed on iMechanica.) So teaching is not a waste of time after all, a subject we should visit some other time.

With the new impetus, Xuanhe and I, along with Bill Greene from a local firm auditing the class, started to work intensely on resolving the problem. Here is the gist of the problem. In his classic text, Maxwell showed that electric forces between conductors in a vacuum could be calculated by invoking a field of stress in the vacuum. The Maxwell stress has since been used in deformable dielectrics. This practice has been on an insecure theoretical foundation, and has led to obvious disagreements with experimental observations.

The three of us re-formulated the theory, showing that the Maxwell stress is not applicable to deformable dielectrics in general, and that the effect of electric field on deformation is material-specific. (I should add that several other groups have reached the similar conclusion. We have discussed the literature in our JMPS paper, which has just become available online.)

By this time, Wei Hong, a postdoc in the group, also joined the project. Wei was a former student of the group, and is unusually intuitive about nearly all aspects of solid mechanics. He also knows about thermodynamics and kinetics. He helped us to realize that the dielectric behavior of elastomers is nearly the same as that of liquid. Consequently, the Maxwell stress is an adequate representation of elastomers. Also joined the project was Jinxiong Zhou, a visitor in the group. He led the effort to implement the theory using the finite element method.

Once Xuanhe saw the basic ingredients coming together, he went off, on his own initiative, to find interesting experimental observations that can be resolved within the new theory. Here is one experimental observation that he focused on. The dielectric elastomer is susceptible to a mode of failure known as pull-in instability. As the electric field increases, the elastomer thins down, so that the same voltage will induce an even higher electric field. The positive feedback may cause the elastomer to thin down drastically, resulting in even larger electric field. This electromechanical instability can be a precursor of electrical breakdown, and has long been recognized in the power industry as a failure mode of polymer insulators. The instability, however, was not properly understood theoretically. In particular, it was not clear how mechanical loads may affect this instability, even though there was clear experimental evidence that they do. He took the initiative and formulated a paper, which has just appeared in APL. We showed that the electromechanical instability occurs when the Hessian of the free-energy function ceases to be positive-definite. Our calculation shows that stability of the actuator is markedly enhanced by pre-stresses, agreeing with existing experimental observations.

He also found in a 2006 IJSS paper experimental evidence of a more subtle instability. It was observed that, when a layer of a dielectric elastomer is subject to a voltage, the homogeneous deformation can be unstable, giving way to an inhomogeneous deformation, such that two regions coexist in the layer, one being flat and the other wrinkled. The underlying cause of this behavior has not been discussed in the literature. We developed a theory to show how a homogenous deformation in the dielectric layer can give way to two coexistent states. This paper has just been accepted by PRB.

During all this time, Xuanhe and Wei have been calling to my attention that a much bigger and more exciting area of research is hydrogels, which are widely used in medical devices, drug delivery and tissue engineering. Maybe we should not spend all our time on dielectric elastomers.

A gel is formed when a large quantity of small molecules migrate into a network of long polymers, causing the network to swell. We have just submitted two papers on gels. In a paper led by Wei Hong, we formulated a theory of coupled mass transport and large deformation. The free energy of the gel results from two molecular processes: stretching the network, and mixing the network with the small molecules. Both the small molecules and the long polymers are taken to be incompressible, a constraint that we enforce by using a Lagrange multiplier, which coincides with the osmosis pressure or the swelling stress. The gel can undergo large deformation of two modes. The first mode results from the fast process of local rearrangement of molecules, allowing the gel to change shape but not volume. The second mode results from the slow process of long-range migration of the small molecules, allowing the gel to change both shape and volume. We assume that the local rearrangement is instantaneous, and model the long-range migration by assuming that the small molecules diffuse inside the gel.

What have I learned from this experience? I have of course learned quite a lot of large deformation and electrostatics. But more importantly, I have leaned to learn from students, particularly when I have no bright ideas. The relationship between a student and a professor is that of apprenticeship. The student has the time and energy, and has a fresh mind capable of asking questions uninhibited. (A Chinese saying: a new-born calf is not afraid of tigers.) The professor can offer his experience and judgment, relating the immediate problem to something deeper or broader. Also, if posing a new problem is a skill critical for the student's future job, perhaps he should learn the skill when he is a student, by getting involved in the process of posing new problems. To extend this idea, I have also involved Xuanhe in writing a proposal, yet another new practice in my group.

I have also started to have weekly meetings with two new students, hoping that they will help to pose better problems than I can do by myself.


Very nice and very instructive, and very honest behind the scenes look at graduate work. However, on a related note, I think the majority of theses fall into the following format, which often leads to disappointment, and lack of interest on part of the student. This is what makes choosing an advisor one of the most important parts of graduate school. 


PHD comics

N. Sukumar's picture

Zhigang, Nice to read about your recent experience on the foray into a new research area.  On a related note, I thought I'd share a link that I was pointed to. It would be of interest and a good read for all researchers---transcription of a seminar talk given by Richard Hamming, which is entitled ``You and Your Research.''

Zhigang Suo's picture

Thank you, Suku, for pointing to Hamming's talk.  Totally fascinating read.  Two points particularly resonate with me:

  • Be ambitious.  Identify the most significant problems in your field and try to work on them.
  • Start small.  Spend time on things that you can do.

I believe most mechanicians will appreciate this talk and learn from it.  From the bio at the end of the transcript, I learned that Hamming was a computer sceintist who worked on numerical analysis, among other things.  So what he did was not too far from what many mechanicians do.  In 1968, he won the top prize in computer science:  the Turing Award

Teng Li's picture

Zhigang, very much enjoyed reading your illuminating post, as usual.  I wish I had spent more time interacting with you back in the years when I was in the group at Princeton and Harvard.  This post should also be of interest to the PhD advisees (I've asked my students to read your post).

Some thoughts along the line. A great portion of the active iMechanica users are junior faculty members like myself.  The above advisor-advisee model is definitely valuable in shaping our advising style. Meanwhile, the sucess of practicing such a model by junior faculty members is often constrained by some other factors. For examples, the trial-and-error learning process takes time to reach a ripe idea, while junior faculty are often tied up with certain APT requirements in their earlier years.  We ourselves are also still accumulating experience and building up expertise. And not everyone (especially junior faculty) will be lucky to get a student or two as intuitive and enthusiastic as Xuanhe and Wei.  I believe I'm not alone suffering from these constraints.  Every senior professor like you was also once in the same boat.  Any valuable mentoring tips for junior faculty members will be appreciated by many of us.

Please keep doing this. 


Pradeep Sharma's picture


Your experience and other comments make interesting reading......Teng's struggles of junior faculty also resonate.

It is somewhat ironic that many of us are by temprament and training, "nerds" yet, our profession (at least the modern vesion of it as practised in US) requires us to be nerds+business manager+marketing manager+people manager+.......! I am reminded of something my former advisor once said when I asked him what it is like to be faculty. His response, "Being a professor is like striking out to start a new business". Over the last few years, I am continuously surprised by how true these words are turning out to be.....Personally, I have found (the hard way) that I am a better advisor if I do the following:

(i) Keep some research to myself and do it without students. Given the other multitude of tasks that we all have to do, this is quite slow going but really this also make me more patient with my students (---they may disagree!). In this category, pick topics that are not necessary fundable or technologically important.....just a twist of irony, all of (what I consider are) my good ideas have emerged from such curiosity driven forays.

(ii) Set the good student free......chances are he will do better without guidance or with only gentle guidance. Learn from him/her. Zhigang: this seems consistent with your recent experience.

(iii) Be selective...learn to say no

(iv) It is better to have a few good students than a large group

(v) Spend as much time as possible as early as possible on getting the student excited about the research topic.. I believe, this may be far more important than anything else.

Roozbeh Sanaei's picture

it was an educational experience about how an adviser can help to choose a problem topic.rule of an advisee is as important as rule of an advisor in progress of the research work. choosing which problems to solve is a very important task in professors profession. and i think it is most significant factor on research impact. unfortunately most proffesors dont pass a course on how to choose a problem!!!. and therefore it is an great idea to share such experiences which can not be learned in most of classrooms. although different fields have different interesting research areas. there are same concepts and principals in choosing a problem! it could be even an area of research in social aspects of science. and forums such as mechanica could be very helpful media to connecting people on help them to choose a problem topic. generally i think it was great post and similar posts would very interesting for me and other readers.


Thanks Zhigang for the very enlightening story. After enjoyed the reading myself, I quickly shared this post with one of my PhD students who is now a tenure track assistant professor and greatly need such advice. I wish to add a very valuable experience which I learned a lot from when working with zhigang. It is about motivating the students: motivate students to think, to explore, to be excited, to be passionate about his work, and to do creative work.


Koffi Enakoutsa's picture

Brillant and inspiring! Thank you Prof. Suo.

It reminds me of my years as graduate sudent with Prof. Jean Baptiste Leblond in Paris, France.

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