Fellow theorist Thoreau just had a cool post "What do theoretical physicists actually do?". In the post, he answers the question by looking at some of his papers and analyzing what the work entailed and how it differed from what students are taught to consider as theory based on their lecture courses.
The purpose of this post is twofold. First, I would like to tell you a little bit about some of the work I do, in a fashion similar to what Thoreau did. I have formal training in theoretical physics as well as an engineering discipline, and I my work is theoretical/computational* in the field of condensed matter physics. I work on problems ranging from very basic (firmly in the physics realm) to very applied (firmly in the engineering realm). Most of my work is published in Physical Review B, Applied Physics Letters, Journal of Applied Physics, and ACS Nano (reputable society level journals). Higher impact papers are published in the prestigious Physical Review Letters (often lovingly called Physical Review Lottery) and certain GlamourMagz (Nature, Nature Materials/Physics/Photonics/Nanotechnology).
My most cited paper is a GlamourMag paper with experimental colleagues. They came to me with some excellent experimental data, but that alone was not enough for a high profile paper, because it was not clear what was going on. We talked a few times about the details of experiments, and we came up with a qualitative picture that we all felt corresponded with the experiment. Then it took me a few days to set up the theoretical model -- in this case, an ordinary differential equation with appropriate boundary conditions; the novelty was in recognizing how the boundary conditions need to be set up in order to have a well-posed problem that corresponds to experiment. The derivations took a few days and another couple of days to code it up, and we had a quantitative model that corresponded with the data well and was intuitively plausible. Ultimately, we published a nice high impact paper, and I often joke that this is the easiest paper I have ever done, yet it brings the best rewards. The code, which is not very complicated or long, is still being used and fiddled with by many of my collaborators' experimental students.
I do a lot of theory connected to experiment (Massimo would call me an "experimentalist without a screwdriver"). My students enjoy such projects, as it means they get to collaborate with experimental students a lot, so the more the merrier. Also, this work helps my students get to know other professors really well (great for when you need those recommendation letters). I also have projects as part of larger theory/experiment collaborations, where the theory is virtually independent. For instance, on one such project, the question we asked was a very broad, general question, which at the time had neither a theoretical nor an experimental answer. So the experimental folks did some serious equipment building, while a theory collaborator and I, with a joint student, did some serious code development. This was a type of problem where you generally know what types of partial differential equations you need to write down to describe the system, but solving them together is extremely complicated. So the challenge for us in this case was to develop a computational tool that could solve all these equations in realistic systems and self-consistently (e.g. output from the solution to one set of equations is input for the second set, output from the second one is input for the first; you need a set of outputs that simultaneously satisfies both sets of equations; this is usually achieved using iterative procedures). It took a full three years with a very talented and independent student (so it would have taken significantly longer with an average one), and we now have a series of papers that promise to become very influential as they open completely new computational vistas.
My own personal inclination and most of my formal training was towards the "pen and paper" theory. However, once I came to the US and started working in a more applied field in grad school, I have come to really enjoy numerical computation, as it really enables you to get much closer to reality (especially in condensed matter physics) than you ever could with just a pen and paper. Some of my best cited "theory only" work deals with careful calculations of properties of systems that have become very "hot" in the last several years. We offered a rigorous analysis of their properties, with many important details, and predicted that the properties were much more modest than some initial flashy experiements suggested. Indeed, several years later, careful experiments showed exactly what we had predicted (quantitatively). Often, I feel my group's job is to deliver bad news -- that things are not as fast, cool, or otherwise shiny as one would hope. That's your fate when you work in the so-called "dirty limit" (means systems with lots of disorder, strain, and various imperfections; realistic systems are nearly always "dirty").
And then there are the super fun theory projects, where perhaps you get to dip into some math that you don't use every day, such as differential geometry or group theory in my work, and you get to derive a completely new and beautiful theoretical model (i.e. a new set of equations) that is capable of describing a whole class of heretofore un- or underexplored systems. I loooove this type of work; my PhD was like that and I published this type of work alone for the first several years on the TT. Now, I find this type of work is very rewarding (intellectually), but it is not for everyone. Most of my students are interested in more applied work, with ties to experiment, where the model (underlying equations) is known at least in principle, and where the bulk of the work is computational. Those who thrive on the more math-heavy project are harder to find; it's even more rare to find a student who is really into these mathematically challenging problems but can also write code well. I am lucky to have one excellent student who is like this (yes, that's the one who gives me the most headaches; but he's super talented. *sigh*), and it seems that one of my newbie students will be like that too. Otherwise, these projects would have to wait for me, and that would unfortunately be a very long wait, considering how busy the rest of my job keeps me.
All in all, I enjoy a diverse research portfolio, even if it makes me "a jack of all trades, a master of none" (and is likely not the best way to quickly achieve upper echelons in your chosen subfield). As doing theory costs much less than experiment, it is much easier to change fields or research directions -- you don't have to raise lots of funds to do the transition, which is a major perk (I wrote previously about the relative benefits of doing experiment vs theory.)
This brings me to the second purpose of this post: to start a carnival of sorts, with people who do theory/computation in the sciences contributing with a post on what their experiences in their daily work are. I have no idea how successful this call would be, but let's say within the next week or so:
If you do theoretical/computational work in the sciences, please consider writing a post that tells us a little bit about what your work entails, what you enjoy/dislike, what types of problems you tackle, what made you chose your specialization, etc. You don't have to be too specific, but you certainly can if you want. Send a link (a comment here or drop me an email) so I can aggregate the posts. Even if you don't blog, consider either writing a lengthier comment here and I will link to that as your post (please don't post as Anonymous, give yourself some nickname for the occasion) or, alternatively, email me the text and I will put it up as a guest post.
Finally, this post would not be complete without a link to the (fairly new) APS Division of Computational Physics news blog.
Happy calculations, and may all your iterations converge!
* See, for instance, this post by Massimo on why computational physics is not a special third branch of physics, but means you are a theorist who does calculations primarily on a computer.