My first academic paper has just been submitted to the publisher! I still can’t quite believe it. Submitting it doesn’t necessarily mean it will actually get published. The journal might refuse it outright, and even if they accept it, it will have to go to the reviewer, then come back to us, be corrected and then be sent of again. But still, I am really proud. I wrote the paper with two other people but I was surprised to find that they listed me as first author, which means the paper will mainly be cited under my name.

The contend of the paper doesn’t have much to do with theoretical physics. Last summer, I joined a research group in the Department for Material Sciences for two months and my results from that time have become this paper.

As you probably know, materials will expand or shrink when you heat them up or cool them down. Generally, things get bigger when they are heated up and smaller when they are cooled down but how much they grow or shrink depends on the actual material itself. If you know what to look for, you can see signs of this everywhere. Big bridges, for example, often have lines across them with a softer material in the cracks. This is so that the big concrete slabs of the bridges can expand or contract without ripping the whole structure apart. Old railroad tracks in warm places are often bent because they expanded in the heat but they didn’t really have any space so they bulge out sideways.

Most of the time, this expansion and contraction is no problem. For a start, it is generally quite small on an everyday scale. Secondly, most of the time things just have space around them. It does however become a problem if you have two materials stuck together very firmly, that expand and contract differently. This is especially bad when you have to deal with very large temperature changes, a few hundred degrees for example. When the layers try to expand, one will expand a lot more than the other. Things will start getting bent out of shape by the internal forces and eventually, the two layers will start breaking apart. In real life, this often forms quite intricate crack patterns. You can see an example of this in paint peeling of metal surfaces in winter.

I looked at a very simple situation of this kind, just two layers of different materials stuck together, and then modelled (using a computer) what happens when you heat this piece up or cool it down. When doing this sort of thing on a computer, one needs equations to describe all that internal pulling, the deformation and the expansion. The problem is that as soon as cracks form, these equations get in trouble because they don’t deal very well with having to work with a gap in the piece. Most of the time this is done using a method called the finite element method but the results have been a bit disappointing. The crack patterns were often much too simple in comparison to the real thing. I now tried to do the same thing using a new method called Peridynamics and it worked a lot better.

Keep your fingers crossed for me that this goes through!

Die Daumen sind gedrückt. Ich habe zwar wirklich keinen Dunst von Physik, aber was du beschrieben hast war einleuchtend, verständlich und durch die lebensnahen Beispiele sehr nachvollziehbar. Okay, die Methoden habe ich mir jetzt nicht angeguckt. Aber ich wollte dir mitgeteilt haben, dass du Physik auf spannende Weise rüberbringen kannst. Jawohl. :D

ReplyDeleteOh, vielen vielen Dank. Ich gebe mir viel Mühe Dinge eindrücklich zu erklären. Ihr dürft gerne Rückfragen stellen :)

DeleteCongratulations! Your first paper, wow. Hope it will be published (If so can you tell the title? Sounds interesting). I agree with Noctua, your explanation about a topic is so good, better than a magazine..

ReplyDeleteOh btw, in my current lecture we talk about visualization of those problems (show you critical areas in components or also detect organs from a MRT :) )

I'll let you know the details once it has actually got published. :) Interesting that you just talked about this sort of thing as well. I was told that there are many many applications but I actually never looked much into it. I'm more of a theory girl ;)

DeleteHerzlichen Glückwunsch!!

ReplyDeleteDanke.

DeleteWelcome to Condensed Matter Physics :mrgreen:! This is so much more fertile than quantum gravity ;).

ReplyDeleteSorry, I forgot to congratulate.

DeleteWhat kind of equations did you use?

:P Maybe it is. I just find quantum gravity that much more

Deleteinteresting.

Peridynamics models the solid materials as a mesh of "bonds" that connect nodes inside the material. It's not on an atomic scale but generally much much coarser. One then needs equations that describe the stretch of every bond in a variety of physical situations. These tend to just be fairly simple equations of node separation and temperature in our case. Once a maximum stretch of a single bond has been reached it "breaks" ie looses its stiffness.

Ah ... integro-differential equations. Interesting, but unfortunately I never worked with them as a scientist. But I was alwas fascinated by the memory effects, especially in the context of deriving macroscopic equations from microscopic model in the context of the Mori-Zwanzig-approach and related theories.

Deletehttp://en.wikipedia.org/wiki/Zwanzig_projection_operator

In May I was just re-reading a textbook on this stuff.

Maybe I am too curious and embarassing, but what numerical methods do you use to solve the equations? Or are you using analytical solutions/approximations?

Actually, we cheated :D and modeled the mesh in Abaqus (http://en.wikipedia.org/wiki/Abaqus) The idea was that it would be fairly easy to use for people who aren't experts on numerical methods.

DeleteWell, I would not call this cheating. It is the recommended way to use a programming package, when doing finite elements.

DeleteBut I am a nerd, who wants to to all numerical computing by writing all the code with plain C++ or Java.

The only subject where I failed so far, was to program a computer algebra module calculating the greatest common divisor of a polynom of degree n in m variables by symbolic manipulation (not numerics). One line of the algorithm in the textbook expands to several hundred lines of C++ code, because of the special cases that have to be considered. This project is halted. Maybe I will finish it after my retirement LOL.

BTW: I realized that the peridynamics models are not integro-differential equations of the Mori-Zwanzig type. There is only integration in space, but not in time.

Hehe, I had only written things from scratch before which is why I said "cheating". Of course I know it's not really cheating, what's the point of constantly reinventing the wheel?

DeleteThat sounds complicated, fun, and a bit like one of the Euler Projects: http://projecteuler.net/ I should get back to doing these.

This is so exciting! Congratulations and best of luck :)

ReplyDeleteI know. You can't believe how excited I am. I have been bouncing about like crazy. I think my flatmates are seriously considering locking me in my room :D

DeleteCongratulations! This is a great achievement (and will make PhD applications much easier!)!

ReplyDeleteThank you! :)

Delete