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# Does anyone understand how Floquet-Bloch boundary conditions work in this context?

## Does anyone understand how Floquet-Bloch boundary conditions work in this context?

(OP)
Does anyone understand how Floquet-Bloch boundary conditions work in this context? Seems like Bloch-Floquet boundary conditions can do anything? Would it be possible to explain in layman's terms how it works? I have spent hours trying to read up on it but still cant figure it out.

### RE: Does anyone understand how Floquet-Bloch boundary conditions work in this context?

I don't think this is the best place for this question... but floquet-bloch b.c.s are used in quantum mechanics to solve schrodingers equation with a periodic potential. You can think of the crystalline structure of a metal as having periodic boundary conditions. Effectively, this allows you to extrapolate out from a single crystal (or periodic element), the behavior on a -macro scale. By looking at a single element, you can see the effects of modes that are larger in span than a single element. Practically, this means you can exploit the periodicity to simplify the calculations (and reduce the meshed region to a single period).

### RE: Does anyone understand how Floquet-Bloch boundary conditions work in this context?

Just what problem are you trying to solve?

### RE: Does anyone understand how Floquet-Bloch boundary conditions work in this context?

You might check out:
Felix Bloch, Z. Physik 52,1955 commonly known as Bloch's theorem, though previously known as Floquet's Theorm.
or
E.I Whittaker and G.N. Watson,"Modern analysis" Cambridge Univ. Press (1948), p.412.

### RE: Does anyone understand how Floquet-Bloch boundary conditions work in this context?

#### Quote:

I don't think this is the best place for this question... but floquet-bloch b.c.s are used in quantum mechanics to solve schrodingers equation with a periodic potential. You can think of the crystalline structure of a metal as having periodic boundary conditions. Effectively, this allows you to extrapolate out from a single crystal (or periodic element), the behavior on a -macro scale. By looking at a single element, you can see the effects of modes that are larger in span than a single element. Practically, this means you can exploit the periodicity to simplify the calculations (and reduce the meshed region to a single period).

Actually this is probably a great place for it, as I've asked questions about elastic wave problems here before and have gotten some good answers. Re-posting what I did on the Structural Board to this question (so maybe we can build on it; I found similar info to what you found):

Going back through some (elastic) wave propagation texts of mine, this appears to be a necessary boundary condition when using the wave types necessary in periodic structures (i.e. structures composed of repetitive similar units) or composite type structures.

[......]

By the way, I came across this today:

https://www.iap.uni-jena.de/iapmedia/de/Lecture/Co...

It goes into Floquet-Bloch boundary conditions. (And in fairly understandable terms.)

One thing about elastic wave propagation analysis (using spectral FEA software; and to put this as close to "layman's terms" as possible): there are all sorts of elements/boundary conditions to get the appropriate response. (I.e. allow certain waves and frequencies to pass.....and in other cases: get rid of them.) The so-called "throw-off" element is another example. It is a element used when modeling a very long structure where the reflection of the elastic waves would not give a significant response. (Ergo you want to "throw-off" (or out) the elastic wave once it reaches a point.....rather than modeling something too big for your purposes.)

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