I saw an interesting post in the Physics Today blog a few weeks ago. Not only was the research presented interesting and important, the post brought up a good point about using limits to better understand physical phenomena.
The researchers verified their model by making one of the parameters unrealistically large. The point being that if the simulation is working correctly, and, in this case, the stiffness of the skull material is made extremely high, the pressure spikes seen in the results should go away. And they did.
In my research, I am looking at numerical simulations of diffraction efficiency in multiplexed volume holograms. It is well-known in optics how a single volume grating operates for a given input beam, but it is less well-known what happens when you have two or three or fifty gratings in the same optical element.
Like the research in the post, limits can be used to help verify the model. Instead of making a parameter very large, though, I make a parameter very small. In the case of two simultaneous gratings, if the index modulation (the depth or strength) of one of the gratings is made very small, the results should approach the well-known results for the case where the other grating exists by itself. And they do.
If you’re not sure if your model is working correctly, be sure take some parameters to a limit for which you know what to expect. This won’t necessarily tell you if your model is correct, but it should tell you if it’s wrong.
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