My eighth, ninth, tenth, and eleventh papers have been published! These require subscriptions to read, so here are alternate links to older preprints for the eighth, ninth, tenth, and eleventh papers, respectively (which have most of the same content, with some minor changes to explanations, citations, and figures relative to the published versions). As with my previous papers, in the interest of explaining these ideas in a way that is easy to understand, I am using the ten hundred most used words in English (except for the two lines that came before this one), as put together from the XKCD Simple Writer. I will use numbers sometimes without completely writing them out, use words for certain names of things without explaining further, and explain less used words when they come up. Keep reading to see what comes next. While these papers aren't as closely related to each other as the previous three, there are enough relations that I'm putting them together in a single post. These papers need a lot more math (note: "math" isn't one of the ten hundred words) than the papers before, and because they need a lot of thinking to get, I actually won't say as much about them.

On another note, this is a milestone for me because these are the last papers from my PhD in which I was a leading author. I still have one more review paper left to be published, but as that has been submitted to the journal and as I'm not the leading author, I don't really need to worry about that at this point. (Of course, once that is published, I will write a blog post summarizing it, though as it is a review paper, that summary will probably be quite short.) Thus, I am truly done with the work from my PhD, and can fully shift my mindset away from physics toward thinking about problems in transportation policy, as I will do in my postdoctoral research at UC Davis.

The eighth paper is called "Fundamental limits to attractive and repulsive Casimir-Polder forces", and is in volume 101, issue 5 of Physical Review A. This one is about van der Waals (vdW) forces, which are also called Casimir forces; these are the forces that let geckos stick to anything, no matter what it is made of. When two things stick together or push away from each other, in which one of the things is much smaller than the other, they are called Casimir-Polder forces. It is hard to change the shape of the small thing, because it is usually too small, but it might not be so hard to change the shape of the big thing. Given this, people have wondered whether a small and large thing can stick together or push away from each other with more force by changing the shape of the big thing. This paper shows that if the big thing is just a simple flat surface, the force by which the big thing sticks to the small thing is almost as much as is possible for two things sticking together. For two things pushing away from each other, the big thing has to have a much less simple shape, but the paper shows that some of those shapes that people have come up with give forces of pushing away from each other that are much smaller than the biggest possible forces of pushing away from each other.

The ninth paper is called "Fluctuational electrodynamics in atomic and macroscopic systems: van der Waals interactions and radiative heat transfer", and is in volume 102, issue 8 of Physical Review B. It is pretty close to the second, third, and fourth papers, being about how to figure out the vdW forces as well as heat (through light) that go between atoms or molecules, which are the tiny things that make up all matter, and bigger things. Those papers were about showing what new ways vdW forces and heat (through light) could act in those groups of things. This paper is more about the math that goes into figuring those ideas out. It works by showing that atoms, molecules, and bigger things are all actually not so different when it comes to the math, and that there are some really hard problems with the math that need to be worked out to go farther with these ideas.

The tenth paper is called "Mechanical relations between conductive and radiative heat transfer", while the eleventh paper is called "Channel-based algebraic limits to conductive heat transfer"; both are also in volume 102, issue 8 of Physical Review B, the ideas of both papers are close to each other, and the ideas of the tenth paper are close to those of the ninth paper, while the ideas of the eleventh paper are close to those of the sixth paper. The tenth paper shows how the math works to figure out how heat, whether through light, two things coming close enough to touch each other, or other ways, can go between two things. This means that the math for figuring out how heat goes through light is actually pretty close to that for how heat goes through two things touching. This also means that the math can be stretched further to figure out how heat goes through light and through two things coming close enough to touch, at the same time, and the heat after thinking about those two ways together is not just the heat from one way added to the heat from the other way. The eleventh paper shows that this math for showing how heat goes through light being so close to the math for showing how heat goes through two things coming close enough to touch means that the math for showing the biggest heat that can go through light can be stretched to figure out the biggest heat that can go between two things that are touching each other. It then shows that the numbers people thought of before for how big the heat could be for two things touching each other were a lot bigger than they should have been.

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