## 2020-01-13

### Fifth, Sixth, and Seventh Papers

My fifth, sixth, and seventh papers have been published! These require subscriptions to read, so here are alternate links to older preprints for the fifth, sixth, and seventh 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. I'm putting these three papers together in a single post because they form a trilogy of sorts, all having to do with finding the biggest number for how much heat, through light, can go from one body to another when they are really close together, or can go from one body into outer space. 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.

The fifth paper is called "T Operator Bounds on Angle-Integrated Absorption and Thermal Radiation for Arbitrary Objects", and is in volume 123, issue 5 of Physical Review Letters. This is the one that has to do with how much heat, through light, can go from one body to outer space. People knew before that the number for how much heat really big bodies can put through light into outer space grows like the surface area of the body, but for really small bodies it grows like the space of the whole body (volume), and they were not sure how these two things join in between. This paper lets people figure out what the most heat is that can go from a body through light into outer space no matter what the largest shape the body can sit in, and shows how to join the things that people knew before for middle-size bodies of different shapes. (Another press release from my department can be found here.)

The sixth paper is called "Fundamental limits to radiative heat transfer: Theory", and is in volume 101, issue 3 of Physical Review B, while the seventh paper is called "Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field", and is in volume 124, issue 1 of Physical Review Letters. Those two papers go together, so I'll write about them together. The sixth paper is about the math behind figuring out the biggest number for heat, through light, to go between two bodies. The seventh paper shows that heat, through light, going between two big flat bodies that are close together can be pretty close to the biggest number possible, so making the shapes of the bodies less simple than just flat surfaces is of no use.