David Bindel
@dbindel.bsky.social
Professing computing and applied math at Cornell. Numerical methods for data science, plasma physics, other stuff depending on the day. Director, Cornell Center for Applied Mathematics; Director, Simons Collaboration on Hidden Symmetries and Fusion Energy.
The movers will come tomorrow to take my stuff to my office in the new building. I will still spend some time in this office (I am CAM director through end of June 2028). But the books are moving.
August 14, 2025 at 8:33 PM
The movers will come tomorrow to take my stuff to my office in the new building. I will still spend some time in this office (I am CAM director through end of June 2028). But the books are moving.
Our wall calendar at home. I am not sure where J got it from.
March 16, 2025 at 12:04 AM
Our wall calendar at home. I am not sure where J got it from.
The walk home is still pretty.
February 11, 2025 at 10:44 PM
The walk home is still pretty.
Indeed, if we build the filter based on what we can see of the signal, we get something well adapted to extracting the limit c_0 from the *specific* signal, rather than something that works in general.
December 18, 2024 at 4:49 PM
Indeed, if we build the filter based on what we can see of the signal, we get something well adapted to extracting the limit c_0 from the *specific* signal, rather than something that works in general.
So: the role of averaging is to "filter out" all the oscillatory parts of the Fourier series. The standard Birkhoff average is an "all ones" filter corresponding to equi-spaced zeros in frequency space. The weighted Birkhoff averages build better filters which decay faster away from zero.
December 18, 2024 at 4:27 PM
So: the role of averaging is to "filter out" all the oscillatory parts of the Fourier series. The standard Birkhoff average is an "all ones" filter corresponding to equi-spaced zeros in frequency space. The weighted Birkhoff averages build better filters which decay faster away from zero.
The way we usually visualize this is with a Poincare plot: that is, we take a planar cross section slicing our "donut" and follow magnetic field lines from a starting point on that cross-section, making a dot each time the field line comes back.
December 18, 2024 at 3:59 PM
The way we usually visualize this is with a Poincare plot: that is, we take a planar cross section slicing our "donut" and follow magnetic field lines from a starting point on that cross-section, making a dot each time the field line comes back.
The idea of optimization under uncertainty (OUU) is to optimize a design in a way that it's robust to slight uncertainties, e.g. due to manufacturing error. We used so-called risk-neutral OUU, where the nominal objective f(x) is replaced by the smoother function E_U[f(x+U)] for random errors U.
![Picture of a sample objective function f(x) and a smoothed risk-neutral version E_U[f(x+U)]. The original objective has two minima, one around -0.5 that is very broad and one near 0.8 that is narrower and deeper. The risk-neutral version has similar minima locations, but the value near 0.8 is much higher than for f(x), because of the risk of evaluating at slightly the wrong input value.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:hgcj6ytfqij6ysadqj7tx7qk/bafkreicfr2xfeww3grphxxzthu5ik3d4tmhbr3rrkztr62zm4ttmh6rn5u@jpeg)
December 16, 2024 at 3:54 PM
The idea of optimization under uncertainty (OUU) is to optimize a design in a way that it's robust to slight uncertainties, e.g. due to manufacturing error. We used so-called risk-neutral OUU, where the nominal objective f(x) is replaced by the smoother function E_U[f(x+U)] for random errors U.
The current has to be there in an axisymmetric device. It's just a part of the physics. But what if we break axisymmetry, and get the "twist" to the magnetic field by changing the magnetic field as we go around? This is the idea of a stellarator.
December 15, 2024 at 9:22 PM
The current has to be there in an axisymmetric device. It's just a part of the physics. But what if we break axisymmetry, and get the "twist" to the magnetic field by changing the magnetic field as we go around? This is the idea of a stellarator.
There are a couple ways to get the field lines to make these spiraling patterns. One involves an axisymmetric device with a strong current inside the plasma that produces the poloidal component of the magnetic field. This is the tokamak concept.
December 15, 2024 at 9:15 PM
There are a couple ways to get the field lines to make these spiraling patterns. One involves an axisymmetric device with a strong current inside the plasma that produces the poloidal component of the magnetic field. This is the tokamak concept.
This is conceptually a little like a honey dipper: when you dip it in honey and spin it around its axis, the honey stays attached because it is sometimes falling away from the center (when it's at the bottom) and sometimes toward the center (when it's at the top).
December 15, 2024 at 9:08 PM
This is conceptually a little like a honey dipper: when you dip it in honey and spin it around its axis, the honey stays attached because it is sometimes falling away from the center (when it's at the bottom) and sometimes toward the center (when it's at the top).
Of course, making a straight magnetic field doesn't really satisfy the goal of confinement -- eventually, things will go flying out an end. We'd like to curve the magnetic field around some central axis, so that particles follow it around like a race track. Unfortunately, then the particles drift.
December 15, 2024 at 9:04 PM
Of course, making a straight magnetic field doesn't really satisfy the goal of confinement -- eventually, things will go flying out an end. We'd like to curve the magnetic field around some central axis, so that particles follow it around like a race track. Unfortunately, then the particles drift.
In a straight magnetic field, charged particles tend to gyrate around the field lines. That is, they follow a spiraling path that stays pretty close to one field line.
December 15, 2024 at 9:00 PM
In a straight magnetic field, charged particles tend to gyrate around the field lines. That is, they follow a spiraling path that stays pretty close to one field line.
Fusion happens when two nuclei combine to form a nucleus of a heavier element. This happens all the time in the sun. One of the easier fusion reactions to get to happen involves combining deuterium and tritium nuclei to get helium nuclei (alpha particles) and neutrons.
December 15, 2024 at 8:49 PM
Fusion happens when two nuclei combine to form a nucleus of a heavier element. This happens all the time in the sun. One of the easier fusion reactions to get to happen involves combining deuterium and tritium nuclei to get helium nuclei (alpha particles) and neutrons.
... and on the other, they sometimes forgot that the mathematicians there had *not* been thinking about these things for decades. Sometimes we mathematicians would ask an innocuous (to us) terminology question, and then the plasma folks would argue about the answer, exacerbating our confusion.
December 15, 2024 at 8:37 PM
... and on the other, they sometimes forgot that the mathematicians there had *not* been thinking about these things for decades. Sometimes we mathematicians would ask an innocuous (to us) terminology question, and then the plasma folks would argue about the answer, exacerbating our confusion.
This is not just used for sensing rotations. We know about things like the sun's magnetic field by an analogous effect. The Zeeman effect is a splitting of a spectral line for a (very symmetric) atom due to a (symmetry-breaking) static magnetic field.
December 5, 2024 at 9:23 PM
This is not just used for sensing rotations. We know about things like the sun's magnetic field by an analogous effect. The Zeeman effect is a splitting of a spectral line for a (very symmetric) atom due to a (symmetry-breaking) static magnetic field.
The basic principle is the same as in Foucault's pendulum, which demonstrates the rotation of the earth. The pendulum has two modes of oscillation: front-to-back and side-to-side, say. Each has the same frequency. And the Coriolis effect results in a transfer of energy between them.
December 5, 2024 at 9:12 PM
The basic principle is the same as in Foucault's pendulum, which demonstrates the rotation of the earth. The pendulum has two modes of oscillation: front-to-back and side-to-side, say. Each has the same frequency. And the Coriolis effect results in a transfer of energy between them.
Anyhow, I started learning about all this stuff when Sunil Bhave (who I had worked on long before) started talking to me about a micro-machined version of the HRG that his student Laura Fegely was working on. It's a device that's much smaller than the HRG, and doesn't cost so much to make.
December 5, 2024 at 9:08 PM
Anyhow, I started learning about all this stuff when Sunil Bhave (who I had worked on long before) started talking to me about a micro-machined version of the HRG that his student Laura Fegely was working on. It's a device that's much smaller than the HRG, and doesn't cost so much to make.
In fact, the Hemispherical Resonant Gyroscope (HRG) uses exactly the same principle that Bryan laid out in his paper to measure rotation. Of course, it's a pretty expensive wineglass -- on the order of 100K / axis. These are mostly used for long-range space missions.
December 5, 2024 at 9:03 PM
In fact, the Hemispherical Resonant Gyroscope (HRG) uses exactly the same principle that Bryan laid out in his paper to measure rotation. Of course, it's a pretty expensive wineglass -- on the order of 100K / axis. These are mostly used for long-range space missions.
Here's what my computer heard when I tried ringing the bowl with the record player off and on, respectively. You can see the beating in the second image!
December 5, 2024 at 8:53 PM
Here's what my computer heard when I tried ringing the bowl with the record player off and on, respectively. You can see the beating in the second image!
I am not primarily an experimentalist, but at some point this paper tempted me into it. Here's a prayer bowl and record player (both borrowed from J), since we don't have any wineglasses nice enough to ring for an extended period.
December 5, 2024 at 8:51 PM
I am not primarily an experimentalist, but at some point this paper tempted me into it. Here's a prayer bowl and record player (both borrowed from J), since we don't have any wineglasses nice enough to ring for an extended period.
We start back in the 19th century, with the work of G.H. Bryan. A Fellow of the Royal Society, Bryan was best known for his work on stability in aviation, but also did important work in thermodynamics and hydrodynamics.
December 5, 2024 at 8:41 PM
We start back in the 19th century, with the work of G.H. Bryan. A Fellow of the Royal Society, Bryan was best known for his work on stability in aviation, but also did important work in thermodynamics and hydrodynamics.
