iiinova — where your digital self keeps evolving

David Bindel @dbindel.bsky.social · 20/04/2026

Spring in Ithaca. Mid 70s on Saturday, snow flurries yesterday and today.

A bush covered with snow in the foreground. In the background, a cherry tree in bloom, with snow dusting the top. Ithaca campus April 20, 2026.

010

David Bindel @dbindel.bsky.social · 27/02/2026

We are hitting the leading edge of spring in Ithaca. I love my walk home this time of year.

Sunset behind the bell tower on the Cornell campus.

040

David Bindel @dbindel.bsky.social · 14/08/2025

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.

060

David Bindel @dbindel.bsky.social · 16/03/2025

Our wall calendar at home. I am not sure where J got it from.

Calendar page for March, with a picture of a sad cat among a bunch of yarn. The caption reads "Due to your refusal to embrace violence, I will no longer be discussing the revolution with you."

030

David Bindel @dbindel.bsky.social · 11/02/2025

The walk home is still pretty.

Cornell Libe slope, covered with snow. Cirrus clouds colored by sunset in the background.

010

David Bindel @dbindel.bsky.social · 18/12/2024

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.

Picture of a signal-adapted filter for weighted Birkhoff averaging. The filter magnitude has zeros closer to multiples of the rotation number.

120

David Bindel @dbindel.bsky.social · 18/12/2024

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.

Picture of the amplitude of two filters. One is the "all ones" filter for Birkhoff averaging, one is the filter for weighted Birkhoff averaging.
This is the case where both have 12 zeros. Both are 1 at the origin, and decay for frequencies away from zero.

110

David Bindel @dbindel.bsky.social · 18/12/2024

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.

Diagram of a Poincare section of the NCSX stellarator. Labels point to magnetic surfaces, chaotic regions, and magnetic islands. An expanded inset shows the islands more clearly.

121

David Bindel @dbindel.bsky.social · 16/12/2024

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.

120

David Bindel @dbindel.bsky.social · 15/12/2024

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.

Schematic of a stellarator. Differently-shaped electromagnetic coils produce the confining magnetic field, with spiraling field lines that follow magnetic surfaces.

120

David Bindel @dbindel.bsky.social · 15/12/2024

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.

Schematic of a tokamak. Poloidal field coils generate a magnetic field in the toroidal direction. Toroidal field coils (and current in the plasma) generate a poloidal field. Together, the two produce a helical magnetic field.

120

David Bindel @dbindel.bsky.social · 15/12/2024

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).

Schematic of a honey dipper. As it is spun on its axis, the honey clinging to the end is sometimes pulled away from the center (when the honey is on the bottom) and sometimes toward the center (when the honey is on the top).

120

David Bindel @dbindel.bsky.social · 15/12/2024

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.

Picture of a curved magnetic field line and associated charged particle trajectory. In addition to gyrating, the charged particle drifts off the field line.

120

David Bindel @dbindel.bsky.social · 15/12/2024

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.

Picture of straight magnetic fields. Charged particles are shown spiraling around the field lines.

120

David Bindel @dbindel.bsky.social · 15/12/2024

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.

Deuterium nucleus (hydrogen with one neutron) and tritium nucleus (hydrogen with two neutrons) fuse to form a helium nucleus with two neutrons (an alpha particle) with 3.5 mega-electron-volts (MeV) extra energy and a free neutron with 14.1 MeV energy.

110

David Bindel @dbindel.bsky.social · 15/12/2024

... 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.

Picture of a bunny with a pancake on its head. Text around the image reads "I have no idea what you're talking about... so here's a bunny with a pancake on its head."

130

David Bindel @dbindel.bsky.social · 05/12/2024

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.

Picture of a spectrum next to a picture of a sunspot. The spectrum shows splitting of the spectral lines associated with the Zeeman effect.

100

David Bindel @dbindel.bsky.social · 05/12/2024

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.

100

David Bindel @dbindel.bsky.social · 05/12/2024

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.

120

David Bindel @dbindel.bsky.social · 05/12/2024

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.

Picture of a hemispherical resonator next to a dime for scale (the hemisphere is just a little bit bigger).

100

David Bindel @dbindel.bsky.social · 05/12/2024

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!

100

David Bindel @dbindel.bsky.social · 05/12/2024

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.

Picture of a metal prayer bowl setting atop a record player.

100

David Bindel @dbindel.bsky.social · 05/12/2024

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.