Saverio E. Spagnolie
@sespagnolie.bsky.social
Professor of Mathematics; Chemical & Biological Engineering, UW-Madison. I dig biological fluid dynamics, soft matter physics, and numerical methods. Vijayanagara (GMT Games).
https://people.math.wisc.edu/~spagnolie/
https://people.math.wisc.edu/~spagnolie/
Not finding ANYTHING helpful in Batchelor
November 13, 2025 at 5:11 AM
Not finding ANYTHING helpful in Batchelor
Engineer, physicist, Cedric Villani
October 8, 2025 at 12:58 AM
Engineer, physicist, Cedric Villani
Psst, your students want to hang out in Boulder next July. Application deadline is Jan. 15.
www.colorado.edu/conference/b...
www.colorado.edu/conference/b...
October 7, 2025 at 7:57 PM
Psst, your students want to hang out in Boulder next July. Application deadline is Jan. 15.
www.colorado.edu/conference/b...
www.colorado.edu/conference/b...
Without describing the experiment (soon!), please just enjoy with me a case where a simple model meets the data this well. Oh man. Math, I tell you. Good stuff.
October 1, 2025 at 5:36 AM
Without describing the experiment (soon!), please just enjoy with me a case where a simple model meets the data this well. Oh man. Math, I tell you. Good stuff.
Here's one from the first site (since it's working right now), a more focused look at higher ed (HERD). China is the red line that's going up up up.
September 23, 2025 at 12:28 AM
Here's one from the first site (since it's working right now), a more focused look at higher ed (HERD). China is the red line that's going up up up.
Yeah that site seems buggy, sometimes it cuts out. Here's a different site. This is gross domestic expenditures on R&D though (GERD), which includes more than just higher-ed R&D support.
ncses.nsf.gov/pubs/nsb2025...
ncses.nsf.gov/pubs/nsb2025...
September 23, 2025 at 12:26 AM
Yeah that site seems buggy, sometimes it cuts out. Here's a different site. This is gross domestic expenditures on R&D though (GERD), which includes more than just higher-ed R&D support.
ncses.nsf.gov/pubs/nsb2025...
ncses.nsf.gov/pubs/nsb2025...
What poster did you have hanging in your room as a kid?
September 14, 2025 at 12:25 AM
What poster did you have hanging in your room as a kid?
Choose your weapon.
September 3, 2025 at 1:03 PM
Choose your weapon.
Dublin has been so weird this week.
August 26, 2025 at 8:41 PM
Dublin has been so weird this week.
Standard practice here, a student's first paper earns some schwag.
August 7, 2025 at 2:53 PM
Standard practice here, a student's first paper earns some schwag.
I really enjoyed working with Jingyi Li and Laurel Ohm on this project. Thanks also to Thomas Chandler and Ido Lavi for very helpful conversations. Ido also has a very related paper on its way out which I like *a lot*, check it out. arxiv.org/pdf/2407.15149 20/20.
August 4, 2025 at 5:06 PM
I really enjoyed working with Jingyi Li and Laurel Ohm on this project. Thanks also to Thomas Chandler and Ido Lavi for very helpful conversations. Ido also has a very related paper on its way out which I like *a lot*, check it out. arxiv.org/pdf/2407.15149 20/20.
Finally, at higher particle activity, we observe a periodic "thrashing" mode. 19/20
August 4, 2025 at 5:06 PM
Finally, at higher particle activity, we observe a periodic "thrashing" mode. 19/20
We were able to analyze these states as well! The wave speed is enhanced by faster swimming, but is reduced by larger activity or particle volume fraction, or smaller LC
elasticity, since these contribute to larger LC deformations, which (as above) hinder particle transport. (Pe_s: Peclet #) 18/20
elasticity, since these contribute to larger LC deformations, which (as above) hinder particle transport. (Pe_s: Peclet #) 18/20
August 4, 2025 at 5:06 PM
We were able to analyze these states as well! The wave speed is enhanced by faster swimming, but is reduced by larger activity or particle volume fraction, or smaller LC
elasticity, since these contribute to larger LC deformations, which (as above) hinder particle transport. (Pe_s: Peclet #) 18/20
elasticity, since these contribute to larger LC deformations, which (as above) hinder particle transport. (Pe_s: Peclet #) 18/20
Why? Motile particles in bent regions move horizontally with their swimming speed, while the swimming motion of particles elsewhere is redirected vertically. This leads to faster particle evacuation from regions with large LC bending, and bands of particles “surfing” ahead of the bent regions. 17/20
August 4, 2025 at 5:06 PM
Why? Motile particles in bent regions move horizontally with their swimming speed, while the swimming motion of particles elsewhere is redirected vertically. This leads to faster particle evacuation from regions with large LC bending, and bands of particles “surfing” ahead of the bent regions. 17/20
So what does an arrested state look like when the particles are also swimming? Does the arrested state just translate with the particle swimming speed? No! Something new. Concentration bands form. Now the color below is the particle concentration. 16/20
August 4, 2025 at 5:06 PM
So what does an arrested state look like when the particles are also swimming? Does the arrested state just translate with the particle swimming speed? No! Something new. Concentration bands form. Now the color below is the particle concentration. 16/20
That \vartheta is the maximum director angle along the arrested curve. It satisfies the equation below, involving the complete elliptic integral of the first kind K(). Anyhow, we found the critical activity parameter beyond which the arrested state emerges: A=1. Nice to have exact solutions! 15/20
August 4, 2025 at 5:06 PM
That \vartheta is the maximum director angle along the arrested curve. It satisfies the equation below, involving the complete elliptic integral of the first kind K(). Anyhow, we found the critical activity parameter beyond which the arrested state emerges: A=1. Nice to have exact solutions! 15/20
You can linearize the equation to determine stability/instability, but to get the arrested state you need the nonlinearity. Fortunately, the equation is integrable! You need, you guessed it, Jacobi elliptic functions. That 'sn' is a function which lives in between a sine and square wave. 14/20
August 4, 2025 at 5:06 PM
You can linearize the equation to determine stability/instability, but to get the arrested state you need the nonlinearity. Fortunately, the equation is integrable! You need, you guessed it, Jacobi elliptic functions. That 'sn' is a function which lives in between a sine and square wave. 14/20
With our model, we were able to analyze these states. In the limit of small rotational viscosity, we derived a fantastic equation for the director angle, which depended only on an 'activity parameter' (A) which lumped a ton of details together (see the paper for definitions!) 13/20
August 4, 2025 at 5:06 PM
With our model, we were able to analyze these states. In the limit of small rotational viscosity, we derived a fantastic equation for the director angle, which depended only on an 'activity parameter' (A) which lumped a ton of details together (see the paper for definitions!) 13/20
These arrested states have been observed in a few experiments now. Here's an active nematic *on top* of a nematic LC, by Bantysh et al. (PRL, 2024). The arrested, flowing state emerges about 5 seconds in. A beautifully intricate system. 12/20
journals.aps.org/prl/abstract...
journals.aps.org/prl/abstract...
August 4, 2025 at 5:06 PM
These arrested states have been observed in a few experiments now. Here's an active nematic *on top* of a nematic LC, by Bantysh et al. (PRL, 2024). The arrested, flowing state emerges about 5 seconds in. A beautifully intricate system. 12/20
journals.aps.org/prl/abstract...
journals.aps.org/prl/abstract...
Diffusivity also plays a role. The mean elastic energy as a function of the anchoring strength is shown. On the right, particle diffusivity is lower. With smaller diffusion (e.g., smaller thermal energy), the anchoring strength
needed to trigger a nontrivial state is also lower, intuitively. 11/20
needed to trigger a nontrivial state is also lower, intuitively. 11/20
August 4, 2025 at 5:06 PM
Diffusivity also plays a role. The mean elastic energy as a function of the anchoring strength is shown. On the right, particle diffusivity is lower. With smaller diffusion (e.g., smaller thermal energy), the anchoring strength
needed to trigger a nontrivial state is also lower, intuitively. 11/20
needed to trigger a nontrivial state is also lower, intuitively. 11/20
The anchoring strength is a parameter which continuously tunes the model between active suspension theory in Newtonian fluids and an active nematic theory. The arrested states only emerge beyond a critical anchoring strength. Thanks to the referees who nudged this part of the investigation! 10/20
August 4, 2025 at 5:06 PM
The anchoring strength is a parameter which continuously tunes the model between active suspension theory in Newtonian fluids and an active nematic theory. The arrested states only emerge beyond a critical anchoring strength. Thanks to the referees who nudged this part of the investigation! 10/20
The higher the activity, the higher the wavenumbers present in the eventual arrested state. We also see what appears to be an elastic snap-through instability in a bulk fluid. Fluid mechanics ASMR? 9/20
August 4, 2025 at 5:06 PM
The higher the activity, the higher the wavenumbers present in the eventual arrested state. We also see what appears to be an elastic snap-through instability in a bulk fluid. Fluid mechanics ASMR? 9/20
At yet higher activity (or reduced elasticity), the system desires to reach the classical aperiodic oscillatory states of active suspensions in Newtonian flows. But the LC is still able to arrest the system into a steady flowing state. These are all at high anchoring strength so far, btw. 8/20
August 4, 2025 at 5:06 PM
At yet higher activity (or reduced elasticity), the system desires to reach the classical aperiodic oscillatory states of active suspensions in Newtonian flows. But the LC is still able to arrest the system into a steady flowing state. These are all at high anchoring strength so far, btw. 8/20
Increasing the activity, those aligned particles become susceptible to a classical bend instability. But rather than exploding into wildly unsteady "turbulence 😬", the development is arrested by LC elasticity, which penalizes bending. A steady flowing state emerges with a big bending wave. 7/20
August 4, 2025 at 5:06 PM
Increasing the activity, those aligned particles become susceptible to a classical bend instability. But rather than exploding into wildly unsteady "turbulence 😬", the development is arrested by LC elasticity, which penalizes bending. A steady flowing state emerges with a big bending wave. 7/20
Let's start in 2D, with extensile, immotile particles. At low activity, randomly initialized particles align with the LC. The background color is the LC elastic energy. Arrows show the average local direction of particles; white dashes show the LC direction. The LC also rotates until happy. 6/20
August 4, 2025 at 5:06 PM
Let's start in 2D, with extensile, immotile particles. At low activity, randomly initialized particles align with the LC. The background color is the LC elastic energy. Arrows show the average local direction of particles; white dashes show the LC direction. The LC also rotates until happy. 6/20