To answer WHY? We dug into structural rigidity theory, and third-order loops have been hypothesized to be the smallest minimal rigid structure. As per Lamans’ theorem (1970s), triangles are the smallest isostatic structures that do not deform under externally applied load. Happy to chat!

FINAL REVEAL: Viscosity collapses beautifully when plotted against the number of 3rd-order loops.
This collapse is universal — independent of stress, volume fraction, or even friction. We even find a power law behavior, signifying max. n3 at jamming.

This is where things got interesting: The mean-field golden standard models suggest viscosity to be driven by the frictional number of contacts. To test this, we performed extensive simulations changing packing fraction, stress, and sliding friction.
Spoiler: NO collapse

Earlier work hinted that DST onset ≈ loop formation.
Here, we visualized them directly. Sure enough, loops first appear right as suspensions undergo DST. We tracked how 3rd–8th order loops evolve with stress, packing fraction, and friction.

To answer the question: "What is the motif that underpins the DST transition?"
Enters network science: We disentangled our frictional network into 1) isolated edges, 2) Connected edges, and 3) closed cycles, aka loops (3-8).

It is established that DST manifests itself as a stress-activated transition from an unconstrained to a constrained state, leading to the formation of the frictional contact network. Now the question we had was “How about the topology/motif of this network that underpins DST?”

Such an amazing story of an excellent researcher in a wonderful lab.. Congrats :)

Thanks, Karen! I would love to chat more!

Thanks so much, Ryan! Appreciate the shoutout! :)

This is massive, and we are excited to go beyond just the contact network. Our dream is to predict the flow of suspension based on a snapshot. Stay tuned for more updates! Feel free to reach out to us if you'd like to chat.

With lots of hard work (2 years), Armin came up with the brilliant framework of deepGNN, inspired by work from Rituparno Mandal, showing that if we know the initial condition (or particle position) and train the model on low viscosity states, we can predict FCN in high viscosity states.

My question to Armin was: Experiments capturing the network are hard (massive respect to experimentalists), simulations are nice (but cumbersome close to jamming). Can we use ML? Can we train a machine on faster simulations and predict conditions close to jamming?

Wondrous works by @lilianhsiao.bsky.social, by Safa Jamali, @emanueladelgado.bsky.social in dense suspensions, and by @karenedaniels.bsky.social in dry granular materials have shown that my crucial contact network is to predict the response of dense amorphous materials, which was our motivation