Counting Particles - Wiggly Lab

This is the hot topic of the Wiggly Lab! Inspired by an idea formulated by Schmoluchowski at the beginning of the 20th century, we count particles in virtual observation boxes of an experimental image or a simulation. The number of particles in a box fluctuates in time to particle dynamics, as they come in and out of the box. This seemingly simple approach is actually extremely powerful. Provided careful models are constructed, we can learn the dynamic properties of the particles from the time-dependent statistics of the counts!

Gallery

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(image credit: Brennan Sprinkle) Counting particles in boxes of different sizes can inform us on various dynamics. Small boxes (yellow) inform on individual dynamics while large boxes (pink) inform on group motion.

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(image credit: Brennan Sprinkle) Counting in multiple boxes of an image or a simulation improves statistics and allows us to learn dynamic properties reliably from the fluctuating signals.

Related Publications

We introduced this approach, we called ``Countoscope'', to measure self and collective diffusion coefficients of colloids at equilibrium [1].
It can also be used in ion simulations to shed light on charge dynamics [2], and bears subtle but important consequences in current fluctuations in nanopores and nanofluidic systems [3].
We are now hoping to investigate out-of-equilibrium suspensions! Stay tuned for more.
[1] The Countoscope: Measuring Self and Collective Dynamics without Trajectories E. K. R. MacKay, S. Marbach, B. Sprinkle, A. Thorneywork arXiv preprint 2311.00647

[2] Ionic fluctuations in finite volumes: fractional noise and hyperuniformity M. T. Hoang Ngoc, B. Rotenberg, S. Marbach Faraday Discussions 2023

[3] Intrinsic fractional noise in nanopores: The effect of reservoirs S. Marbach J. Chem. Phys. 154 (17), 171101