Detecting active L’evy particles using differential dynamic microscopy

arXiv:2511.00775v1 Announce Type: cross
Abstract: Detecting L’evy flights of cells has been a challenging problem in experiments. The challenge lies in accessing data in spatiotemporal scales across orders of magnitude, which is necessary for reliably extracting a power-law scaling. Differential dynamic microscopy has been shown to be a powerful method that allows one to acquire statistics of cell motion across scales, which is a potentially versatile method for detecting L’evy walks in biological systems. In this article, we extend the differential dynamic microscopy method to self-propelled L’evy particles, whose run-time distribution has a algebraic tail. We validate our protocol using synthetic imaging data and show that a reliable detection of active L’evy particles requires accessing length scales of one order of magnitude larger than its persistence length. Applying the protocol to experimental data of E. coli and E. gracilis, we find that E. coli exhibits no signature of L’evy walks, while E. gracilis is better described as active L’evy particles.