Events

Date: 15 October 2025   Time: 12:00 - 13:00

Location: Hybrid: School of Mathematical Sciences, MB503 or via the Teams link below

How do living organisms move in their environment? While random walk models provide a foundation for understanding biological movement, they fall short in capturing the full complexity of movement patterns generated by living organisms. This study explores stochastic processes in two dimensions, defined in the Cartesian frame, and how they transform into a frame comoving with an organism. We argue that this comoving frame provides the correct description for the self-generated fluctuations of an organism leading to movement. By transforming stochastic equations of motion and by examining corresponding probability distributions and autocorrelations, we identify key features of these processes in the comoving frame. For the example of the generic Ornstein–Uhlenbeck process, we derive analytically two simple equations in the comoving frame that reproduce the stochastic behavior generated in the Cartesian frame. The talk will also discuss models of active Brownian particles and their corresponding stochastic dynamics in the comoving frame, highlighting the connection between self-propelled motion and stochasticity in biological systems by offering new insights into modeling active biological movement.

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