# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 44: Poster: Statistical Physics

### DY 44.14: Poster

### Donnerstag, 30. März 2023, 13:00–16:00, P1

Dividing Active Brownian Particles — •Till Welker and Holger Stark — Institut für Theoretische Physik, Technische Universität Berlin, Germany.

We aim to combine active motion with cell division to answer questions like: Does nutrient input induce clustering? How does a non-uniform nutrient distribution effects population dynamics?

To include cell division and death in the model of active Brownian particles, we propose a simple rule: in a time interval dt, each particle has a probability dt · g(s) to divide and dt · d to die.
The growth rate g depends on the nutrient concentration s at the position of the bacterium
and is described by the Monod function. The nutrient diffuses with the diffusion coefficient D_{N}. We add a source with steady input rate S_{0}, in addition, each particle takes up nutrient with a rate γ g(s).

The population dynamics strongly depends on nutrient diffusion: For large D_{N}, the population oscillates before reaching a steady population number N^{*}. For small D_{N}, the population is stronger damped and equilibrates quickly. N^{*} is independent of D_{N}, but the population fluctuation decreases for lower D_{N} due to the damping. The collective behavior is also influenced by the nutrient: First, for large D_{N} the swarm has a strongly asymmetric shape during the transient phase which then becomes symmetric in the steady state. Second, the swarm is less dense for larger D_{N}, but the relationship between spread of nutrient and bacteria is not linear.

We show that combining two key aspects of microbial life, mobility and growth, gives rise to interesting population and spatial dynamics.