B01 – Toward intelligent light-propelled nano- and microsystems | Wittkowski
Julian Jeggle
In this project we work on developing theoretical models for suspensions of refractive light-driven particles with a symmetry breaking in shape and/or refractive index profile. While models such as Active Brownian Particles (ABP) only consider the close-range repulsive interaction between particles, refractive particles can also be subject to long-range interactions mediated by the light field as well as feedback effects created by external control of the light field via optical means. This makes them a viable building block for adaptive matter.
When it comes to theoretical descriptions of classical particle systems, there are two general approaches:
- Microscopic models, that describe the dynamics of each individual particle. Examples of this are Langevin dynamics1, Brownian dynamics1 or Ornstein-Uhlenbeck particles2
- Field theories, that describe the dynamics of order parameter fields like density and polarization. Example of this are (Active) Phase Field Crystal (PFC) models3, Dynamical Density Functional Theory (DDFT) models4, (Active) Model B5 or (Active) Model H6
While microscopic models are typically easier for formulate based on experimental observations of individual particles, they give less insight into collective phenomena like phase transitions emerging in many-particle systems. Field theories on the other hand are harder to formulate, but give a much better theoretical grip on collective effects.

Methods:
Besides the analytical methods connected to the models mentioned above we also make heavy use of numerical methods. At the level of particle dynamics this includes molecular dynamics simulations of many-particle systems as well as ray optic simulations to determine the interaction between refractive particles and a light field. At the level of field theories this mainly includes solving of partial differential equations by various means such as finite-difference or finite-element methods.
The numerical methods described above can require very large amounts of computational resources. To increase efficiency and make simulations of larger systems computationally feasible we are also invested in modern approaches to high-performance computing like offloading computations to GPUs, novel approaches to safe parallelism (Rust) or JIT-compilation via domain specific languages.

References
1. T. Schlick, Molecular Modeling and Simulation (Springer New York, 2002)
2. L. L. Bonilla, Physical Review E 100 (2019)
3. M. te Vrugt, J. Jeggle, R. Wittkowski, New Journal of Physics 23, 063023 (2021)
4. M. te Vrugt, H. Löwen, R. Wittkowski, Advances in Physics 69, 121–247 (2020)
5. R. Wittkowski et al., Nature Communications 5 (2014)
6. A. Tiribocchi, R. Wittkowski, D. Marenduzzo, M. E. Cates, Physical Review Letters 115 (2015)