Many-body soft matter systems under external fields

01/10/2025 to 30/09/2030

This project has three main theoretical research areas on soft matter systems and material science. The shared focus among the three proposed research areas is the investigation of many-body systems under the influence of external fields. The first research area focuses on how the gravitational field affects the equilibrium phase behavior of colloidal mixtures. Classical density functional theory and sedimentation path theory will be applied and compared with experimental data. The impact of polydispersity on sedimentation-diffusion-equilibrium will also be explored. The second research line studies effectively two-dimensional materials that support topologically protected transport of magnetic colloids. The colloidal particles are subject to a time-dependent magnetic field coupled with a static magnetic field created by a magnetic pattern. The transport is topologically protected and hence dispersion-free and robust against external perturbations. Among others, we want to understand how to control the transport of magnetic microparticles of different shapes, as well as their transport above complex inhomogeneous magnetic patterns. In the third research line, we will use machine learning to rationalize the response of a many-body system to randomized external one-body fields. Using neural networks, we will construct neural density functionals for anisotropic colloidal particles to understand and predict their equilibrium phase behavior. In non-equilibrium, we will develop neural force functionals to predict and analyze the time evolution of the many-body system at the one-body level with near-simulation accuracy. By studying the response of many-body systems to external fields, we will gain a profound understanding of how to control their structural and dynamical properties. The proposed research integrates several theories, particle-based computer simulations, and cutting-edge machine learning methodologies. For the most theoretical aspects, we will use sedimentation path theory, topology, as well as density and power functional theories. Many-body computer simulations such as Monte Carlo, Brownian, and Molecular Dynamics will be used to simulate the systems. We will employ machine learning methods, particularly neural networks, to integrate and rationalize the simulation data within the theoretical frameworks of density and power functional theories. Moreover, we will collaborate with two experimental groups to validate theoretical findings.