Writing

* Equal contribution · † Corresponding authors

The simulation of sand–water mixtures requires capturing the stochastic behavior of individual sand particles within a uniform, continuous fluid medium, such as the characteristic of migration, deposition, and plugging across various scenarios. In this paper, we introduce a Granule-in-Cell (GIC) method for simulating such sand–water interaction. We leverage the Discrete Element Method (DEM) to capture the fine-scale details of individual granules and the Particle-in-Cell (PIC) method for its continuous spatial representation and particle-based structure for density projection. To combine these two frameworks, we treat granules as macroscopic transport flow rather than solid boundaries for the fluid. This bidirectional coupling allows our model to accommodate a range of interphase forces with different discretization schemes, resulting in a more realistic simulation with fully respect to the mass conservation equation. Experimental results demonstrate the effectiveness of our method in simulating complex sand–water interactions, while maintaining volume consistency. Notably, in the dam-breaking experiment, our simulation uniquely captures the distinct physical properties of sand under varying infiltration degree within a single scenario. Our work advances the state of the art in granule–fluid simulation, offering a unified framework that bridges mesoscopic and macroscopic dynamics.

The collective behaviour of swarms, governed by magnetic and hydrodynamic interactions, emerges from the properties of their individual constituents. With combining simulation-guided design and droplet-based microfluidics, we present a versatile, high-throughput technique for fabricating soft microrobots with programmable structural and magnetic anisotropy. Such microrobots consist of iron oxide nanoparticles organized into supra-domain structures and entrapped in a hydrogel matrix that can be elongated independently of its magnetic properties. By applying rotating magnetic fields to resulting swarms, distinct collective behaviours are produced, including gas-like formations, variable crystals, and heterogeneous motions.

My part: the magnetization simulation and data analysis.

This paper proposes a particle-in-cell style method, which based on the port-Hamiltonian formulation, to enhance continuity near interfaces when simulating multi-phase flow. We employ the enhanced particle-in-cell method to ensure phase variables bounded and deploy an interpolation method based on vector potential for multiply connected domains. This paper experimentally justifies the enhanced particle-in-cell method and elucidate the importance of divergence-free velocity field.

Notes for the first part of a short course that Andreas Čap taught with Kaibo Hu in the ESI thematic programme “Differential Complexes: Theory, Discretization, and Applications” in Vienna. They introduce differential forms on open domains in ℝⁿ and the Bernstein–Gelfand–Gelfand construction, which builds complexes of differential operators, such as the Hessian and elasticity complexes, by twisting the de Rham complex and then compressing it. Representation theory of semisimple Lie groups and Lie algebras explains where the ingredients of the construction come from.

My part: the first version of the text, written from photos of the blackboards taken during the lectures, and its first edit (as acknowledged in the notes).