(642a) Causal Dynamics of Hierarchical Reorganization in Particulate Gels Via Topological Analysis

Particulate gels are structurally rich soft materials whose mechanical behavior emerges from complex hierarchical dynamics across multiple scales[1]. These gels, formed by interacting colloidal particles with bending rigidity, exhibit distinctive responses to mechanical perturbations, characterized by local bond rearrangements and large-scale structural reorganization. Understanding the underlying physical mechanisms connecting microscale interactions to macroscale mechanical properties remains critical for advancing soft matter theory and engineering responsive materials [2,3].

In this work, we uncover how cyclic shear deformation drives hierarchical structural adaptation in particulate gels. Using molecular dynamics simulations, we investigate gels subjected to oscillatory strain, revealing nonlinear phenomena such as localized yielding, transient network restructuring, and progressive void coalescence. Employing persistent homology, we characterize these phenomena through topological features—specifically loops and voids—that encode critical mechanical information such as connectivity, deformation modes, and porosity evolution [4].

We leverage the Automatic Topologically-Oriented Learning (ATOL) algorithm to translate topological descriptors into low-dimensional feature vectors that capture essential structural dynamics [5,6]. By applying the VARLiNGAM causal discovery approach to these feature vectors, we identify explicit pathways of structural influence [7,8]. Remarkably, our analysis demonstrates a reciprocal interplay: mesoscale void deformation under shear induces localized microstructural rearrangements, while these microscale bond dynamics cumulatively reshape the macroscopic gel network. This bidirectional coupling underscores a robust, hierarchical mechanism by which particulate gels dynamically adapt their internal structure to mechanical stimuli.

Our findings provide a physically intuitive framework for describing structural adaptability in soft particulate systems. By linking explicit topological descriptors to causal dynamics, this approach advances our understanding of gel mechanics and guides the development of new models tailored for predicting and controlling the behavior of responsive, structurally dynamic soft matter [9,10].

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[7] A. Smith, D. Ghosh, A. Tan, X. Cheng, and P. Daoutidis, “Multi-scale causality in active matter,” Comput. Chem. Eng., vol. 197, p. 109052, 2025.

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[9] S. Zhu, I. Ng, and Z. Chen, “Causal discovery with reinforcement learning,” arXiv preprint arXiv:1906.04477, 2019.

[10] M. Sader, Y. Wang, D. Huang, C. Shang, and B. Huang, “Causality-informed data-driven predictive control,” IEEE Trans. Control Syst. Technol., 2025.