In June, assistant professor of chemical engineering Abhishek Sharma presented two research posters, “Coupled Dynamics on Hypergraphs: Impact of Random Architecture on Unstable Fixed Points” and “Network Science Techniques Applied to Soft Matter Simulations,” at the 2026 Network Science Conference (NetSci 2026), held in Boston, Massachusetts. 

The conference allowed Professor Sharma to share his research, exchange ideas with fellow researchers, and explore advancements in network science. Read more about the conference and his research in the NetSci 2026 program.

Abstract: Coupled Dynamics on Hypergraphs: Impact of Random Architecture on Unstable Fixed Points

Building upon previous finite-size analyses of globally coupled oscillator systems, we investigate the dynamics of a finite population of Kuramoto oscillators in which pairwise interactions are defined on an Erdős–Rényi (ER) random graph, while higher-order interactions are globally (all-to-all) coupled. The higher-order coupling contributes exclusively to the backward transition, thereby generating a bistable (hysteretic) regime. The global nature of the higher-order interaction facilitates analytical treatment and reduces numerical complexity. We demonstrate, through a combination of numerical simulations and analytical arguments, that finite-size fluctuations induce a transition to the synchronized state in ER networks. In contrast, analysis in the thermodynamic limit predicts the absence of a forward synchronization transition, reflected in the divergence of the critical coupling as the system size tends to infinity. To elucidate this behavior, we develop a numerical procedure to determine unstable fixed points for network-based interactions. The structure of these unstable solutions explains the indeterminate nature of the forward critical coupling in ER networks and supports the absence (presence) of a forward transition in the infinite-size (finite-size) regime. We further characterize finite-size effects by systematically varying the average degree, connection probability of the ER network, and the higher-order coupling strength. The resulting distributions of the critical coupling exhibit qualitatively distinct features compared to the globally coupled case, consistent with the behavior of the corresponding unstable fixed points.

Abstract: Network Science Techniques Applied to Soft Matter Simulations

Soft matter provides a concrete instance of networks leading to complex physical properties. In this poster, we demonstrate the use of network science tools to study transitions in connectivity and mechanics of soft matter systems. These tools provide tangible evidence for the physical mechanisms that underlie material properties in two systems of interest: percolation robustness in ion exchange membranes, and graph coarsening in granular systems. For material systems, the transition between a state of percolation to a state of disjointedness can have important ramifications on their properties. To computationally track a percolation process, we propose the use of k-stub decomposition (KSD) [1], which excludes particles with degree less than k from the network. In physical networks, increasing k has the effect of peeling back layers from the surface; hence, increasing k can remove weakly connected surface dendrites and bottlenecks. For example, in our study [2], anion exchange membranes undergo a sharp increase in ionic conductivity at specific relative humidities, presumably due to percolation of ion channels comprising water molecules. KSD analysis of molecular simulations reveals that this transition takes place when channels are robust at the k = 3 level, revealing that 3 water molecules are needed in the channel at a minimum to enable a vehicular transport of ions. The second system we have studied deals with dense granular suspensions: under the right conditions, these systems undergo shear thickening due to frictional constraints between the particles. As these systems flow, the frictional force chain network (FFCN) evolves as frictional contacts are formed and broken. The properties of FFCN are dependent on the kind of constraints (frictional constants, rolling/sliding frictions, etc.) and conditions (density, shear rate). In this study [3], we used graph coarsening to identify independent force chains, hubs, and terminals. The force chain length distribution and the connectivity of the FFCN provide useful insight into the trends in rheology of these systems. Beyond these two examples, we are currently applying these techniques to other soft matter systems, including complex polymeric mesophases, metamaterials, and nanoparticle self-assembly.