Analysing structure-property relations in equilibrium and non-equilibrium hyperuniform systems

• Applicants: Professor Dr. Marco Salvalaglio; Professor Dr. Axel Voigt
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics ; Theoretical Condensed Matter Physics ; Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 556185784

Hyperuniform systems are a class of point arrangements or fields featuring strongly suppressed density fluctuations on large scales. Ordered systems, e.g. crystals, are trivially hyperuniform, but also disordered systems featuring correlations can be hyperuniform. Such disordered hyperuniform (HU) systems emerge in patterns studied among different disciplines, can be observed as equilibrium and non-equilibrium states, and have been exploited to obtain peculiar properties used in technological innovations, e.g., in optics. However, the study of other emerging behaviors, e.g., elastic or rheological properties, is still in its early stages. Also, in active matter and biological systems, the properties associated with HU systems and their implications remain largely unknown. This research project aims to significantly advance our understanding of these structure-property relations. We therefore develop a general, advanced description and control of HU patterns across scales (from global to local). We extend classical descriptions based on global properties only, including (topological) information on local arrangements and structures. This allows the characterisation of realistic finite systems, thus accounting for the actual complexity of simulations and experiments rather than ideal scenarios only, and the study of their emergent structure-property relations. We address energy-based formulations to target prototypical static and equilibrium properties like the elastic response to load or the effect of anisotropy on HU characteristics in spinodal patterns. In addition, we explore the impact of hyperuniformity and local structures in transport and non-equilibrium phenomena, e.g., by studying flow through porous media and the connection between HU and characteristics of active turbulence.

• DFG Programme: Research Grants