Key research themes
1. How can mathematical and computational modeling improve the understanding and prediction of mixing processes in powders and granular materials?
This research area focuses on developing and applying computational methods such as Discrete Element Method (DEM), Markov chain models, and analytic tools to model the dynamics of powder mixing and granular flows. Accurately simulating mixing processes is critical for industrial applications involving granular or powder materials, where segregation phenomena and equipment design challenges arise. The studies provide mechanistic insight into mixing efficiency, segregation control, and process optimization.
2. What role do geometric, dynamical system, and pattern-based theories play in understanding and enhancing mixing processes across fluid and granular media?
This theme covers the conceptual and mathematical framework of mixing, emphasizing patterns, geometric phases, piecewise isometries, and resonances that govern mixing dynamics. By leveraging theoretical constructs such as geometric phases in Stokes flows, spherical PWIs in granular mixing, or pattern languages from software engineering applied to complex systems, researchers seek to characterize, predict, and optimize mixing beyond empirical approaches. These insights inform the design of mixers and elucidate fundamental mixing mechanisms.
3. How can mixing performance be enhanced and optimized in fluid and multiphase systems through shape, stirring strategies, and micro-mixing designs using computational optimization and machine learning?
This area investigates methods to improve mixing efficiency and homogeneity leveraging computational fluid dynamics, PDE-constrained optimization, machine learning, and microfluidic device design. By optimizing stirrer shapes, protocols, and leveraging split-and-recombine mechanisms, researchers aim to generate complex vortical structures and filamentation that accelerate mixing. Machine learning is applied to predict mixing quality and identify optimal control strategies in micro- and macro-scale mixing systems for industrial and biomedical applications.






















![Figure 1.2: The Smallpox virus. The smallpox virus consists of genetic material (one molecule of double stranded DNA) contained in a core (red). In this illustration, the virus is tilted, showing the rounded biconcave brick shape of the core, in whose depressions nestle the "lateral bodies" (purple). The function of the lateral bodies is unknown. The virus includes several layers of host cell membrane (green & blue) added at various points in its life cycle. Source: Russell Kightley Media [73].](https://figures.academia-assets.com/107725831/figure_001.jpg)
































![Figure 1.3: Variola virus life cycle. Source: Russell Kightley Media [73].](https://figures.academia-assets.com/107725831/figure_002.jpg)


