Transport in Complex Environments

Dear Colleagues,

Brownian motion (BM), pioneered by Einstein, Smoluchowski, and Langevin in the early 20th century, is a well-established theory with applications across nearly all scientific, engineering, and mathematical finance disciplines. However, despite its universality, the BM theory cannot accurately describe transport phenomena in complex environments. These phenomena include molecular diffusion in supercooled liquids, colloidal suspensions, and intracellular environments, as well as examples of active motion, such as synthetic nanomotors, cell movement, motility of microorganisms, and animal foraging.

Transport in complex environments deviates from the standard Brownian motion primarily due to the presence of anomalous diffusion with prominent non-Gaussian characteristics. Even seemingly Fickian diffusion processes may display persistent or transient non-Gaussianity. To add to these intriguing observations, transport in complex environments often exhibits aging characteristics with slow power-law-like relaxation dynamics and ergodicity breaking.

This Special Issue provides a platform for theoretical and computational studies that aim to advance our understanding of transport in complex environments. We welcome diverse approaches, such as continuous-time random walks, fractional diffusion and Fokker-Planck equations, fractional Brownian motion, the Langevin equation, its generalizations, and other types of correlated random walks. We also encourage the submission of review articles as well as studies that directly compare theoretical models with experimental results.

Dr. Nikolaos Voulgarakis
Guest Editor

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• anomalous diffusion
• active Brownian motion
• Fickian yet non-Gaussian diffusion
• aging phenomena
• ergodicity breaking
• complex fluids
• cell migration
• animals foraging