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The ability of many living systems to actively self-propel underlies critical biomedical, environmental, and industrial processes. While such active transport is well-studied in uniform settings, environmental complexities such as geometric constraints, mechanical cues, and external stimuli such as chemical gradients and fluid flow can strongly influence transport. In this chapter, we describe recent progress in the study of active transport in such complex environments, focusing on two prominent biological systems -- bacteria and eukaryotic cells -- as archetypes of active matter. We review research findings highlighting how environmental factors can fundamentally alter cellular motility, hindering or promoting active transport in unexpected ways, and giving rise to fascinating behaviors such as directed migration and large-scale clustering. In parallel, we describe specific open questions and promising avenues for future research. Furthermore, given the diverse forms of active matter -- ranging from enzymes and driven biopolymer assemblies, to microorganisms and synthetic microswimmers, to larger animals and even robots -- we also describe connections to other active systems as well as more general theoretical/computational models of transport processes in complex environments.
We develop a theory of thermodynamic instabilities for complex fluids composed of many interacting species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from ra
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and super-diffusive spr
The excited state dynamics of chromophores in complex environments determine a range of vital biological and energy capture processes. Time-resolved, multidimensional optical spectroscopies provide a key tool to investigate these processes. Although
Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional struct
As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the dynamical transition at the Mode-Coupling temperature $T_d$. We show that active particles