Motion in small live systems has many challenges. Prominent environmental conditions are high viscosity and warmth. Not only is it difficult to move, but maintaining a course is rendered difficult by immersion in a highly fluctuating bath. This holds especially for the motor proteins responsible for much of eukaryotic cellular traffic. The situation falls under the rubric of diffusion mediated transport. We recount how the mass transport idea leads to a dissipation principle for this type of situation, which gives rise to a special system of PDE's. Appropriate collaboration between molecular conformational change and potentials leads to transport. We hope to discuss several other types of system in both soft matter and hard matter.
Back to Workshop I: Aspects of Optimal Transport in Geometry and Calculus of Variations