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We report a new phenomenon, called self-recovery, in the process of diffusionin a region with boundary. Suppose that a diffusing quantity is uniformlydistributed initially and then gets excited by the change in the boundaryvalues over a time interval. When the boundary values return to their initialvalues and stop varying afterwards, the value of a physical quantity related tothe diffusion automatically comes back to its original value. Thisself-recovery phenomenon has been discovered and fairly well understood forfinite-dimensional mechanical systems with viscous damping. In this paper, weshow that it also occurs in the process of diffusion. Several examples areprovided from fluid flows, quasi-static electromagnetic fields and heatconduction. In particular, our result in fluid flows provides a dynamicexplanation for the famous experiment by Sir G.I. Taylor with glycerine in anannulus on kinematic reversibility of low-Reynolds-number flows.

On the Self-Recovery Phenomenon in the Process of Diffusion