Facilitated target search
= Facilitated target search
A facilitated target search combines bulk <diffusion> with lower-dimensional motion on a substrate, such as sliding on <DNA>. In the scaling model $\tau=A/\lambda+B\lambda$, positive constants $A,B$ balance relocation and local exploration. Differentiation gives $\lambda_*=\sqrt{A/B}$ and $\tau_{\min}=2\sqrt{AB}$. These expressions require an accessible optimum within the physically allowed range of sliding lengths.