= Diffusion length
{title2=$\sqrt{D/\mu}$}
{wiki}
For <diffusion coefficient> $D>0$ and first-order removal rate $\mu>0$, the <diffusion length> is
$$
\ell=\sqrt{\frac D\mu}.
$$
It measures the spatial range reached when <diffusion> competes with removal on the mean timescale $\tau=1/\mu$.
For example, a one-dimensional <reaction-diffusion equation> with constant coefficients is
$$
\partial_t c=D\,\partial_x^2c-\mu c.
$$
A steady <concentration> maintained at $c(0)=c_0$ in $x>0$, decaying at infinity, satisfies
$$
c(x)=c_0e^{-x/\ell}.
$$
Substitution gives $D/\ell^2=\mu$. Thus $\ell$ is an exact decay <length> for this geometry.
A root-mean-square displacement uses a different numerical convention. For ordinary diffusion in $d$ dimensions and an independent exponential removal time with mean $\tau$, the mean squared displacement at removal is $2dD\tau$; its square root is $\sqrt{2d}\,\ell$. Calling $\ell$ a characteristic travel distance does not equate these two definitions.
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