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\item Why do the swimmers float on top?  \item For now consider the simple case of a single inert particle in a (fixed) concentration gradient. Say it moves towards the source of the chemical. It will follow some mean trajectory, but with plenty of scatter. This is an out-of-equilibrium process.  \begin{enumerate}[a)] \begin{enumerate}  \item Understand why it moves (diffusiophoresis): how fast and in what direction on average?  \begin{itemize}  \item See e.g. \citet{http://adsabs.harvard.edu/abs/2010PhRvL.104m8302P}, \ldots