\subsection{Proton decay sensitivity}
For proton decay, no specific simulation for MEMPHYS has been carried out yet.
We therefore rely on the study done by UNO, adapting the results to MEMPHYS
(which has an overall better coverage) when possible.
\subsubsection{$p \rightarrow e^+\pi^0$}

Following UNO study,
the detection efficiency of $p \rightarrow e^+\pi^0$
(3 showering rings event) is $\epsilon=$43\% 
for a 20 inch-PMT coverage of 40\% or its equivalent, as envisioned for
MEMPHYS. The corresponding estimated
atmospheric neutrino induced background is at the level of 2.25 events/Mt.yr. 
From these efficiencies and background levels,
proton decay sensitivity as a function of detector exposure can be
estimated (see Fig. \ref{pdk1}).
 
\begin{figure}[htb]
 \begin{minipage}[c]{0.44\textwidth}
\epsfig{figure=./figures/epi0-WC-Shiozawa.eps,width=\textwidth,angle=0}
\caption{\it \label{pdk1} Sensitivity for $e^+\pi^0$ proton decay
lifetime, as determined by UNO \cite{uno}. MEMPHYS corresponds to case (A).}
\end{minipage}
 \begin{minipage}[c]{0.05\textwidth}
~
\end{minipage}
 \begin{minipage}[c]{0.44\textwidth}
\epsfig{figure=./figures/Knu-WC-Shiozawa.eps,width=\textwidth,angle=0}
\caption{\it \label{pdk9_jbz}
Expected sensitivity on $\nu K^+$ proton decay as a function of MEMPHYS
exposure \cite{uno} (see text for details).}
\end{minipage}
\end{figure}

$10^{35}$ years partial
lifetime could be reached at the 90\% CL for a 5 Mt.yr exposure with MEMPHYS
(similar to case A in figure~\ref{pdk1}).


\subsubsection{$p \rightarrow \overline{\nu}K^+$}

Since the $K^+$ is below the \v{C}erenkov threshold, this channel is
detected via the decay products of the kaon: a 256 MeV/c muon and
its decay electron (type I) or a 205 MeV/c $\pi^+$ and $\pi^0$
(type II), with the possibility of a delayed (12 ns) coincidence
with the 6 MeV nuclear de-excitation prompt $\gamma$ (Type III).
In Super-Kamiokande, the efficiency for the reconstruction of
$p \rightarrow \overline{\nu}K^+$ is $\epsilon=$ 33\% (I), 6.8\% (II)
and 8.8\% (III),
and the background is at the 2100, 22 and 6/Mt.yr level. For the
prompt $\gamma$ method, the background is dominated by
mis-reconstruction. As stated by UNO, there are good 
reasons to believe that this
background can be lowered at the level of 1/Mt.yr corresponding
to the atmospheric neutrino interaction $\nu p \rightarrow \nu
\Lambda K^+$. In these conditions, and using Super-Kamiokande performances,
a 5 Mt.yr MEMPHYS exposure would
allow to reach the $2\times10^{34}$ years partial lifetime
(see Fig. \ref{pdk9_jbz}).

%\subsubsection{Comparison with liquid argon detectors}
%Comparisons have been done between megaton scale \v{C}erenkov detectors
%and liquid argon TPC's with a mass of 100 kilotons. The main results show an
%advantage to \v{C}erenkov detectors for the $e^+ \pi^0$ channel, due to their
%higher mass, while liquid argon TPC's get better results for the
%$\bar\nu K^+$ channel, due to a much better detection efficiency.
%The two techniques look therefore quite complementary.