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Attempt to fix the manual
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GiovanniBussi committed Nov 12, 2020
1 parent 2f40306 commit 7400767
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9 changes: 3 additions & 6 deletions src/ves/TD_Multicanonical.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -58,12 +58,9 @@ The advantage with respect to Wang-Landau is that instead of sampling the potent
The algorithm works as follows.
The target distribution for the potential energy is chosen to be:
\f[
p(E)= \begin{cases}
\frac{1}{E_2-E_1} & \mathrm{if} \quad E_1<E<E_2 \\
0 & \mathrm{otherwise}
\end{cases}
\f]
MISSING EQUATION TO BE FIXED
where the energy limits \f$E_1\f$ and \f$E_2\f$ are yet to be determined.
Clearly the interval \f$E_1–E_2\f$ chosen is related to the interval of temperatures \f$T_1-T_2\f$.
To link these two intervals we make use of the following relation:
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12 changes: 2 additions & 10 deletions src/ves/TD_Uniform.cpp
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Expand Up @@ -35,16 +35,8 @@ Uniform target distribution (static).
Using this keyword you can define a uniform target distribution which is a
product of one-dimensional distributions \f$p_{k}(s_{k})\f$ that are uniform
over a given interval \f$[a_{k},b_{k}]\f$
\f[
p_{k}(s_{k}) =
\begin{cases}
\frac{1}{(b_{k}-a_{k})}
& \mathrm{if} \ a_{k} \leq s_{k} \leq b_{k} \\
\\
\ 0
& \mathrm{otherwise}
\end{cases}
\f]
MISSING EQUATION TO BE FIXED
The overall distribution is then given as
\f[
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11 changes: 3 additions & 8 deletions user-doc/tutorials/others/ves-lugano2017-02-ves1.txt
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Expand Up @@ -272,14 +272,9 @@ files needed for this example are contained in the directory Example2. Instead
of introducing a barrier as done in the example above, in this case we will
use a uniform target distribution in the interval [0.23:0.6] nm and decaying to
zero in the interval [0.6:0.8] nm. The expression is:
\f[
p(s)=
\begin{cases}
\frac{1}{C} \: & \mathrm{if} \: s<s_0 \\
\frac{1}{C} e^{-\frac{(s-s_0)^2}{2\sigma^2}} \: &
\mathrm{if} \: s>s_0\\
\end{cases}
\f]

MISSING EQUATION TO BE FIXED

where \f$ s_0=0.6\f$ nm and \f$ \sigma=0.05\f$.
To define this \f$ p(s) \f$ in Plumed the input is:
\plumedfile
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11 changes: 3 additions & 8 deletions user-doc/tutorials/others/ves-lugano2017-03-ves2.txt
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Expand Up @@ -75,14 +75,9 @@ p(s)=\frac{p_{\mathrm{WT}}(s) \, p_{\mathrm{barrier}}(s)}
{\int ds \, p_{\mathrm{WT}}(s) \, p_{\mathrm{barrier}}(s)}
\f]
where \f$ p_{\mathrm{WT}}(s) \f$ is the well-tempered target distribution and:
\f[
p_{\mathrm{barrier}}(s)=
\begin{cases}
\frac{1}{C} \: & \mathrm{if} \: s<s_0 \\
\frac{1}{C} e^{-\frac{(s-s_0)^2}{2\sigma^2}} \: &
\mathrm{if} \: s>s_0\\
\end{cases}
\f]

MISSING EQUATION TO BE FIXED

with \f$ C \f$ a normalization factor.
The files needed for this exercise are in the directory Example1.
This target distribution can be specified in plumed using:
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