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| This is part of the ves module | |
| It is only available if you configure PLUMED with ./configure –enable-modules=ves . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |
Target distribution given by product combination of distributions (static or dynamic).
Employ a target distribution that is a product combination of the other distributions, defined as
\[ p(\mathbf{s}) = \frac{\prod_{i} p_{i}(\mathbf{s})} {\int d \mathbf{s} \prod_{i} p_{i}(\mathbf{s})} \]
where the distributions \(p_{i}(\mathbf{s})\) are in full dimensional space of the arguments used.
Note the difference between this target distribution and the one defined in TD_PRODUCT_DISTRIBUTION. Here we have a non-separable distribution given as a product of distribution \(p_{i}(\mathbf{s})\) which are in full dimensional space of the arguments used.
The labels of the distributions \(p_{i}(\mathbf{s})\) to be used in the product combination are given in the DISTRIBUTIONS keyword.
The target distribution resulting from the product combination will be automatically normalized. Therefore, the product combination needs to be a proper distribution that is non-negative and that can be normalized. The code will perform checks to make sure that this is indeed the case.
The product combination will be a dynamic target distribution if one or more of the distributions used is a dynamic distribution. Otherwise it will be a static distribution.
| DISTRIBUTIONS | The labels of the target distribution actions to be used in the product combination. |
| SHIFT_TO_ZERO | ( default=off ) Shift the minimum value of the target distribution to zero. This can for example be used to avoid negative values in the target distribution. If this option is active the distribution will be automatically normalized. |
| WELLTEMPERED_FACTOR | Broaden the target distribution such that it is taken as [p(s)]^(1/ \(\gamma\)) where \(\gamma\) is the well tempered factor given here. If this option is active the distribution will be automatically normalized. |
In the following example the overall interval on which the target distribution is defined is from 0.23 to 0.8. We employ a product combination of a well-tempered distribution and a uniform distribution that decays to zero at 0.6. This results in a target distribution that is well-tempered from 0.23 to 0.6 and then decays to zero. In other words, we cut off the tail of the well-tempered distribution at 0.6
td_welltemp: TD_WELLTEMPERED BIASFACTOR=5 td_uniform: TD_UNIFORM MINIMA=0.23 MAXIMA=0.6 SIGMA_MAXIMA=0.05 td_combination: TD_PRODUCT_COMBINATION DISTRIBUTIONS=td_uniform,td_welltemp
In the following example the overall interval on which the target distribution is defined is from -4 to 4. We employ a product of a Gaussian distribution with two centers and distribution that is uniform on the interval -3 to 3 and then smoothly decays to zero outside that interval. The overall effect will then be to cut off the tails of the Gaussian distribution
TD_GAUSSIAN ... CENTER1=-2.9 SIGMA1=1.0 CENTER2=+2.9 SIGMA2=0.4 LABEL=td_gauss ... TD_GAUSSIAN TD_UNIFORM ... MINIMA=-3.0 SIGMA_MINIMA=0.20 MAXIMA=+3.0 SIGMA_MAXIMA=0.15 LABEL=td_uni ... TD_UNIFORM td_pc: TD_PRODUCT_COMBINATION DISTRIBUTIONS=td_gauss,td_uni
1.8.14