ABF:Controls: Difference between revisions
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The relationships between the sampled instantaneous collective and smoothed forces is given: | The relationships between the sampled instantaneous collective and smoothed forces is given: | ||
<center><math>\bold F_{aplied}(\ | <center><math>\bold F_{aplied}(\boldsymbol \xi_i) = \frac{ \sum\limits_{j=1}^{N_{bins}} K(\boldsymbol \xi_i,\boldsymbol \xi_j)\bold F_{estimated}(\boldsymbol \xi_j)} {\sum\limits_{j=1}^{N_{bins}} K(\boldsymbol \xi_i,\boldsymbol \xi_j) }</math></center>, | ||
with the Gaussian smoothing kernel defined as: | with the Gaussian smoothing kernel defined as: | ||
<center><math>K(\ | <center><math>K(\boldsymbol \xi_i,\boldsymbol \xi_j) = exp\left( - \frac {1}{2} \sum\limits_{k=1}^{N_{CVS}} \frac { (\xi_{i,k} - \xi_{j,k})^2} { w_{k}^2 h_{k}^2 } \right)</math></center>, | ||
where <math>h_{k}^2</math> is a bin width and <math>w_{k}^2</math> is an user provided factor (wfac), see [[ABF:Collective variables]]. | where <math>h_{k}^2</math> is a bin width and <math>w_{k}^2</math> is an user provided factor (wfac), see [[ABF:Collective variables]]. | ||