# Interdisciplinary Applied Mathematics

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4. Freezing a Group of Atoms. Atoms that are supposed to remain stationary can be frozen to reduce the computational time. This is also useful during equilibration, e.g., to avoid badly placed solvent molecules from interacting unreasonably with other species (say protein atoms), although the same effect can also be obtained by putting a restraining potential on the atoms that must be protected (van der Spoel et al., 2004). The freeze option can be used, if desired, on just one or two coordinates of an atom, thereby freezing the atoms in a plane or in a line (van der Spoel et al., 2004). 21 correlated, it is usually not necessary to store the trajectory at each time step. However, for the analysis of certain variables, e.g., streaming velocity, which has huge statistical fluctuations, one has to store the data at each step to obtain a reasonable estimation of the variable, which will result in prohibitive disk space consumption. In this case, the data analysis is usually performed in an “on-the-fly” manner.

6. Number of Bins. In the binning method (described in Section 16.1.4), the system is partitioned into cells. The total number of cells or the size of the individual cell is an important choice. Since we want to estimate a certain variable, which varies continuously in the space, a larger number of bins means a finer grid and thus a better estimation (small systematic error). However, because of the statistical nature of data analysis in MD simulations, a smaller-sized bin or cell means a smaller number of particles in the bin and thus a larger statistical error. Thus there is a trade-off between systematic error and statistical error. It is to be noted that since the computation time for data analysis using the binning method is negligible compared to the other computational steps of MD simulation, coarser or finer partitioning (for the purpose of binning) does not affect the speed of the simulation significantly. The choice of the number of bins also depends on the parameter that needs to be extracted.

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