Averaging, dynamics, deviations

They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

Large fluctuations in the three-way junction suggest the presence of dynamical hinge points. In the Prod-D and Prod-U simulations, the virtual torsions associated with the residues that form the junction region (J) are characterized by a residue-average standard deviation (RASD) of 16.1° and 18.5°, respectively,... 

As a whole, static elastic moduli scatter around dynamic values with an average standard deviation of 15 percent, indicating no bias toward higher or lower values. 

I h e calcti lation of average energies and their deviations from the mean are useful in several aspects of molectilar dynam ics simulation s, such as tb ese ... 

Moli cii lar dynamics is csscn Lially a sLiidy of ih c evniiitioii in tim c of energetic and siniclnral molecular data. The data is often best represented as a graph of a molecular quantity as a function of iime. The values to be plotted can be any qnantity x that is being averaged over the trajectory, or the standard deviation. Dx. You can create as many as four simultaneous graphs at once. 

Besides the deviation mentioned above, the main problem with the dynamical information from the MF approximation is that it contains only one positive frequency and so the resulting real-time correlations cannot be damped or describe localizations on one side of the double well due to interference effects, as one expects for real materials. Thus we expect that the frequency distribution is not singly peaked but has a broad distribution, perhaps with several maxima instead of a single peak at an average mean field frequency. In order to study the shape of the frequency distribution we analyze the imaginary-time correlations in more detail. 

Fig. 3.46 Dynamical pivfiles for graph sequences Gs (defined in section 3.3.2), representing averages over Ng sequence samples. The x-axis labels each g G Gs, dashed lines denote pure range-r topologies r with gi = range-1, 1-dira lattice and vertical bars give the mean absolute deviations of a particular rneasiire. Each system has size. N = 12, with Ng and rules TZ as follows (a) Ng = 50, K = OTIO, (b) Ng = 25, Ti= OT26, (c) Ng = 50, 7 = T16, (d) dg = 50, 7 = T4.

Fig. 6.10. Comparison of overlap sampling and FEP calculation results for the free energy change along the mutation of an adenosine in aqueous solution (between A = 0.05 and 0.45) in a molecular dynamics simulation. The results represent the average behavior of 14 independent runs. (MD time step.) The sampling interval is 0.75 ps. The upper half of the plot presents the standard deviation of the mean (with gives statistical error) for AA as a function of sample size N the lower half of the plot gives the estimate of A A - for comparison of the accuracy, the correct value of AA is indicated by the bold horizontal line...

For the following we assume that the atmospheric variations in C02 and in its carbon isotopic composition are entirely due to atmospheric system disturbances, such as the input of 14C-free C02 from fossil C02 production, and deviations from the average rate of 14C production by cosmic radiation. The system dynamics, i.e., the exchange coefficients and the eddy diffusivity are kept constant. We approximate the fossil C02 input p(t) by... 

---