RMS fluctuations

The relative molecular dynamics fluctuations shown in Figure 7-17 can be compared with the crystallographic B-factors, which are also called temperature factors. The latter name, especially, indicates the information content of these factors they show how well defined within the X-ray structure the position of an atom is. Atoms with high temperature have an increased mobility. In principle, this is the same information as is provided by the molecular dynamics fluctuations. Using Eq. (48), the RMS fluctuation of an atom j can be converted into a B-factor... 

Table IV. RMS Fluctuations and Displacements for the Last 100 Picoseconds of Each Simulation (in Angstroms)...

Squared Fluctuation Functions F2(f, /), Expressed in Terms of Autocorrelation Functions p(/,/) and the Limiting Forms Taken by the Scaled rms Fluctuation Functions (/(/,/) at Short and Long Times, for the Functions /Shown and the Following Systems . (A) Harmonically bound particle. (B) One-dimensional particle in a box. (C) Plane rotor. (D) Spherical rotor. The limiting behaviour at short times is given in terms of e = 1 — p. 

Comparison of Rates of Relaxation of Scaled rms Fluctuation Functions U(f t) and Autocorrelation Functions p(f t) at Short, Intermediate, and Long Times, for the Functions /Shown and the Systems Described in Table I... 

According to the DFA method, the time series y t) is first integrated and then divided into boxes of equal length, At. In each box, a least squares line (or polynomial curve of order /, DFA-/) is then fitted, in order to detrend the integrated time series by subtracting the locally fitted trend in each box. The root-mean-square (rms) fluctuation Fd(At) of this integrated and detrended time series is calculated over all timescales (box sizes). 

Fig. 13. RMS fluctuations per residue about the time-averaged structure during molecular dynamics simulations of (a) subtilisin E at 350°K, (b) subtilisin E at 300°K, (c) 5-3H5 at 350% (d) 5-3H5 at 300°K (Colombo and Merz, 1999).

The RMS fluctuations in both LES and experimental results (Fig. 9.3 and 9.5) are very intense around the axis, close to the injector nozzle (of the order of 20 m/s at x = 1.5 mm). These oscillations are t3rpical of most swirled burners. They may be due to ... 

An electrical measuring instrument contains electrical circuits incorporating capacitance, inductance, and resistance. In the absence of resistance, a circuit tends to oscillate with a definite frequency /when disturbed. For optimum performance an amount of resistance is incorporated that is barely sufficient to damp the oscillations resulting from transient inputs the circuit is then said to be critically damped. For a critically damped circuit it can be shown that the root-mean-square (rms) fluctuations in voltage V and in current /are given by... 

In the paper by Paul Treybal.thev showed that the reaction products of a competitive, consecutive second order reaction do depend on the RMS fluctuation value at the injection point. 

We were also interested in how the active site residues were affected by the non-aqueous solvent. The calculated RMS deviations and the RMS fluctuations for the active site residues in the three simulations are lower than the protein s average (Table 2). An MD simulation of acyl-chymotrypsin in water by Yu et. al. have found that the active site triad residues to have... 

Table 1. Summary of the RMS Deviation, RMS Fluctuation, Radius of Gyration, SASA, Hydrophobic exposed SASA, Solvent Diffusion, Average Distances and Hydrogen...

Table 2. RMS Deviation and RMS Fluctuation of the active site residues...

Our studies have shown that both hydration and the placement of "essential" water molecules affect the RMS deviation, but not RMS fluctuation, of the protein when placed in a non-aqueous environment. As hydration increases, the structural similarities of the protein to the crystal structure increases. Although the deviation of the protein from the X-ray structure is higher in organic solvent than in water, the flexibility of the protein is higher in water. The protein remained spherical and the major movement is due to the folding back of the hydrophilic side chains on the protein surface exposed to hexane. The placement of bound water molecules affects the "local" mobility of the protein, mainly the surface loops. The total... 

Between temperatures of 28 and 29 K the rms bond length fluctuations of the 13-particle system increase dramatically. Similar results have been obtained for all the other clusters N = 5, 6, and 7) for which S(T) is cal-culated. - The curves of S T) for these systems are similar to those occurring with first-order phase transitions of macroscopic systems.Lindemann s criterion states that melting occurs for such systems when rms fluctuations reach 10%.For the small clusters studied, the rise in this function occurs at values of S slightly below 10%—an effect that can be attributed to the large ratio of surface to core atoms. 

Stream is turbulent. Torobin and Guvin AlChE J., 7,615-619 [1961]) found that the drag crisis Reynolds nnmber decreases with increasing free-stream turbulence, reaching a valne of 400 when the relative turbulence intensity, dejlned as VuVC/jj is 0.4. Here Vu is the rms fluctuating velocity and C/r is the relative velocity between the particle and the fluid. 

The dimensionless group that appears on the right-hand side is the ratio of the particle stop distance, rnu,//. to the characteristic turbulence length, w/n. The stop distance so dehned is based on the friction vekx ity, which is approximately equal to the rms. fluctuating velocity component normal to the wall in the turbulent core. The dimensionless stop distance... 

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