Cloud points show bead positions of a test chain from 28 MD trajectories spanning the time . The center thick line is the average of bead positions, called the mean path. The confining tube surrounding the primitive path is easily visualized.
Primitive paths approximated with trajectory mean paths, for a single chain in the C400 system. (a) Results for different average times , for , , and . (b) Results for the same average time (), but at different elapsed times.
Equilibrium tangent–tangent correlation functions of primitive paths for , 20, 40, 100, and 200, for C400 system. The apparent spikes right off the maximum are associated with the immediate neighboring bonds. The averages have been taken over primitive paths at different snapshots, and over different chains. Inset: same data plotted on log-linear scale.
Data points: integrated tangent–tangent correlation functions, , for , at times , 6, 12, 36, and , respectively, which corresponding to 0, 0.01, 0.02, 0.06, and . (a) Solid curves are prediction of dynamics theory of flexible tube. (b) Solid curves are prediction of dynamics theory of semiflexible tube (see Sec. III).
Normalized autocorrelation function of six independent stress components for C400 system, computed using multi- correlator. Inset: time dependence of .
Average of the autocorrelation functions of independent stress components (solid curve with circles), and tube EOM predictions (solid and dashed curves; see Sec. III).
Early time bead MSD of a semiflexible tube. Solid line: numerical results from Eq. (7). Thin lines: asymptotic limits by integrating Eq. (7) using the (slope = 1/2) and the (slope = 3/4) modes alone.
Solution of EOM with only reptation and CR mechanisms () for . Initial condition: exponential decay. Time: , , , and . Number of mesh points: 40.
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