Average radius of gyration (diamonds) and end-to-end distance (points) for polymers of various chain lengths from simulations where HI was calculated with Fixman’s Chebyshev approximation (open symbols) and with our TEA (filled symbols), respectively. The lines indicate the theoretically predicted scaling .
Diffusion coefficient of the center of mass of bead-spring polymers of various chain lengths from simulations without HI (diamonds) and with HI using Fixman’s Chebyshev approximation (open points) or our TEA (filled points). The dashed line indicates the observed scaling of .
Relaxation times of the autocorrelation function of the end-to-end vector of polymers of various lengths from BD simulations without HI (diamonds) and with HI according to Fixman’s Chebyshev approximation (open points) and our TEA (filled points), respectively. The relaxation times were obtained by fitting a stretched exponential to the autocorrelation function. The dashed line indicates the scaling with .
Comparison of the runtime behavior of BD simulations with the different methods to include HI vs the chain length of the bead-spring polymer. The data points give the times required to simulate time steps, the lines are polynomial fits to the data as explained in the text.
Comparison of the center of mass diffusion coefficient and the rescaled correlation time of the orientation of a dimer of spherical beads with radius connected by a spring of length from BD simulations with HI to their respective theoretical values. The actual average separation during the simulation is given by and is used to calculate the theoretical predictions from Eqs. (30) and (31). The headings “Geyer” and “Ermak” denote the respective type of HI that was used in the simulations.
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