Schematic drawing of two-particle contact in the center of mass reference frame. Shown are the relative velocity of the contact points, the impact angle of the contact points, and the angle between the relative translational velocity of the particles and their contact normal.
Tangential restitution as function of the impact angle for different values of the coefficient of friction .
Plots of the probability distribution of from simulations (symbols) and from Eq. (12) with values from the simulations. The arrows indicate the corresponding , while the parameters are (a) , and variable , and (b) , and variable .
Expected mean tangential restitution, , as function of the friction coefficient for models A, B, and C. The parameters used are , (for A, B) and different , 0.40, and 0.15 (model C: solid lines from right to left).
Simulation results (symbols) and theory (lines) for the parameters , , , and , plotted against the maximum tangential restitution . (a) Translational temperature , and (b) rotational temperature , plotted against , and scaled by , the mean field value for smooth particles. (c) Ratio of rotational and translational temperature , plotted against .
Translational temperature scaled by the mean field value for smooth particles , plotted against , for the parameters as in Fig. 5. The tangential restitution coefficients are fixed to (a) , and (b) . Data with normal restitution (solid symbols and thick lines) and (open symbols and thin lines) are compared. Models A and B are shown for only.
plotted against , for the same parameters as in Fig. 6. The tangential restitution coefficients are again fixed to (a) , and (b) .
Deviation from equipartition, , plotted against the inverse friction coefficient, , for simulations from Fig. 6(b). Note the double-logarithmic scale of this plot.
Ratio of rotational and translational temperature, , plotted against , for some simulations from Fig. 6(b). Note the double-logarithmic scale of this plot.
Relaxation rates , close to steady state for as a function of .
Evolution of temperatures with rescaled time, with , for simulations with , , , , and (a) , (b) . Note that there are no fit parameters.
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