Long-range interactions in dilute granular systems

摘要: In this thesis, on purpose, we focussed the most challenging, longest ranging potentials. We analyzed granular media of low densities obeying 1/r long-range interaction potentials between granules. Such systems are termed granular gases and differ in their behavior from ordinary gases by dissipative interactions, i.e., they do not conserve energy. Due to dissipation, a unique wealth of structures can occur, enhanced or hampered long-range interactions. Numerics For analysis such systems, developed soft sphere Molecular Dynamics (MD) method three dimensions, taking properly into account interplay between contacts interaction forces. infi- nite range potential, would have consider all particles with all others, resulting computational time effort that scales like O(N2), where N is particle number. were able bypass pair-wise treatment exploiting linked cell structure use for neighborhood search particles cells considered as pseudo grouped together hierarchical way. This set-up based new to our knowledge. The combination multipole expansion mass distri- bution inside gives reduced number partners. The implementation Hierarchical Linked Cell (HLC) algorithm including periodic wall boundary conditions shows scaling O(NlogN), as confirmed various simulations. found results HLC algo- rithm agree those direct summation code long temperature is higher about same repulsion/attraction energy barrier. Dilute Homogeneous Granular Systems The second part thesis was devoted investigation cooling behavior presence mutual repulsive and attractive order obtain reference results, exclusively treated the pair-wise, limiting us small numbers simulations. In understand cooling behavior, applied Liouville op- erator theory. Although dealing spheres under influence mutual long-range forces, observed good agreement theory simulations in the limit weak dissipation. case repulsive long-range forces, dissipation rate reduced, energy barrier relative velocity two approaching must exceed order to collide. increased due to an escape barrier separating must overcome experience collision. Both qualitative effects vanish if vanishing force intensity density. Our repulsive confirms earlier heuristic [?], while theory is new knowledge. Even though, works dilute limit, finite densities, dissi- pation changes increasing density allows us empirically provide predictive analytical correction factor dependent on the performed elastic different and attractive strengths 0.010 0.152. correction is non-linear linear case, at least stable homogeneous state examined. We used empirical findings solution equations energy evolution obtained improved prediction, quantitative agreement Small deviations remain supposed be a consequence because increase strength. In the improvement less successful. Surprisingly, mod- erate strengths, show same dissipation without attraction forces. Dilute Ring-Shaped third contains self-gravitating ring- shaped systems. tested it strongly inhomogeneous It well and, the computational expense O(NlogN). sufficiently strong clustering even though perma- nent shear heating present. Strong also leads to inhomogeneous rings, formation clusters, “planetesimals”. Moreover, numerically solved approximate Navier-Stokes hydrodynamic set projected Ansatzes for kinematic viscosity compared solutions simulation re- sults. only intermediate times, whereas short times, besides initial equilibration effects, rings spread faster later times the rings slower than predicted