A model for granular materials is presented that describes both the internal deformation of each granule and the interactions between grains. The model, which is based on the FLIP-material point, particle-in-cell method, solves continuum constitutive models for each grain. Interactions between grains are calculated with a contact algorithm that forbids interpenetration, but allows separation and sliding and rolling with friction. The particle-in-cell method eliminates the need for a separate contact detection step. The use of a common rest frame in the contact model yields a linear scaling of the computational cost with the number of grains. The properties of the model are illustrated by numerical solutions of sliding and rolling contacts, and for granular materials by a shear calculation. The results of numerical calculations demonstrate that contacts are modeled accurately for smooth granules whose shape is resolved by the computation mesh. Ó
The results of kinetic simulations of magnetic reconnection in Harris current sheets are analyzed. A range of guide fields is considered to study reconnection in plasmas characterized by different  values, Ͼm e /m i . Both an implicit particle-in-cell ͑PIC͒ simulation method and a parallel explicit PIC code are used. Simulations with mass ratios up to the physical value are performed. The simulations show that the reconnection rate decreases with the guide field and depends weakly on the mass ratio. The off-diagonal components of the electron pressure tensor break the frozen-in condition, even in low  plasmas. In high  plasmas, evidence is presented that whistler waves play a key role in the fast reconnection physics, while in low  plasmas the kinetic Alfvén waves are important. The in-plane and the out-of-plane ion and electron motion are also considered, showing that they are influenced by the mass ratio and the plasma .
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