Schweigert, Schweigert, and Peeters Reply:

Abstract

Schweigert, Schweigert, and Peeters Reply: Rinn and Maass [1] claim that the Brownian dynamics (BD) simulation results of Schweigert et al. [2] are analyzed incorrectly. Furthermore, they claim that the definition for the intershell diffusion coefficient ͑D u ͒ used by Schweigert et al. [2] makes sense only when the particles remain in the same shell.The whole misunderstanding is based on the fact that Rinn et al. [1] believe that one needs to follow the trajectory of each individual particle in order to calculate D u . Within such an approach, one is in trouble when a particle jumps from one shell to another shell. In order to remove this switching of particles between shells they analyzed their data in two different ways: (1) ignoring shell jumps (open symbols in Fig. 2 of Ref. [1]); and (2) taking care of shell jumps (solid symbols in Fig. 2 of Ref. [1]).When Rinn et al. ignored shell jumps they found a very large "unrealistic" reduction of D u with decreasing G , 20. Notice that for G , 20 the diffusion coefficient D u attains values which are even smaller than in the G . 100 region, where the rigid crystal phase sets in. On physical grounds, this makes no sense.In their second approach, Rinn et al. calculated D u by "taking care of shell jumps." It is not clear what they mean with this and how they calculated D u . Did they remove the particles which performed a shell jump from their calculation of D u ? If so, it is not surprising that the results are different from those of Schweigert et al. [2]. As explained in Refs. [2,3], the radial fluctuations (and shell jumps) are essential for the stabilization of the intershell (or angular) diffusion in the reentrant region. The numerical results of Rinn et al. (solid symbols in Fig. 2 of Ref. [1]) saturate for G , 20 which is hard to understand physically.

Freezing and melting criteria in non-equilibrium

“…For other anisotropic equilibrium systems, such as interacting particles in one-dimensional periodic grooves, it is known that the anisotropy of particle displacements may trigger unusual phenomena such as re-entrant melting [41][42][43][44][45] which violates the Lindemann rule (so-called laser-induced melting [24]). The same is true for freezing of circular rings in two-dimensional confined systems [46,47]. In our case, as the external electric field sets a preferred direction, the particle displacements are inherently anisotropic.…”

Subnanosecond breakdown development in high-voltage pulse discharge: Effect of secondary electron emission

“…This is a very powerful method for simulation of plasma dynamics, with wide spectrum of applications (see, for example [14]). The system of equations (1) 12 s −1 for our cases.…”

Finite-size effects in the dynamics and thermodynamics of two-dimensional Coulomb clusters

“…More stable structures are obtained when the core is based on a triangular lattice, thus resembling most observed Wigner crystals. More importantly, the very different nature of orientational and radial melting has led to some confusion about how suitable observables should be defined to probe these processes separately [14,28,29]. In their study of binary 2D clusters, Drocco et al [16] chose an order parameter based on the polar angles of the particles in order to quantify the extent of orientational motion in Langevin molecular dynamics simulations.…”