doi:10.1016/S0167-2789(03)00233-1 
Copyright © 2003 Elsevier B.V. All rights reserved.
A dissipative one-dimensional collision model with intermediate energy storage
J. Dunkela, 
, 
, W. Ebelinga, J. W. P. Schmelzerb, c and G. Röpkeb, c
a Institute of Physics, Humboldt-University, Newtonstraße 15, D-12489, Berlin, Germany
b Department of Physics, University of Rostock, 18051, Rostock, Germany
c Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia
Received 27 September 2002;
accepted 2 May 2003;
Communicated by R.P. Behringer
Available online 2 August 2003.
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Abstract
We study a simple model for a dissipative collision process of two one-dimensional chains, consisting of point-particles. In this model, the particles interact with their nearest neighbors via nonlinear Morse potentials. In addition, each particle is subject to nonlinear friction, modeling the transfer of energy between the translational degree of freedom and energy depots, representing further (internal) degrees of freedom. Depending on the momentary state of the system, this energy exchange mechanism can decrease or increase the kinetic energy of the particles on the cost of the depots. In particular, the clusters are assumed to have the ability to store parts of their initial energy in the depots. In later stages of a collision process, the stored depot energy can be used for an acceleration of the fragments, i.e., it can be converted into kinetic energy of motion. Both, analytically and by means of computer simulations, we investigate the dependence of the fragmentation channels, observed after the collisions, on different initial conditions (e.g. initial particle energy, cluster size) and system parameters.
Author Keywords: Energy storage in depots; Dissipative cluster collisions; Fragmentation channels
PACS classification codes: 05.45.−a; 24.10.−i; 25.70.−z
Fig. 1. Morse potential as used in the numerical simulations. The parameter b is given in units σ−1.
Fig. 2. Shape of the friction coefficient γ(
v) for different values of κ in units [κ]=μ. The region, where γ(
v)<0 holds, corresponds to the transformation of stored depot energy into translational kinetic energy of motion. On the other hand, if γ(
v) is positive, then kinetic energy is transformed into (dissipative) depot energy.
Fig. 3. Shape of the dissipative potential as defined in
Eq. (8).
Fig. 4. Schematic representation of the initial configuration at time
t=0 for
N=7 particles.
Fig. 5. (a) Traces of the two particles in case of a quasi-elastic collision. (b) Kinetic energy per particle during the collision as a function of time. Further parameter values are
b=5,κ=1 (in c.u.).
Fig. 6. (a) Traces of the two particles in case of a fusion. (b) The stationary (bound) state corresponds to (optical) anti-phase oscillations. According to the analytic estimate (
31) the maximum/minimum distance between the particles is given by
r±=(1±0.16) (in c.u.). (c) Kinetic energy per particle as a function of time. All three pictures are taken from the same simulation run (further parameter values are
b=5,κ=1 in c.u.).
Fig. 7. Fragmentation channels for
N=2 particles and symmetric initial state [
N1,
N2]=[1,1]. The solid curve 1 was numerically calculated. The dashed–dotted line 2 shows the analytical approximation of the upper branch and is obtained from the numerical solutions of the transcendental
equation (47). The dotted curve 4 represents the analytical estimate for the lower branch according to (
41). The other parameter values used here are
b=5,κ=1 (in c.u.). (b) Enlarged section of the part (a).
Fig. 8. Fragmentation channels for
N=3 with asymmetric initial state [
N1,
N2]=[1,2]. Further parameter values are
b=5,κ=1 (in c.u.). The results are very similar to those obtained for
N=2 and
N=4.
Fig. 9. Fragmentation channels for
N=4 with (a) asymmetric initial state [1,3] and (b) symmetric initial state [2,2]. Further parameter values are
b=5,κ=1 (in c.u.). For the asymmetric initial condition in (a) the parameter region leading to a fusion is significantly larger compared with the symmetric initial state.
Fig. 10. Fragmentation channels for
N=8 and different initial states [
N1,
N2]. As already observed for
N=4, the parameter region leading to a fusion decreases with increasing symmetry of the initial state. Further parameter values are
b=5,κ=1 (in c.u.).
Fig. 11. Two different realizations of the fragmentation channel [
N]=[3] characterized by different stationary c.o.m. velocities
vs(∞). (a) A process leading to a stationary configuration with
vs(∞)=0. (b) A fusion with stationary c.o.m. velocity . Further parameter values are
b=5,κ=1 (in c.u.).
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directions with dissipation to the lattice at each collision. Therefore, the relationship between the energy transfer processes in the simulation and that in the standard binary collision cascade model of energy transport is examined.
