Local (in time) maximal lyapunov exponents of fragmenting drops

Abstract

We analyze the dynamics of fragment formation in simulations of exploding three-dimensional Lennard-Jones hot drops, using the maximum local (in time) Lyapunov exponent (MLLE). The dependence of this exponent on the excitation energy of the system displays two different behaviors according to the stage of the dynamical evolution: one related to the highly collisional stage of the evolution, at early times, and the other related to the asymptotic state. We show that in the early, highly collisional, stage of the evolution the MLLE is an increasing function of the energy, as in an infinite-size system. On the other hand, at long times, the MLLE displays a maximum, depending mainly on the size of the resulting biggest fragment. We compare the time scale at which the MLLE's reach their asymptotic values with the characteristic time of fragment formation in phase space. Moreover, upon calculation of the maximum Lyapunov exponent (MLE) of the resulting fragments, we show that their dependence with the mass can be traced to bulk effects plus surface corrections. Using this information the asymptotic behavior of the MLLE can be understood and the fluctuations of the MLE of the whole system can be easily calculated. These fluctuations display a sudden increase for that excitation energy which produces a power-law-like asymptotic distribution of fragments.