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Motivated to explore the dynamical mechanism of multi-fragmentation phase transition and expand our knowledge on the deterministic chaos in nonlinear dynamic process, we study systematically the nonlinear dynamical behaviors of heavy ion collisions at intermediate energy. In order to highlight the general characteristics of the collision dynamics, in the present paper, we simulate a simple collision system, $Ca+Ca$, and obverse the performances of the typical nonlinear characteristic quantities such as the production of generalized entropy and the fractal structure of the semiclassical phase space during the reaction process. The multifragmentation entropy, information dimension and the dynamical fluctuations of fragment mass distribution in the final state of the reaction are also evaluated. Our results about the intermediate processes and the final products of the reaction are verified mutually so that confirm strongly the existence of nonlinear chaos in the heavy ion collisions at intermediate energy. Meanwhile, we find that the typical characteristics of the critical phase transition obtained in the analysis of the final production of the reaction are relatively more clear in the vicinity of the incident energies $E=100 MeV$., Comment: Nuclear Physics A

Started from the static excited finite atomic nucleus, we have simulated the dynamical propagation of the nucleons using Quantum Molecular Dynamics model (QMD) without the collision term and calculated the Largest Lyapunov Exponent (LLE). The sensitivity of the nonlinear mean field dynamics to the initial conditions, in particular to the initial spatial distribution of the nucleons in certain thermodynamical stable condition, has been confirmed numerically by calculating the LLE defined in the event space. Comparatively, the Lyapunov-like exponent defined in phase space represents more clearly the sensitivity of the nonlinear dynamics to the mechanical stability of the initial conditions within the nuclear reaction time at intermediate energies. These conclusions are not only helpful for us to understand more deeply the mechanism of the nuclear reaction dynamics at intermediate energies, but it is also beneficial for clarifying further the concrete performances of deterministic chaos in the heavy-ion collisions., Comment: 18 pages and 5 figures

The directed and elliptic flows of positively charged Kaon produced in $^{58}_{28}$Ni + $^{58}_{28}$Ni reaction at incident kinetic energy 1.91 AGeV, experimental data are released newly by V. Zinyuk,et.al. in Ref.[arXiv: 1403.1504v2 [nucl-ex] 8 Apr 2014], are reproduced by using the covariant kaon dynamics. Our numerical results indicate qualitatively the Lorentz force is necessary to explained reasonably the data as soon as the space-like part of kaon's vector potential is involved. The sensitivity of $K^+$ directed as well as differential directed flow on the Lorentz force are also observed near target rapidity., Comment: arXiv admin note: text overlap with arXiv:nucl-th/9812001 by other authors

The influence of the chiral mean field on the $K^+$ transverse flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the $K^+$ in-plane flow. The FOPI data can be reasonably described using in-medium kaon potentials based on effective chiral models. The information on the in-medium $K^+$ potential extracted from kaon flow is consistent with the knowledge from other sources., Comment: 24 pages, 6 figures

The dependence of $K^+$ production on the nuclear equation of state is investigated in heavy ion collisions. An increase of the excitation function of $K^+$ multiplicities obtained in heavy ($Au+Au$) over light ($C+C$) systems when going far below threshold which has been observed by the KaoS Collaboration strongly favours a soft equation of state. This observation holds despite of the influence of an in-medium kaon potential predicted by effective chiral models which is necessary to reproduce the experimental $K^+$ yields., Comment: 4 pages Revtex, 4 PS figures, to appear in Phys. Rev. Lett

The proton elliptic flow in collisions of Ca on Ca at energies from 30 to 100 MeV/nucleon is studied in an isospin-dependent transport model. With increasing incident energy, the elliptic flow shows a transition from positive to negative flow. Its magnitude depends on both the nuclear equation of state (EOS) and the nucleon-nucleon scattering cross section. Different elliptic flows are obtained for a stiff EOS with free nucleon-nucleon cross sections and a soft EOS with reduced nucleon-nucleon cross sections, although both lead to vanishing in-plane transverse flow at the same balance energy. The study of both in-plane and elliptic flows at intermediate energies thus provides a means to extract simultaneously the information on the nuclear equation of state and the nucleon-nucleon scattering cross section in medium., Comment: 6 pages, 2 figures