In order to describe the heavy ion collision dynamics in hot and very dense nuclear matter formed in the overlapping region of the two colliding nuclei, we used simulated numerical calculations for FAIR available energies. We used the anti-k_T jet-detection algorithm for highlighting the main directions of flow in Au-Au collisions at CBM energies, thus obtaining structures of the events depending on the number of flow streams. The jet-finder algorithm identified domains in the y-ψ (rapidity-azimuthal angle) plane, where the number of charged particles, momenta and energy take higher values than in other areas of this plane. The anisotropic flow coefficients vn may offer information about the pressure gradients in the early stages of the collision and about the high-density nuclear matter properties. The observation of K⁺ mesons in heavy ion collisions is of interest since K⁺ mesons, due to their strangeness, have a mean free path that exceeds the dimensions of the "fireball". In the numerical calculations the interval of rapidity 0 < y < 0.8 is highlighted, for which the fluctuations of the antiparticle to particle ratio excitation functions show non-monotonic behavior in the 10-13 A GeV energy interval.

An overview of the most important experimental results obtained in the first three running years with the BRAHMS experiment from Brookhaven National Laboratory(USA) is presented. The design of the experiment permits to measure the interesting physical quantities in a large ranges of rapidity and transverse momentum. Therefore, properties of hadron production vs rapidity and transverse momenta are presented.

In order to describe the heavy ion collision dynamics which implies the formation of hot and very dense nuclear matter in the overlapping region of the two colliding nuclei, we used simulated numerical calculations for FAIR available energies. We used the anti-$k_T$ jet-detection algorithm for highlighting the main directions of flow in Au-Au collisions at CBM energies, thus obtaining structures of the events depending on the number of flow streams. The jet-finder algorithm identified domains in the y-$\psi$ (rapidity-azimuthal angle) plane, where the number of charged particles, momenta and energy take higher values compared to other areas of this plane. The anisotropic flow coefficients $v_n$ may offer information about the pressure gradients in the early stages of the collision and about the high-density nuclear matter properties. The observation of $K^{+}$ mesons in heavy ion collisions is of interest since $K^{+}$ mesons, due to their strangeness, have a mean free path that exceeds the dimensions of the “fireball”. In the numerical calculations the interval of rapidity $0<y<0.8$ is highlighted, for which the fluctuations of the antiparticle to particle ratio excitation functions show non-monotonic behavior in the 10–13 A GeV energy interval.

We present a study of the mean transverse momentum $⟨p_{\mathrm{T}}⟩$ of identified strange hadrons (${\mathrm{K}}_{\mathrm{S}}^0,\Lambda ,\overline{\Lambda },{\Xi }^{-},{\overline{\Xi }}^{+},\varphi ,{\Omega }^{-},{\overline{\Omega }}^{+}$) produced in Au+Au collisions at RHIC-BES energies (the nucleon–nucleon center-of-mass energy $\sqrt{s_{\mathrm{N}\mathrm{N}}}=7.7 \mathrm{G}\mathrm{e}\mathrm{V},11.5 \mathrm{G}\mathrm{e}\mathrm{V},19.6 \mathrm{G}\mathrm{e}\mathrm{V},27 \mathrm{G}\mathrm{e}\mathrm{V}$ and $39 \mathrm{G}\mathrm{e}\mathrm{V}$). The mean transverse momentum is obtained from transverse momentum spectra of the strange hadrons as measured by the STAR experiment and its dependence on the number of participants $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$ is studied. For RHIC-BES energies, experimental data indicate a centrality dependence of $⟨p_{\mathrm{T}}⟩$, with an increase towards central collisions. This dependency is described using a power-law function to fit the data. The power-law exponent $\alpha$ is used to characterize the degree of flattening of $⟨p_{\mathrm{T}}⟩$ with respect to $N_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}}$ and its dependency on the collision energy and particle mass is studied. Special emphasis is placed on $\varphi$-meson that has a smaller interaction cross-section, thus reflecting the properties of the early stages of the system’s evolution. The $⟨p_{\mathrm{T}}⟩$ of $\varphi$-mesons produced in Au+Au collisions at RHIC-BES energies are compared with the results obtained in Au+Au collisions at higher RHIC energies and in Pb+Pb collisions at SPS and LHC energies. A distinct energy dependence of $\varphi ⟨p_{\mathrm{T}}⟩$ values is identified. Furthermore, data indicate, when comparing peripheral and central heavy-ion collisions, that $\varphi$-meson $⟨p_{\mathrm{T}}⟩$ increases with system size, following two distinct trends. The results are compared with the predictions of the default and string-melting versions of the AMPT generator. We observe that the string-melting AMPT version describes the strange meson $⟨p_{\mathrm{T}}⟩$, but underpredicts the strange baryon $⟨p_{\mathrm{T}}⟩$ centrality dependence. The default AMPT overpredicts the ${\mathrm{K}}_{\mathrm{S}}^0$ and $\varphi$ meson $⟨p_{\mathrm{T}}⟩$ centrality dependence, while the strange baryon data are in general better described by this version of the model. The exponent $\alpha$ obtained from AMPT-simulated results does not describe the measurements satisfactorily.