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We calculated the azimuthal angle dependence of the local spin polarization of hyperons in 200 GeV Au+Au and 2.76 TeV Pb+Pb collisions in the framework of the (3+1)D viscous hydrodynamic model CLVisc with AMPT initial conditions encoding initial orbital angular momenta. We find that the azimuthal angle dependence of the hyperon polarization strongly depends on the choice of the spin chemical potential $\Omega_{\mu\nu}$. With $\Omega_{\mu\nu}$ chosen to be proportional to the temperature vorticity, our simulation shows coincidental results with the recent measurements at RHIC., Comment: Contribution to the Proceedings of the 28th international conference on ultrarelativistic nucleus-nucleus collisions (Quark Matter 2019)

We have developed a numerical framework for a full solution of the relativistic Boltzmann equations for the quark-gluon matter using the multiple Graphics Processing Units (GPUs) on distributed clusters. Including all the $2 \to 2$ scattering processes of 3-flavor quarks and gluons, we compute the time evolution of distribution functions in both coordinate and momentum spaces for the cases of pure gluons, quarks and the mixture of quarks and gluons. By introducing a symmetrical sampling method on GPUs which ensures the particle number conservation, our framework is able to perform the space-time evolution of quark-gluon system towards thermal equilibrium with high performance. We also observe that the gluons naturally accumulate in the soft region at the early time, which may indicate the gluon condensation., Comment: 32 pages, 12 figures

In this updated vesion of ZMCintegral, we have added the functionality of integrations with parameter scan on distributed Graphics Processing Units(GPUs). Given a large parameter grid (up to 10^{10} parameter points to be scanned), the code will evaluate integrations for each parameter grid value. To ensure the evaluation speed, this new functionality employs a direct Monte Carlo method for the integraion. The Python API is kept the same as the previous ones and users have a full flexibility to define their own integrands. The performance of this new functionality is tested for both one node and multi-nodes conditions., Comment: 14 pages, 7 figures(including sub-figures)

We revisit the azimuthal angle dependence of the local spin polarization of hyperons in heavy-ion collisions at 200 GeV in the framework of the (3+1)D viscous hydrodynamic model CLVisc. Two different initial conditions are considered in our simulation: the optical Glauber initial condition without initial orbital angular momentum and the AMPT initial condition with an initial orbital angular momentum. We find that the azimuthal angle dependence of the hyperon polarization strongly depends on the choice of the so-called "spin chemical potential" $\Omega_{\mu\nu}$. With $\Omega_{\mu\nu}$ chosen to be proportional to the temperature vorticity, our simulation shows qualitatively coincidental results with the recent measurements at RHIC for both the longitudinal and transverse polarization. We argue that such a coincidence may be related to the fact that the temperature vorticity is approximately conserved in the hot quark-gluon matter., Comment: RevTex 4, 18 pages, 9 figures. A bug has been corrected in the numerical calculation of results for the non-relativistic vorticity. A number of typos are corrected. To appear in Physical Review Research

We have developed a Python package ZMCintegral for multi-dimensional Monte Carlo integration on multiple Graphics Processing Units(GPUs). The package employs a stratified sampling and heuristic tree search algorithm. We have built three versions of this package: one with Tensorflow and other two with Numba, and both support general user defined functions with a user-friendly interface. We have demonstrated that Tensorflow and Numba help inexperienced scientific researchers to parallelize their programs on multiple GPUs with little work. The precision and speed of our package is compared with that of VEGAS for two typical integrands, a 6-dimensional oscillating function and a 9-dimensional Gaussian function. The results show that the speed of ZMCintegral is comparable to that of the VEGAS with a given precision. For heavy calculations, the algorithm can be scaled on distributed clusters of GPUs., Comment: 18 pages, 9 figures