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Relativistic hydrodynamics is a powerful tool to simulate the evolution of the quark gluon plasma (QGP) in relativistic heavy ion collisions. Using 10000 initial and final profiles generated from 2+1-d relativistic hydrodynamics VISH2+1 with MC-Glauber initial conditions, we train a deep neural network based on stacked U-net, and use it to predict the final profiles associated with various initial conditions, including MC-Glauber, MC-KLN and AMPT and TRENTo. A comparison with the VISH2+1 results shows that the network predictions can nicely capture the magnitude and inhomogeneous structures of the final profiles, and nicely describe the related eccentricity distributions $P(varepsilon_n)$ (n=2, 3, 4). These results indicate that deep learning technique can capture the main features of the non-linear evolution of hydrodynamics, showing its potential to largely accelerate the event-by-event simulations of relativistic hydrodynamics.
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In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {tt stacked U-net}, can capture the main features of the non-linear evolution of hydrodynamics, which could also rapidly predict the final profiles for various testing initial conditions.
A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The incorporation of the angular-momentum conservation requires that the spin polarization tensor is introduced. It plays a role of a Lagrange multiplier conjugated to the spin tensor. The space-time evolution of the spin polarization tensor depends on the specific form chosen for the spin tensor.
We utilize nonequilibrium covariant transport theory to determine the region of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken scenario, appropriate for the early longitudinal expansion stage of the collision. In the scale invariant case of a constant shear viscosity to entropy density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate in calculating dissipative effects if initially the expansion timescale exceeds half the transport mean free path tau0/lambda0 > ~2. The same accuracy with Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics driven by a constant cross section, on the other hand, about 50% larger tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we find that the naive approximation to Israel-Stewart theory, which neglects products of gradients and dissipative quantities, has an even smaller range of applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and Navier-Stokes solutions in 0+1D, and present further tests for numerical dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized conservation laws.
We study the conditions for the formation and propagation of Korteweg-de Vries (KdV) solitons in nuclear matter. In a previous work we have derived a KdV equation from Euler and continuity equations in non-relativistic hydrodynamics. In the present contribution we extend our formalism to relativistic fluids. We present results for a given equation of state, which is based on quantum hadrodynamics (QHD).
The partition function of nonequilibrium distribution which we recently obtained [arXiv:0802.0259] in the framework of the maximum isotropization model (MIM) is exploited to extract physical information from experimental data on the proton rapidity and transverse mass distributions. We propose to partition all interacting nucleons into ensembles in accordance with the number of collisions. We analyze experimental rapidity distribution and get the number of particles in every collision ensemble. We argue that even a large number of effective nucleon collisions cannot lead to thermalization of nucleon system; the thermal source which describes the proton distribution in central rapidity region arises as a result of fast thermalization of the parton degrees of freedom. The obtained number of nucleons which corresponds to the thermal contribution is treated as a ``nucleon power of the created quark-gluon plasma in a particular experiment.
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