Ott, Josh | Search NASA

DOE OSTI2024

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram

Here, we present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of quantum chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a crossover from the dynamical exponent of critical diffusion, z≃4, to the expected scaling exponent of model H, z≃3. We use our method to investigate the time-dependent correlation function of non-Gaussian moments M n (t) of the order parameter. We find that the relaxation time depends in a nontrivial manner on the power n.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Dynamic scaling of order parameter fluctuations in model B

Brookhaven National Laboratory has performed a dedicated set of experiments, called the Beam Energy Scan (BES), with the goal of location a possible critical point in the phase diagram of nuclear matter, This point is analogous to the endpoint of the liquid-gas phase transition in water, where the liquid phase corresponds to a phase of hadrons, and the gas phase to a plasma of quarks and gluons. In order to describe the data generated by these experiments we have studied numerical simulations of the stochastic diffusion equation with a conserved charge. Here, we focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z ≃ 3.972(2), which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗