UCLA

In this dissertation, I investigate the limits of the hydrodynamic approach to many-body systems. Due to the impracticality of solving equations of motion for individual particles, hydrodynamics provides an effective description, reducing complex systems to a few macroscopic variables, such as density, entropy, and velocity. However, the validity of hydrodynamic equations has to be carefully assessed when applied to small length scales comparable to the average interparticle distance. I explore this limitation by analyzing systems under extreme physical conditions in two scenarios.First, I study strongly coupled plasmas, where traditional hydrodynamic methods fail. In such plasmas, the electrostatic interaction is sufficiently strong to influence their equilibrium and out-of-equilibrium behavior. I use a variational approach to derive generalized hydrodynamic equations from first principles, where the effects of strong coupling are included using nonlocal terms. The obtained results are compared in the linear regime to numerical experiments, showing excellent agreement for a wide range of coupling strengths. This suggests exploring the developed framework for nonlinear problems and other long-range systems in the future. Second, I examine extreme bubble collapse when the bubble is surrounded by a compressible fluid. The goal is to evaluate the response of the compressible fluid when its motion reaches high Mach numbers. This is challenging to describe with existing numerical methods due to the presence of large gradients within the fluid. I implement a uniform density and pressure approximation inside the bubble, which allows for quick and accurate computations that include the effects of compressibility of the surrounding fluid. To check the accuracy of the created solver, I derive an asymptotic analytic benchmark for late stages of the collapse. This key limit was achieved in the simulations. The obtained results in the future can be coupled with molecular dynamics for the gas inside the cavity to estimate the possibility of thermal fusion in such collapses.