Breakdown of hydrodynamics in a one-dimensional cold gas

Area of Science:

• Physics
• Statistical Mechanics
• Dynamical Systems

Background:

• Investigates the dynamics of point particles with varying masses (m ≥ μ) on a positive half-axis.
• Focuses on systems initiated with elastic collisions and positive initial velocities.

Purpose of the Study:

• To analytically and numerically study particle dynamics under specific mass ratios (m/μ).
• To identify conditions leading to hydrodynamic evolution versus ballistic behavior.
• To characterize the motion of the blast front and particle splatter.

Main Methods:

• Analytical investigation of particle dynamics.
• Numerical simulations of particle interactions and collisions.
• Analysis of specific mass ratios (m/μ) and initial particle distributions.

Main Results:

• For certain m/μ ratios and equidistant initial states, systems exhibit hydrodynamic behavior: blast front velocity (t^δ, δ<1), particle recoil to negative axis, and ballistic splatter.
• Identified specific mass ratios (M_i) where splatter is absent, particle motion is limited (≤3 particles), and the blast front moves ballistically.
• For these M_i ratios, uniform initial distributions still result in hydrodynamic evolution.

Conclusions:

• The mass ratio (m/μ) critically determines the emergent dynamics of colliding particle systems.
• Distinct dynamical regimes (hydrodynamic vs. ballistic) exist, influenced by initial conditions and mass ratios.
• The study reveals conditions for controlled particle behavior, including the absence of splatter.