The following model is studied analytically and numerically: point particles with masses m , μ , m , ⋯ ( m ≥ μ ) are distributed over the positive half-axis. Their dynamics is initiated by giving a positive velocity to the particle located at the origin; in its course, the particles undergo elastic collisions.

We show that, for certain values of m / μ , starting from the initial state where the particles are equidistant, the system evolves in a hydrodynamic way: (i) the rightmost particle (blast front) moves as t δ with δ < 1 ; (ii) recoiled particles behind the front enter the negative half-axis; and (iii) the splatter—the particles with locations x ≤ 0 —moves in the ballistic way and eventually takes over the whole energy of the system.

These results agree with those obtained in S. Chakraborti , , for m / μ = 2 , and random initial particle positions. At the same time, we explicitly found the collection of positive numbers { M i , i ∈ N } such that, for m / μ = M i ,   i ≤ 700 , the following holds: (a) the splatter is absent; (b) the number of simultaneously moving particles is at most three; and (c) the blast front moves in the ballistic way.

However, if, similarly as in S. Chakraborti ., the particle positions are sampled from a uniformly distributed ensemble, for m / μ = M i the system evolves in a hydrodynamic way. T. Holovatch,

Y. Kozitsky, K. Pilorz, Y. Holovatch, Breakdown of hydrodynamics in a one-dimensional cold gas, Physical Review E 112(5) (2025) l052101.