Nature of Newton’s cradle-like convecton dynamics

Determine whether the cyclic Newton’s cradle-like traveling bound states observed in convection within an inclined porous layer with asymmetric thermal boundary conditions are stable two-frequency states that connect branches of single-frequency traveling spatially localized convective states at either end of their existence interval.

Background

The paper reports cyclic, Newton’s cradle-like behavior in direct numerical simulations of traveling bound states of spatially localized convective structures (convectons) in an inclined porous medium when midplane reflection symmetry is weakly broken via an imperfectly conducting top boundary. In these simulations, multi-pulse bound states periodically reorganize through collisions, reproducing the initial structure in a cyclic manner.

In the discussion, the authors conjecture that these cyclic solutions are examples of stable two-frequency states that connect branches of single-frequency traveling states, a scenario known from pattern-forming systems with broken reflection symmetry. Confirming this interpretation would require establishing the two-frequency nature and the branch-connection role of these states within the bifurcation structure of the governing Darcy–Oberbeck–Boussinesq system with the specified boundary conditions.