Introduction to movies of large-dispersivity regimes
1. Parameters etc.
These are movies of flow regimes in parametric domains with \(\varepsilon \ll 1\). We see the surface of a film flowing down a vertical plane \((\kappa = 0)\). The view direction is obliquely up the plane. For convenience of presentation, different coordinate axes may have different scales. In reality, all structures have small slopes and are nearly axisymmetric. The values of parameters for all these movies (except for the last one that shows collisions of structures) are \(\varepsilon = 1/50\), p = 16, and q = 16. For the last movie, they are \(\varepsilon = 1/25\), p = 5, and q = 40.
2. Strange attractor and spatiotemporal order
The movie 1 shows the spatiotemporal pattern characteristic of the strange attractor (the largest Liapunov exponent is positive) of this dynamical system. The system arrives at this attractor only after a long-time evolution, having passed through many stages.
3. Transient stages
Some of the transient stages in computer simulation which starts from random, "white noise'' initial conditions appear as movies 2 through 8.
4. Collisions of bulges
The last movie (movie 9) shows intriguing "inelastic collisions'' of localized surface structures ("bulges''), which occur in a transient stage of the evolution to the attractor.
The movie 1 shows the spatiotemporal pattern characteristic of the strange attractor (the largest Liapunov exponent is positive) of this dynamical system. The system arrives at this attractor only after a long-time evolution, having passed through many stages.
3. Transient stages
Some of the transient stages in computer simulation which starts from random, "white noise'' initial conditions appear as movies 2 through 8.
4. Collisions of bulges
The last movie (movie 9) shows intriguing "inelastic collisions'' of localized surface structures ("bulges''), which occur in a transient stage of the evolution to the attractor.