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Alexander Frenkel

  • Biosketch
  • Publications
  • Movies
  • Biosketch
  • Publications
  • Movies
MOVIES 
(Made in collaboration with Dr. K. Indireshkumar; with technical assistance of Dr. I. Yakushin.)

Here is a general introduction to all three groups of movies (see also the review paper, Section 3.1; for more details, see a related paper ).

Movies of large-dispersivity regimes (see introduction to this group of movies)

Movie number; clicking it opens the first frame and the last one
Link
to movie
A brief description

Comments

1 
Movie
The outcome of evolution: Spatiotemporal pattern of strange attractor, 159696 < t < 159816.
Two subpatterns.


2
Movie
Evolution starts from the ``white noise'' initial conditions.
0 < t < 8.2 .
The fastest growing mode in linear theory is 1D.

3
Movie
A transient stage,
160 < t < 520.
So, the waves become nearly 1-dimensional.

4
Movie
A transient stage,
1760 < t < 2360.
Now, the 1D waves break down into 2D
structures due to nonlinearity.

5
Movie
A transient stage,
3200 < t < 3280.
Structures have separated into larger-amplitude ``bulges'' and small-amplitude background.

6
Movie
A transient stage,
4960 < t < 5080.
Background is nearly 1D. Bulges are identical but disarranged.

7
Movie
A transient stage,
6480 < t < 6880.
The number of bulges has decreased to 13 (through inelastic collisions; see movie 9).

8
Movie
A transient stage,
23000 < t < 26192.
Bulges are almost aligned. Background breaks down into 2D-localized ``bumps''.

9
Movie
Collisions of 2D localized surface structures.
A transient stage,
85200 < t < 86200.

Movies of small-dispersivity regimes (see introduction to this group of movies)


10
Movie
Subharmonic instability (simplified initial wave);
0 < t < 1.73.
High frequencies of forcing:
Checkerboard pattern

11
Movie
Subharmonic instability (more realisitic initial wave);
0 < t < 2.62.
High frequencies of forcing:
Checkerboard pattern.

12
Movie
Synchronous instability;
0 < t < 7.
Intermediate frequencies of forcing:
Spanwise-wavy crests.

13
Movie
Steepening of solitary waves; 
0 < t < 1.37. 
Low frequencies of forcing:
Solitary waves.

Movies of intermediate-dispersivity regimes (see intro to this group of movies)


14
Movie
Time-asymptotic regime;
dispersivity=0.125.
Normal view.


15
Movie
Time-asymptotic regime; dispersivity=0.5:
Horseshoe structures.
Normal view.


16
Movie
Time-asymptotic regime; dispersivity=1.0:
Horseshoe structures.
Normal view.


17
Movie
Time-asymptotic regime; dispersivity=2.0:
Horseshoe structures.
Normal view.


18
Movie
Time-asymptotic regime;
dispersivity=8.0.
Oblique view.


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