workshop on renormalization group, kyoto 2005 b. tirozzi, s.yu. dobrokhotov, s.ya....
TRANSCRIPT
![Page 1: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/1.jpg)
Workshop On Renormalization Group, Kyoto 2005
B. Tirozzi, S.Yu. Dobrokhotov,
S.Ya. Sekerzh-Zenkovich,
T.Ya. Tudorovskiy
Analytical and numerical analysis of the wave profiles near the fronts appearing in
Tsunami problems
![Page 2: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/2.jpg)
“Gaussian” source of Earthquake
-5
-2.5
0
2.5
5-5
-2.5
0
2.5
5
00.250.5
0.751
-5
-2.5
0
2.5
5
![Page 3: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/3.jpg)
Level curves of perturbation
-2-1
01
2
-4-2
024
![Page 4: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/4.jpg)
Wave profiles at the front at time t at different angles
-4 -2 2 4
-0.5
0.5
1
1.5
![Page 5: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/5.jpg)
3D wave profile for elliptic source
-20
-10
0
10
20-20
-10
0
10
20
-0.500.511.5
-20
-10
0
10
20
![Page 6: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/6.jpg)
“Modulated gaussian” source of Earthquake
-5
-2.5
0
2.5
5-5
-2.5
0
2.5
5
-2
0
2
-5
-2.5
0
2.5
5
![Page 7: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/7.jpg)
Level curves of perturbation
-2-1
01
2
-4-2
024
![Page 8: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/8.jpg)
Wave profiles at the front at time t at different angles
-4 -2 2 4
-1
-0.75
-0.5
-0.25
0.25
0.5
0.75
1
![Page 9: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/9.jpg)
3D wave profile for elliptic source
-20
-10
0
10
20-20
-10
0
10
20
-2-1012
-20
-10
0
10
20
![Page 10: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/10.jpg)
The ridge near the source of Eathquake
-5
0
5
-5
0
5
-3
-2
-1
0
-5
0
5-6 -4 -2 0 2 4 6
-6
-4
-2
0
2
4
6
![Page 11: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/11.jpg)
Fronts at different times
![Page 12: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/12.jpg)
The set of profiles
-20 -15 -10 -5 5 10 15 20
-20
-15
-10
-5
5
10
15
20
0.658889
1.48386
1.03988
0.0444183
1.03364
1.47197
0.658554
0.00228282
![Page 13: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/13.jpg)
-20 -15 -10 -5 5 10 15 20
-20
-15
-10
-5
5
10
15
20
0.658889
1.48386
1.03988
0.0444183
1.03364
1.47197
0.658554
0.00228282
![Page 14: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/14.jpg)
![Page 15: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/15.jpg)
![Page 16: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/16.jpg)
Simulations for Tyrrhenian Sea
-400 -200 0 200 400
-400
-200
0
200
400
-400 -200 0 200 400
-400
-200
0
200
400
Relief data:National Oceanic and Atmospheric Administration (NOAA)National Geophysical Data Center (NGDC)ETOPO2 2-minute Global Reliefhttp://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html
![Page 17: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/17.jpg)
Rays for imaginary source at Stromboli: 38.8 N, 15.2 E
50 100 150 200 250 300 350 400
-400
-350
-300
-250
-200
-150
-100
-50
![Page 18: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/18.jpg)
Amplitudes of wave at different points of the coast
150 200 250 300 350 400 450
-350
-300
-250
-200
-150
-100
0.155356
0.0916952
0.118962
0.019779
0.00317829
0.09830570.0886875
0.306578
0.1297210.00840296
![Page 19: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/19.jpg)
3D wave profile
![Page 20: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/20.jpg)
Density plot
![Page 21: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/21.jpg)
DD7-29/05/07-01/06/07
Special session on tsunami and typhoons
Scattering of tsunami on the beach
S.Dobrokhotov Inst. Probl. of Mechanics R. Ac Sc. Moscow
Petya ZhevandrovEscuela de Ciencias Fisico-Matematicas, Morelia, Mexico
Brunello TirozziDepartment of Physics, Univ. “La Sapienza”, Rome
![Page 22: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/22.jpg)
... Workshop on Extreme Events ...Max Planck Institut for Complex SystemDresden, 30 October-2 November 2006
Analysis of the tsunami event in Algeria 2003
B. Tirozzi (1),F. Raicich (2)
(1) Department of Physics, University “La Sapienza”, Rome, Italy(2) CNR, Institute of Marine Sciences, Trieste, Italy
![Page 23: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/23.jpg)
Valencia
Barcelona
Ibiza
Earthquake data (USGS): t0: 18:44:19 GMT, 21 may 2003 USGS: epicenter 36.96°N, 3.63°E, M=6.9, hf=12 km Borerro: epicenter 36.90°N, 3.71°E, M=6.8, hf=10 km, strike=56°
![Page 24: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/24.jpg)
![Page 25: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/25.jpg)
Ellipsoidal deformation
M = 6.9
hf = 12 km
(Pelinovsky et al., 2001)
a = 34 km
b = 12 km
b56°
a
Coordinates: model gridpoints
![Page 26: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/26.jpg)
(Dobrokhotov et al., 2006)
a1= 1.2 10-2 km-1
Gaussian*cosine deformation
= 0
a2 = 2.7 10-2 km-1
b1 = 0.5 10-2 km-2
b2 = 4.0 10-2 km-2
= 56°
Coordinates: model gridpoints
![Page 27: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/27.jpg)
![Page 28: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/28.jpg)
![Page 29: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/29.jpg)
![Page 30: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/30.jpg)
![Page 31: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/31.jpg)
![Page 32: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/32.jpg)
![Page 33: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/33.jpg)
Linear theory of the scattering of localized waves on a beach of constant slope
S. Dobrokhotov, Petya Zhevandrov, Brunello Tirozzi
![Page 34: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/34.jpg)
![Page 35: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/35.jpg)
![Page 36: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/36.jpg)
Shape of perturbation
![Page 37: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/37.jpg)
Amplitude of the waves at tsunami front
![Page 38: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/38.jpg)
![Page 39: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/39.jpg)
Average of the too fast oscillating WKB solution
![Page 40: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/40.jpg)
Example: beach of costant slope
![Page 41: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/41.jpg)
Momentum equation
![Page 42: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/42.jpg)
Singular Lagrangian manifold
![Page 43: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/43.jpg)
Dynamic on the lagrangian manifold
![Page 44: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/44.jpg)
Dynamic on the phase space
![Page 45: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/45.jpg)
Solutions before and after the scattering of the beach (1/2)
![Page 46: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/46.jpg)
Solutions before and after the scattering of the beach (2/2)
![Page 47: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/47.jpg)
Graphics 1
![Page 48: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/48.jpg)
Graphics 2
![Page 49: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/49.jpg)
Graphics 3
![Page 50: Workshop On Renormalization Group, Kyoto 2005 B. Tirozzi, S.Yu. Dobrokhotov, S.Ya. Sekerzh-Zenkovich, T.Ya. Tudorovskiy Analytical and numerical analysis](https://reader035.vdocuments.site/reader035/viewer/2022070415/56649ec55503460f94bd09e1/html5/thumbnails/50.jpg)
End