Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cousins, Will [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014transfer abstract |
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| Schlagwörter: |
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| Umfang: |
11 |
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| Übergeordnetes Werk: |
Enthalten in: Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation - Thude, Hansjörg ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:280 ; year:2014 ; day:1 ; month:07 ; pages:48-58 ; extent:11 |
| Links: |
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| DOI / URN: |
10.1016/j.physd.2014.04.012 |
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ELV039255530 |
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| 520 | |a The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. | ||
| 520 | |a The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. | ||
| 650 | 7 | |a Prediction of extreme events |2 Elsevier | |
| 650 | 7 | |a Rogue waves |2 Elsevier | |
| 650 | 7 | |a Nonlinear energy transfers |2 Elsevier | |
| 650 | 7 | |a Probabilistic quantification of rare events |2 Elsevier | |
| 650 | 7 | |a Intermittent instabilities |2 Elsevier | |
| 650 | 7 | |a Dispersive nonlinear waves |2 Elsevier | |
| 700 | 1 | |a Sapsis, Themistoklis P. |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Thude, Hansjörg ELSEVIER |t Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation |d 2015transfer abstract |g Amsterdam [u.a.] |w (DE-627)ELV018422527 |
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10.1016/j.physd.2014.04.012 doi GBVA2014006000028.pica (DE-627)ELV039255530 (ELSEVIER)S0167-2789(14)00092-X DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Cousins, Will verfasserin aut Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Prediction of extreme events Elsevier Rogue waves Elsevier Nonlinear energy transfers Elsevier Probabilistic quantification of rare events Elsevier Intermittent instabilities Elsevier Dispersive nonlinear waves Elsevier Sapsis, Themistoklis P. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 https://doi.org/10.1016/j.physd.2014.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 280 2014 1 0701 48-58 11 045F 530 |
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10.1016/j.physd.2014.04.012 doi GBVA2014006000028.pica (DE-627)ELV039255530 (ELSEVIER)S0167-2789(14)00092-X DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Cousins, Will verfasserin aut Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Prediction of extreme events Elsevier Rogue waves Elsevier Nonlinear energy transfers Elsevier Probabilistic quantification of rare events Elsevier Intermittent instabilities Elsevier Dispersive nonlinear waves Elsevier Sapsis, Themistoklis P. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 https://doi.org/10.1016/j.physd.2014.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 280 2014 1 0701 48-58 11 045F 530 |
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10.1016/j.physd.2014.04.012 doi GBVA2014006000028.pica (DE-627)ELV039255530 (ELSEVIER)S0167-2789(14)00092-X DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Cousins, Will verfasserin aut Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Prediction of extreme events Elsevier Rogue waves Elsevier Nonlinear energy transfers Elsevier Probabilistic quantification of rare events Elsevier Intermittent instabilities Elsevier Dispersive nonlinear waves Elsevier Sapsis, Themistoklis P. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 https://doi.org/10.1016/j.physd.2014.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 280 2014 1 0701 48-58 11 045F 530 |
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10.1016/j.physd.2014.04.012 doi GBVA2014006000028.pica (DE-627)ELV039255530 (ELSEVIER)S0167-2789(14)00092-X DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Cousins, Will verfasserin aut Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Prediction of extreme events Elsevier Rogue waves Elsevier Nonlinear energy transfers Elsevier Probabilistic quantification of rare events Elsevier Intermittent instabilities Elsevier Dispersive nonlinear waves Elsevier Sapsis, Themistoklis P. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 https://doi.org/10.1016/j.physd.2014.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 280 2014 1 0701 48-58 11 045F 530 |
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10.1016/j.physd.2014.04.012 doi GBVA2014006000028.pica (DE-627)ELV039255530 (ELSEVIER)S0167-2789(14)00092-X DE-627 ger DE-627 rakwb eng 530 530 DE-600 610 VZ 570 VZ BIODIV DE-30 fid Cousins, Will verfasserin aut Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model 2014transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. Prediction of extreme events Elsevier Rogue waves Elsevier Nonlinear energy transfers Elsevier Probabilistic quantification of rare events Elsevier Intermittent instabilities Elsevier Dispersive nonlinear waves Elsevier Sapsis, Themistoklis P. oth Enthalten in Elsevier Thude, Hansjörg ELSEVIER Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV018422527 volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 https://doi.org/10.1016/j.physd.2014.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA AR 280 2014 1 0701 48-58 11 045F 530 |
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Enthalten in Role of the Fyn −93A>G polymorphism (rs706895) in acute rejection after liver transplantation Amsterdam [u.a.] volume:280 year:2014 day:1 month:07 pages:48-58 extent:11 |
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quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
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Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model |
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The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. |
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The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. |
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The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda–McLaughlin–Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. |
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