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Eeltink D, Armaroli A, Luneau C, Branger H, Brunetti M, Kasparian J. Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping. Nonlinear Dyn 2020; 102:2385-2398. [PMID: 33364681 PMCID: PMC7749097 DOI: 10.1007/s11071-020-06043-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 10/19/2020] [Indexed: 06/12/2023]
Abstract
We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation. In the latter, the spectrum is truncated to only the fundamental frequency and the upper and lower sidebands. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general for NLSE systems. By means of experimentally obtained phase-space trajectories, we demonstrate that forcing and damping cause a separatrix crossing during the evolution. When the system is damped, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside the separatrix, lifting the phase-shift. Furthermore, we observe a growth and decay cycle for modulated plane waves that are conventionally considered stable. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution.
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Affiliation(s)
- D. Eeltink
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - A. Armaroli
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - C. Luneau
- Institut Pytheas, AMU,CNRS,IRD, Marseille, France
| | - H. Branger
- IRPHE, AMU, CNRS, ECM, Marseille, France
| | - M. Brunetti
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - J. Kasparian
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
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Gherardi S, Bovolenta M, Passarelli C, Falzarano MS, Pigini P, Scotton C, Neri M, Armaroli A, Osman H, Selvatici R, Gualandi F, Recchia A, Mora M, Bernasconi P, Maggi L, Morandi L, Ferlini A, Perini G. Corrigendum to: "Transcriptional and epigenetic analyses of the DMD locus reveal novel cis-acting DNA elements that govern muscle dystrophin expression". [Biochim. Biophys. Acta Gene Regul. Mech. 2017 Nov;1860(11):1138-1147.]. Biochim Biophys Acta Gene Regul Mech 2020; 1863:194646. [PMID: 33144059 DOI: 10.1016/j.bbagrm.2020.194646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Affiliation(s)
- S Gherardi
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy; Department of Pharmacy and Biotechnology, University of Bologna, Bologna, Italy; CIRI Health Sciences & Technologies (HST), Bologna, Italy
| | - M Bovolenta
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - C Passarelli
- Paediatric Hospital Bambino Gesù, Laboratory of Medical Genetics, Rome, Italy
| | - M S Falzarano
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - P Pigini
- Department of Pharmacy and Biotechnology, University of Bologna, Bologna, Italy
| | - C Scotton
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - M Neri
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - A Armaroli
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - H Osman
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - R Selvatici
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - F Gualandi
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy
| | - A Recchia
- Department of Life Sciences, University of Modena & Reggio Emilia, Modena, Italy
| | - M Mora
- Neuromuscular Disease and Immunology Unit, Fondazione IRCCS Istituto Neurologico "C. Besta", Milan, Italy
| | - P Bernasconi
- Neuromuscular Disease and Immunology Unit, Fondazione IRCCS Istituto Neurologico "C. Besta", Milan, Italy
| | - L Maggi
- Neuromuscular Disease and Immunology Unit, Fondazione IRCCS Istituto Neurologico "C. Besta", Milan, Italy
| | - L Morandi
- Neuromuscular Disease and Immunology Unit, Fondazione IRCCS Istituto Neurologico "C. Besta", Milan, Italy
| | - A Ferlini
- Unit of Medical Genetics, Department of Medical Sciences, University of Ferrara, Italy; Neuromuscular Unit, Great Ormond Street Hospital, University College London, UK.
| | - G Perini
- Department of Pharmacy and Biotechnology, University of Bologna, Bologna, Italy; CIRI Health Sciences & Technologies (HST), Bologna, Italy.
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Eeltink D, Armaroli A, Ducimetière YM, Kasparian J, Brunetti M. Single-spectrum prediction of kurtosis of water waves in a nonconservative model. Phys Rev E 2019; 100:013102. [PMID: 31499826 DOI: 10.1103/physreve.100.013102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2019] [Indexed: 06/10/2023]
Abstract
We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher-order nonlinear Schrödinger equation. During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up, and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted.
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Affiliation(s)
- D Eeltink
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - A Armaroli
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - Y M Ducimetière
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - J Kasparian
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
| | - M Brunetti
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Geneva, Switzerland
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Selvatici R, Neri M, Scotton C, Falzarano M, Rossi R, Armaroli A, Gualandi F, Fini S, Ferlini A. Whole genome sequencing in neuromuscular diseases: the UNIFE experience within the neuromics project. Neuromuscul Disord 2017. [DOI: 10.1016/j.nmd.2017.06.366] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Scotton C, Schwartz E, Falzarano M, Bovolenta M, Rossi R, Armaroli A, Osman H, Gualandi F, Neri M, Lochmuller H, Pesole G, Sabatelli P, Merlini L, Bonaldo P, Muntoni F, Gelfi C, Lebowitz M, Esser K, Ferlini A. Transcriptomics analysis in collagen VI myopathy: Role of circadian genes using novel fluidic card tools. Neuromuscul Disord 2016. [DOI: 10.1016/j.nmd.2016.06.022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Conforti M, Mussot A, Kudlinski A, Rota Nodari S, Dujardin G, De Biévre S, Armaroli A, Trillo S. Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation. Phys Rev Lett 2016; 117:013901. [PMID: 27419569 DOI: 10.1103/physrevlett.117.013901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Indexed: 06/06/2023]
Abstract
We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearized Floquet analysis.
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Affiliation(s)
- M Conforti
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - A Mussot
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - A Kudlinski
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - S Rota Nodari
- IMB UMR 5584, CNRS, Université Bourgogne Franche-Comté, F-21000 Dijon, France
| | - G Dujardin
- Univ. Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé; Equipe MEPHYSTO, INRIA, F-59000 Lille, France
| | - S De Biévre
- Univ. Lille, CNRS, UMR 8524-Laboratoire Paul Painlevé; Equipe MEPHYSTO, INRIA, F-59000 Lille, France
| | - A Armaroli
- FOTON (CNRS-UMR 6082) Université de Rennes 1, ENSSAT, 6 rue de Kerampont, CS 80518, F-22305 Lannion Cedex, France
| | - S Trillo
- Dipartimento di Ingegneria, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
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Scotton C, Armaroli A, Osman H, Falzarano M, Capogrosso R, Cozzoli A, Camerino G, De Luca A, Ferlini A. RNA profiling discloses a link between circadian genes and muscle damage in Duchenne Muscular Dystrophy. Neuromuscul Disord 2015. [DOI: 10.1016/j.nmd.2015.06.222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Neri M, Selvatici R, Scotton C, Trabanelli C, Armaroli A, De Grandis D, Levy N, Gualandi F, Ferlini A. A patient with limb girdle muscular dystrophy carries a TRIM32 deletion, detected by a novel CGH array, in compound heterozygosis with a nonsense mutation. Neuromuscul Disord 2013; 23:478-82. [DOI: 10.1016/j.nmd.2013.02.003] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2012] [Revised: 01/28/2013] [Accepted: 02/06/2013] [Indexed: 11/26/2022]
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Fatome J, Finot C, Armaroli A, Trillo S. Observation of modulationally unstable multi-wave mixing. Opt Lett 2013; 38:181-183. [PMID: 23454955 DOI: 10.1364/ol.38.000181] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We demonstrate experimentally that multiple four-wave mixing (FWM) pumped by a dual-frequency input in a single-mode fiber is modulationally unstable. This collective type of instability leads, in the anomalous dispersion regime, to sideband growth around all orders of FWM. This is in contrast with the normal dispersion regime where our measurements show that FWM exhibits no instability. Our conclusions are based on the first systematic mapping of the phenomenon as a function of the dual-pump input frequency separation.
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Affiliation(s)
- J Fatome
- Laboratoire Interdisciplinaire Carnot de Bourgogne, Unité Mixte de Recherche 6303 Centre National de la Recherche Scientifique-Université de Bourgogne, Dijon, France. jfatome@u‑bourgogne.fr
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Anthony K, Arechavala-Gomeza V, Ricotti V, Torelli S, Feng L, Tasca G, Guglieri M, Barresi R, Armaroli A, Ferlini A, Bushby K, Straub V, Ricci E, Sewry C, Morgan J, Muntoni F. T.P.31 Biochemical and clinical variability of Becker muscular dystrophy: Predicting optimal target exons for exon skipping therapy in Duchenne muscular dystrophy. Neuromuscul Disord 2012. [DOI: 10.1016/j.nmd.2012.06.196] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Anthony K, Cirak S, Torelli S, Tasca G, Feng L, Arechavala-Gomeza V, Armaroli A, Guglieri M, Straathof C, Verschuuren J, Artsma-Rus A, Helderman-van den Enden P, Bushby K, Straub V, Sewry C, Ferlini A, Ricci E, Morgan J, Muntoni F. P01 Correlation of internally deleted dystrophin and dystrophin-associated protein expression with clinical severity in Becker muscular dystrophy. Neuromuscul Disord 2012. [DOI: 10.1016/s0960-8966(12)70009-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Merlini L, Armaroli A, Sabatelli P, Gnudi S, Michelini M, Bleve C, Franchella A, Ferlini A, Angelin A, Bonaldo P, Bernardi P. P4.50 Mitochondrial therapy with Cyclosporine A in patients with Ullrich Congenital Muscular Dystrophy. Neuromuscul Disord 2011. [DOI: 10.1016/j.nmd.2011.06.1015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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