Resonant interaction (original) (raw)
In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most non
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| dbo:abstract | In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most nonlinear systems; instabilities offer insight into high-dimensional chaos and turbulence. (en) Nei sistemi dinamici non lineari, un'interazione risonante è l'interazione di tre o più onde, spesso ma non sempre di piccola ampiezza. Le interazioni risonanti si verificano quando vengono soddisfatti dei criteri che accoppiano i vettori d'onda e la relazione di dispersione. Le sue applicazioni più importanti e ben sviluppate compaiono nello studio delle onde di gravità, ma se ne trovano numerose dall'astrofisica e dalla biologia all'ingegneria e alla medicina. Il lavoro teorico sulle equazioni alle derivate parziali fornisce importanti approfondimenti sulla teoria del caos. Le interazioni risonanti permettono alle onde di compiere processi di scattering elastico o di diffusione, o di diventare instabili. I processi di diffusione sono responsabili dell'eventuale termalizzazione della maggior parte dei sistemi non lineari; le instabilità offrono informazioni sul caos in sistemi con un gran numero di gradi di libertà e sulla turbolenza. (it) |
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| rdfs:comment | In nonlinear systems, a resonant interaction is the interaction of three or more waves, usually but not always of small amplitude. Resonant interactions occur when a simple set of criteria coupling wave-vectors and the dispersion equation are met. The simplicity of the criteria make technique popular in multiple fields. Its most prominent and well-developed forms appear in the study of gravity waves, but also finds numerous applications from astrophysics and biology to engineering and medicine. Theoretical work on partial differential equations provides insights into chaos theory; there are curious links to number theory. Resonant interactions allow waves to (elastically) scatter, diffuse or to become unstable. Diffusion processes are responsible for the eventual thermalization of most non (en) Nei sistemi dinamici non lineari, un'interazione risonante è l'interazione di tre o più onde, spesso ma non sempre di piccola ampiezza. Le interazioni risonanti si verificano quando vengono soddisfatti dei criteri che accoppiano i vettori d'onda e la relazione di dispersione. Le sue applicazioni più importanti e ben sviluppate compaiono nello studio delle onde di gravità, ma se ne trovano numerose dall'astrofisica e dalla biologia all'ingegneria e alla medicina. Il lavoro teorico sulle equazioni alle derivate parziali fornisce importanti approfondimenti sulla teoria del caos. Le interazioni risonanti permettono alle onde di compiere processi di scattering elastico o di diffusione, o di diventare instabili. I processi di diffusione sono responsabili dell'eventuale termalizzazione della magg (it) |
| rdfs:label | Interazione risonante (it) Resonant interaction (en) |
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