R Krechetnikov and J E Marsden 2009 J. Phys. A: Math. Theor. 42 412004 doi:10.1088/1751-8113/42/41/412004
On the origin and nature of finite-amplitude instabilities in physical systems
FREE ARTICLER Krechetnikov1 and J E Marsden2
Show affiliationsFAST TRACK COMMUNICATION
Finite-amplitude instabilities are ubiquitous, but their theory and precise definitions require clarification. In this work, we discuss the interrelation of various notions connected with finite-amplitude instabilities and offer a precise context for these phenomena. Then we establish a connection between non-normality of linear operators, energy conservation by nonlinear operators and the existence of finite-amplitude instabilities in finite- and infinite-dimensional dynamical systems, both in the conservative and dissipative cases. Such a connection may at first appear counter-intuitive since it relates intrinsically linear and nonlinear phenomena, but it follows naturally from the properties of linear and nonlinear operators when they appear together in a dynamical system. In particular, the main theorem of this communication proves that non-normality is a necessary condition for a finite-amplitude instability. It is demonstrated that this phenomenon is relevant to a wide class of physical systems with energy-conserving nonlinearities.
- PACS
-
47.10.ad Navier-Stokes equations
- MSC
-
76D05 Navier-Stokes equations (See also 35Q30)
- Subjects
- Dates
-
Issue 41 (16 October 2009)
Received 26 May 2009, in final form 10 September 2009
Published 29 September 2009
-
On the origin and nature of finite-amplitude instabilities in physical systems
R Krechetnikov and J E Marsden 2009 J. Phys. A: Math. Theor. 42 412004
-
Chirality, magnetic charge and other strange entities in resonant x-ray Bragg diffraction
Stephen W Lovesey and Valerio Scagnoli 2009 J. Phys.: Condens. Matter 21 474214
-
First-principles study of hydrogen-passivated single-crystalline silicon nanotubes: electronic and optical properties
Ming Ni et al 2007 Nanotechnology 18 505707
-
Covalent sidewall functionalization of single-walled carbon nanotubes: a photoreduction approach
Liangming Wei and Yafei Zhang 2007 Nanotechnology 18 495703
-
Real-time in situ Raman imaging of carbon nanotube growth
K Kaminska et al 2007 Nanotechnology 18 165707
-
Entanglement generation by collisions of quantum solitons in the Born approximation
Maciej Lewenstein and Boris A Malomed 2009 New J. Phys. 11 113014
-
Structure of positive streamers inside gaseous bubbles immersed in liquids
Natalia Yu Babaeva and Mark J Kushner 2009 J. Phys. D: Appl. Phys. 42 132003
-
Multiscale-failure criteria of carbon nanotube systems under biaxial tension–torsion
Byeong-Woo Jeong et al 2007 Nanotechnology 18 485715
-
On vector analogs of the modified Volterra lattice
V E Adler and V V Postnikov 2008 J. Phys. A: Math. Theor. 41 455203
-
Asymmetric hysteresis loop in magnetostatic-biased multilayer nanowires
S Allende et al 2009 Nanotechnology 20 445707
Users also read
What's this?- Short-distance expansion for the electromagnetic half-space Green's tensor: general results and an application to radiative lifetime computations
- Parity-odd effects and polarization rotation in graphene
- Konishi at strong coupling from ABE
supergravity chiral projection operatorRelated review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
-
Notes on Yang–Mills–Higgs monopoles and dyons on
, and Chern–Simons–Higgs solitons on 
: dimensional reduction of Chern–Pontryagin densities
- T-systems and Y-systems in integrable systems*