• Corpus ID: 30017298

Pattern formation in Hamiltonian systems with continuous spectra; a normal-form single-wave model

  title={Pattern formation in Hamiltonian systems with continuous spectra; a normal-form single-wave model},
  author={Neil J. Balmforth and Philip J. Morrison and Jean-Luc Thiffeault},
  journal={arXiv: Statistical Mechanics},
Pattern formation in biological, chemical and physical problems has received considerable attention, with much attention paid to dissipative systems. For example, the Ginzburg--Landau equation is a normal form that describes pattern formation due to the appearance of a single mode of instability in a wide variety of dissipative problems. In a similar vein, a certain "single-wave model" arises in many physical contexts that share common pattern forming behavior. These systems have Hamiltonian… 
Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations
Preface xiii Chapter 1. Surprising Instabilities of Simple Elastic Structures 1 Davide BIGONI, Diego MISSERONI, Giovanni NOSELLI and Daniele ZACCARIA Chapter 2. WKB Solutions Near an Unstable
Structure and structure-preserving algorithms for plasma physics
Hamiltonian and action principle (HAP) formulations of plasma physics are reviewed for the purpose of explaining structure preserving numerical algorithms. Geometric structures associated with and
Vlasov–Fokker–Planck equation: stochastic stability of resonances and unstable manifold expansion
We investigate the dynamics close to a homogeneous stationary state of Vlasov equation in one dimension, in presence of a small dissipation modeled by a Fokker-Planck operator. When the stationary
Nonlinear echoes and Landau damping with insufficient regularity
We prove that the theorem of Mouhot and Villani on Landau damping near equilibrium for the Vlasov-Poisson equations on $\mathbb{T}_x \times \mathbb{R}_v$ cannot, in general, be extended to high
Trapping scaling for bifurcations in the Vlasov systems.
Through an unstable manifold expansion, it is shown that in one spatial dimension the dynamics is very sensitive to the initial perturbation: the instability may saturate at small amplitude-generalizing the "trapping scaling" of plasma physics-or may grow to produce a large-scale modification of the system.
Unstable manifold expansion for Vlasov-Fokker-Planck equation
We investigate the bifurcation of a homogeneous stationary state of Vlasov-Newton equation in one dimension, in presence of a small dissipation mod-eled by a Fokker-Planck operator. Depending on the
Shearless transport barriers in unsteady two-dimensional flows and maps
Abstract We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps defined over a finite time
Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the 2 D Couette flow
In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the qualitative behavior
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D inviscid Euler equations on T×R. That is, given an initial perturbation of the Couette flow small in a suitable
Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\textbf{Re}$. We prove that for sufficiently regular initial


Plasma Physics and Controlled Fusion
The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic
The Hamiltonian Hopf Bifurcation
Preliminaries.- Normal forms for Hamiltonian functions.- Fibration preserving normal forms for energy-momentum maps.- The Hamiltonian Hopf bifurcation.- Nonintegrable systems at resonance.- The
The Physics of Fluids
A localized arc-filament plasma actuator, which in this application is recessed in a small cavity near the nozzle lip, causes intense local heating. This heating is thought to be the root mechanism
Introduction to Fourier Analysis on Euclidean Spaces.
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action
Scientific Papers
IN this fourth volume Sir1 George Darwin has for the present completed the task of editing his papers, a task which he commenced four years ago on the invitation of the syndics of the Cambridge
Boundary Value Problems
Boundary Value Problems in Physics and EngineeringBy Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s
Communications in Nonlinear Science and Numerical Simulation
  • 2012
Electrons, Ions, and Waves
Izvestiya, Atmosph
  • Phys. Fluids
  • 1960
Large-Scale Atmosphere-Ocean Dynamics 2: Geo
  • 2001