Lyapunov stability of Vlasov equilibria using Fourier-Hermite modes.

@inproceedings{Pavskauskas2009LyapunovSO,
  title={Lyapunov stability of Vlasov equilibria using Fourier-Hermite modes.},
  author={Rytis Pavskauskas and Giovanni De Ninno},
  year={2009}
}
We propose an efficient method to compute Lyapunov exponents and Lyapunov eigenvectors of long-range interacting many-particle systems, whose dynamics is described by the Vlasov equation. We show that an expansion of a distribution function using Hermite modes (in velocity variable) and Fourier modes (in configuration variable) converges fast if an appropriate scaling parameter is introduced and identified with the inverse of the temperature. As a consequence, dynamics and linear stability… Expand

Figures from this paper

References

SHOWING 1-10 OF 22 REFERENCES
The Vlasov equation and the Hamiltonian Mean-Field model
We show that the quasi-stationary states of homogeneous (zero magnetization) states observed in the N-particle dynamics of the Hamiltonian mean-field (HMF) model are nothing but Vlasov stableExpand
Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model
We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field model, a prototype for long-range interactions in N-particle dynamics. In particular, we point out theExpand
Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation.
TLDR
In specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations. Expand
Chaos and statistical mechanics in the Hamiltonian mean field model
Abstract We study the dynamical and statistical behavior of the Hamiltonian mean field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is aExpand
Fourier‐Hermite Solutions of the Vlasov Equations in the Linearized Limit
The properties of the Fourier‐Hermite transformation of the one‐dimensional Vlasov equation for the motion of electrons against a uniform positive neutralizing background are examined in theExpand
Maximum entropy principle explains quasistationary states in systems with long-range interactions: the example of the Hamiltonian mean-field model.
TLDR
It is demonstrated that a maximum entropy principle applied to the associated Vlasov equation explains known features of quasistationary states with non-Gaussian single particle velocity distributions for a wide range of initial conditions. Expand
Numerical Studies of the Nonlinear Vlasov Equation
The nonlinear one‐dimensional Vlasov equation is solved numerically as an initial‐value problem. The problem is the same as that considered by Knorr, and is related to, but not the same as, variousExpand
Vlasov Simulations Using Velocity-Scaled Hermite Representations
The efficiency, accuracy, and stability of two different pseudo-spectral methods using scaled Hermite basis and weight functions, applied to the nonlinear Vlasov?Poisson equations in one dimensionExpand
Algebraic correlation functions and anomalous diffusion in the Hamiltonian mean field model
We numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions in the quasi-stationary states of the Hamiltonian mean field model. This is anExpand
Clustering and relaxation in Hamiltonian long-range dynamics.
  • Antoni, Ruffo
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1995
TLDR
A two-cluster drifting state with zero magnetization forms spontaneously at very small temperatures; at larger temperatures an initial density modulation produces this state, which relaxes very slowly, which suggests the possibility of exciting magnetized states in a mean-field antiferromagnetic system. Expand
...
1
2
3
...