Von der Verantwortung der Wissenschaftler

Neunzert, Helmut; Rosenberger, Bernd

doi:10.1007/978-3-322-81038-0_9

Search citation statements

Order By: Relevance

Paper Sections

Select...

Vlasov Equation On a Lattice1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and then derive the Klimontovich equation as done in [35,36]. The Vlasov equation could be then derived using a convenient averaging method.…”

Section: Vlasov Equation On a Latticementioning

confidence: 99%

Vlasov equation for long-range interactions on a lattice

et al. 2011

View full text Add to dashboard Cite

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.

show abstract

“…and then derive the Klimontovich equation as done in [35,36]. The Vlasov equation could be then derived using a convenient averaging method.…”

Section: Vlasov Equation On a Latticementioning

confidence: 99%