Finite-N corrections to Vlasov dynamics and the range of pair interactions.
نویسندگان
چکیده
We explore the conditions on a pair interaction for the validity of the Vlasov equation to describe the dynamics of an interacting N-particle system in the large N limit. Using a coarse graining in phase space of the exact Klimontovich equation for the N-particle system, we evaluate, neglecting correlations of density fluctuations, the scalings with N of the terms describing the corrections to the Vlasov equation for the coarse-grained one-particle phase space density. Considering a generic interaction with radial pair force F(r), with F(r)∼1/r(γ) at large scales, and regulated to a bounded behavior below a "softening" scale ɛ, we find that there is an essential qualitative difference between the cases γd, i.e., depending on the the integrability at large distances of the pair force. In the former case, the corrections to the Vlasov dynamics for a given coarse-grained scale are essentially insensitive to the softening parameter ɛ, while for γ>d the amplitude of these terms is directly regulated by ɛ, and thus by the small scale properties of the interaction. This corresponds to a simple physical criterion for a basic distinction between long-range (γ≤d) and short-range (γ>d) interactions, different from the canonical one (γ≤d+1 or γ>d+1) based on thermodynamic analysis. This alternative classification, based on purely dynamical considerations, is relevant notably to understanding the conditions for the existence of so-called quasistationary states in long-range interacting systems.
منابع مشابه
Long Range Corrections to the Vapor-Liquid Equilibrium and Surface Tension of Methane with NVT Molecular Dynamics Simulations
متن کامل
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 (HMF) model, a prototype for long-range interactions inN -particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated N → ∞ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous dist...
متن کاملThe Vlasov Equation for Systems with Velocity Dependent Interactions
This work contains a discussion of the Vlasov approximation for the system of particles interacting not only via the pair-wise central potential, but also via the velocity dependent interactions (V.D.I). The VDI are assumed to be similar in nature to those encountered in the classical plasma when the higher order in (v/c) corrections to the Coulomb forces are taken into account. Using the Klimo...
متن کاملThermodynamic investigation of the interaction between Mono-s-chloroTriazinyl MCT Reactive Dyes and cetylpyridinium chloride inaqueous solution
The interactions two synthetic triazinyl reactive dyes Mono-s-chloro Triazinyl reactive dyes DI and DII with the cationic surfactant N-hexadecyl pyridinium chloride CPC were studied using a conductometric method in 25, 30, 35, 40 and 45ºC. The equilibrium constants and other thermodynamic parameters for the ion pair formation were calculated on the basis of a theoretical model using the data ob...
متن کاملVlasov stability of the Hamiltonian Mean Field model
We investigate the dynamical stability of a fully-coupled system of N inertial rotators, the so-called Hamiltonian Mean Field model. In the limit N → ∞, and after proper scaling of the interactions, the μ-space dynamics is governed by a Vlasov equation. We apply a nonlinear stability test to (i) a selected set of spatially homogeneous solutions of Vlasov equation, qualitatively similar to those...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 90 6 شماره
صفحات -
تاریخ انتشار 2014