Numerical resolution of the Vlasov equation for the Hamiltonian Mean-Field model

Abstract

We present in this paper detailed numerical Vlasov simulations of the Hamiltonian Mean-Field model. This model is used as a representative of the class of systems under long-range interactions. We check existing results on the stability of the homogeneous situation and analyze numerical properties of the semi-Lagrangian time-split algorithm for solving the Vlasov equation. We also detail limitations due to finite resolution of the method.

9 pages. Submitted to Communications in Nonlinear Science and Numerical Simulation

References in corpus (4)

• A maximum entropy principle explains quasi-stationary states in systems with long-range interactions: the example of the Hamiltonian Mean Field model
• Out-of-equilibrium tricritical point in a system with long-range interactions
• Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation
• Lynden-Bell and Tsallis distributions for the HMF model

Cited by in corpus (11)

• Algebraic damping in the one-dimensional Vlasov equation
• Nonlinear response for external field and perturbation in the Vlasov system
• Solving the Vlasov equation for one-dimensional models with long range interactions on a GPU
• Statistical mechanics of collisionless relaxation in a noninteracting system
• Conditions for predicting quasistationary states by rearrangement formula
• Non-diagonalizable and non-divergent susceptibility tensor in the Hamiltonian mean-field model with asymmetric momentum distributions
• Discontinuous codimension-two bifurcation in a Vlasov equation
• The vmf90 program for the numerical resolution of the Vlasov equation for mean-field systems
• Phase transitions of quasistationary states in the Hamiltonian Mean Field model
• On the effectiveness of mixing in violent relaxation
• Nondivergent and negative susceptibilities around critical points of a long-range Hamiltonian system with two order parameters