Publication

Single speed solutions of the Vlasov-Poisson equations for Coulombian and Newtonian systems in nD

2008
Conference Papers

Abstract

Results of theoretical and numerical investigations concerning the space-time evolution in nD of Coulombian systems known in Plasma Physics and Newtonian systems known in Cosmology are reported here. A generic, canonical Hamiltonian formulation is given (1) for studying single speed solutions of their Coulomb- or Jeans-Vlasov-Poisson descriptions. (2) It is shown that their equations of motion are integrable for vorticity free planar motions in nD (3) and that their characteristics are solutions of explicit non-linear ODES in general (4). Some simple examples of trajectories are illustrated and the problem of their crossing is evoked. (c) 2007 Elsevier B.V. All rights reserved.

Official source

https://infoscience.epfl.ch/entities/publication/8e9c183b-7e3f-4dbf-98f7-075431daf618

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2008
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/8e9c183b-7e3f-4dbf-98f7-075431daf618

About this result

Related concepts (32)

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Hamiltonian mechanics

Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical and quantum mechanics.

Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details.

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Single speed solutions of the Vlasov-Poisson equations for Coulombian and Newtonian systems in nD

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