905 research outputs found
The Hess-Appelrot system and its nonholonomic analogs
This paper is concerned with the nonholonomic Suslov problem and its
generalization proposed by Chaplygin. The issue of the existence of an
invariant measure with singular density (having singularities at some points of
phase space) is discussed
Noble internal transport barriers and radial subdiffusion of toroidal magnetic lines
Single trajectories of magnetic line motion indicate the persistence of a
central protected plasma core, surrounded by a chaotic shell enclosed in a
double-sided transport barrier : the latter is identified as being composed of
two Cantori located on two successive "most-noble" numbers values of the
perturbed safety factor, and forming an internal transport barrier (ITB).
Magnetic lines which succeed to escape across this barrier begin to wander in a
wide chaotic sea extending up to a very robust barrier (as long as L<1) which
is identified mathematically as a robust KAM surface at the plasma edge. In
this case the motion is shown to be intermittent, with long stages of
pseudo-trapping in the chaotic shell, or of sticking around island remnants, as
expected for a continuous time random walk.Comment: TEX file, 84 pages including 32 color figures. Higher quality figures
can be seen on the PDF file at
http://membres.lycos.fr/fusionbfr/JHM/Tokamap/JSP.pd
Contributions of plasma physics to chaos and nonlinear dynamics
This topical review focusses on the contributions of plasma physics to chaos
and nonlinear dynamics bringing new methods which are or can be used in other
scientific domains. It starts with the development of the theory of Hamiltonian
chaos, and then deals with order or quasi order, for instance adiabatic and
soliton theories. It ends with a shorter account of dissipative and high
dimensional Hamiltonian dynamics, and of quantum chaos. Most of these
contributions are a spin-off of the research on thermonuclear fusion by
magnetic confinement, which started in the fifties. Their presentation is both
exhaustive and compact. [15 April 2016
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