1,713 research outputs found
Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
We describe a magnetohydrodynamic (MHD) constrained energy functional for
equilibrium calculations that combines the topological constraints of ideal MHD
with elements of Taylor relaxation.
Extremizing states allow for partially chaotic magnetic fields and
non-trivial pressure profiles supported by a discrete set of ideal interfaces
with irrational rotational transforms.
Numerical solutions are computed using the Stepped Pressure Equilibrium Code,
SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted to Plasma Physics and Controlled Fusion for publication
with a cluster of papers associated with workshop: Stability and Nonlinear
Dynamics of Plasmas, October 31, 2009 Atlanta, GA on occasion of 65th
birthday of R.L. Dewar. V2 is revised for referee
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Revealing the state space of turbulent pipe flow by symmetry reduction
Symmetry reduction by the method of slices is applied to pipe flow in order
to quotient the stream-wise translation and azimuthal rotation symmetries of
turbulent flow states. Within the symmetry-reduced state space, all travelling
wave solutions reduce to equilibria, and all relative periodic orbits reduce to
periodic orbits. Projections of these solutions and their unstable manifolds
from their -dimensional symmetry-reduced state space onto suitably
chosen 2- or 3-dimensional subspaces reveal their interrelations and the role
they play in organising turbulence in wall-bounded shear flows. Visualisations
of the flow within the slice and its linearisation at equilibria enable us to
trace out the unstable manifolds, determine close recurrences, identify
connections between different travelling wave solutions, and find, for the
first time for pipe flows, relative periodic orbits that are embedded within
the chaotic attractor, which capture turbulent dynamics at transitional
Reynolds numbers.Comment: 24 pages, 12 figure
Generation of Multi-Scroll Attractors Without Equilibria Via Piecewise Linear Systems
In this paper we present a new class of dynamical system without equilibria
which possesses a multi scroll attractor. It is a piecewise-linear (PWL) system
which is simple, stable, displays chaotic behavior and serves as a model for
analogous non-linear systems. We test for chaos using the 0-1 Test for Chaos of
Ref.12.Comment: Corresponding Author: Eric Campos-Cant\'o
Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial
A new computational technique based on the symbolic description utilizing
kneading invariants is proposed and verified for explorations of dynamical and
parametric chaos in a few exemplary systems with the Lorenz attractor. The
technique allows for uncovering the stunning complexity and universality of
bi-parametric structures and detect their organizing centers - codimension-two
T-points and separating saddles in the kneading-based scans of the iconic
Lorenz equation from hydrodynamics, a normal model from mathematics, and a
laser model from nonlinear optics.Comment: Journal of Bifurcations and Chaos, 201
- …