Journal ArticleDOI
Nonlinear Dynamical Models of Plasma Turbulence
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TLDR
In this paper, an exact pole-type truncation expansion technique has been used to study nonlinear dynamical systems which can be considered models for plasma turbulence, including the mode coupling saturation of a linearly unstable, one-dimensional homogeneous plasma, and the situation where waves with k < 0 are completely damped.Abstract:
An exact pole-type truncation expansion technique has been used to study nonlinear dynamical systems which can be considered models for plasma turbulence. One of the models describes the mode coupling saturation of a linearly unstable, one-dimensional homogeneous plasma. Another describes the situation where waves with k < 0 are completely damped. The solutions exhibit a rich variety of complex behaviors including successive bifurcations to increasingly complicated periodic motion and the onset of chaotic behavior, as well quasi-periodic-like behavior with highly complex topology.read more
Citations
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Application of pole decomposition to an equation governing the dynamics of wrinkled flame fronts
TL;DR: In this paper, the Sivashinsky integral equation governing certain hydrodynamical instabilities of one-dimensional flame fronts is a special case of Lee and Chen's ( Phys. Scr. 2 (1982) 41) non linear plasma models; as such it has a pole decomposition.
References
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A universal instability of many-dimensional oscillator systems
TL;DR: In this article, the authors demonstrate the mechanism for a universal instability, the Arnold diffusion, which occurs in the oscillating systems having more than two degrees of freedom, which results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations.
Journal ArticleDOI
Quantitative universality for a class of nonlinear transformations
TL;DR: In this article, a large class of recursion relations xn+l = Af(xn) exhibiting infinite bifurcation is shown to possess a rich quantitative structure essentially independent of the recursion function.
Journal ArticleDOI
Solution of the One‐Dimensional N‐Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
TL;DR: In this paper, the quantum-mechanical problems of N 1-dimensional equal particles of mass m interacting pairwise via quadratic (harmonical) and/or inverse (centrifugal) potentials is solved.
Journal ArticleDOI
Exact Results for a Quantum Many-Body Problem in One Dimension
TL;DR: In this paper, a system of either fermions or bosons interacting in one dimension by a two-body potential with periodic boundary conditions was investigated, and expressions for the one-particle density matrix at zero temperature and particular (nontrivial) values of the coupling constant $g, as a determinant of order $N\ifmmode\times\else\texttimes\fi{}N$ were presented.
Journal ArticleDOI
Roads to turbulence in dissipative dynamical systems
TL;DR: In this article, three scenarios leading to turbulence in theory and experiment are outlined, and the respective mathematical theories are explained and compared, and three different models of turbulence are discussed. But none of the scenarios are discussed in detail.