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

On the importance of nonlinear modeling in computer performance prediction

Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models are adequate for predicting computer performance and when they are not. Specifically, we build linear and nonlinear models of the processor load of an Intel i7-based computer as it executes a range of different programs. We then use those models to predict the processor loads forward in time and compare those forecasts to the true continuations of the time seriesComment: Appeared in "Proceedings of the 12th International Symposium on Intelligent Data Analysis

Nonexistence of Chaotic Solutions of Nonlinear Differential Equations

We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely misinterpreted, and even viewed as "laws" by some. This paper hopes to stimulate appropriate corrections and to realign thinking, with the overall goal being sound future progress in dynamical systems and fluid dynamics.Comment: 12 page

New quantum algorithm for studying NP-complete problems

Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm which is a combination of the ordinary quantum algorithm with a chaotic dynamical system. We consider the satisfiability problem as an example of NP-complete problems and argue that the problem, in principle, can be solved in polynomial time by using our new quantum algorithm.Comment: 11 pages, 1 figur

Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev