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Dynamical Systems Approach to Turbulence
TLDR
In this article, a reduced model for hydrodynamic turbulence and coupled map lattices is proposed, and a reduction to a finite-dimensional dynamical system is presented. But the model is not suitable for high-dimensional systems.Abstract:
Introduction 1. Turbulence and dynamical systems 2. Phenomenology of turbulence 3. Reduced models for hydrodynamic turbulence 4. Turbulence and coupled map lattices 5. Turbulence in the complex Ginzburg-Landau equation 6. Predictability in high-dimensional systems 7. Dynamics of interfaces 8. Lagrangian chaos 9. Chaotic diffusion Appendix A. Hopf bifurcation Appendix B. Hamiltonian systems Appendix C. Characteristic and generalised Lyapunov exponents Appendix D. Convective instabilities Appendix E. Generalised fractal dimensions and multifractals Appendix F. Multiaffine fields Appendix G. Reduction to a finite-dimensional dynamical system Appendix H. Directed percolation.read more
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The world of the complex Ginzburg-Landau equation
Igor S. Aranson,Lorenz Kramer +1 more
TL;DR: The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community as mentioned in this paper, it describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity, and Bose-Einstein condensation to liquid crystals and strings in field theory.
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Chaos, fractional kinetics, and anomalous transport
TL;DR: In this article, the concept of fractional kinetics is reviewed for systems with Hamiltonian chaos, where the notions of dynamical quasi-traps, Poincare recurrences, Levy flights, exit time distributions, phase space topology, etc.
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The Solar Wind as a Turbulence Laboratory
Roberto Bruno,Vincenzo Carbone +1 more
TL;DR: In this paper, the authors focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state.
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Particles and fields in fluid turbulence
TL;DR: In this paper, the first analytical description of anomalous scaling laws in turbulent transport has been obtained and the underlying physical mechanism reveals the role of statistical integrals of motion in nonequilibrium systems.
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Fluctuation-dissipation: Response theory in statistical physics
TL;DR: In this paper, the relation between the relaxation of spontaneous fluctuations and the response to an external perturbation is discussed, and the connection of these works with large deviation theory is analyzed.