The Complexity Of Dynamical Systems - A Multi-Disciplinary Perspective

Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the
broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.

Johan Dubbeldam holds a PhD in theoretical physics from the Department of Physics, Vrije Universiteit of Amsterdam, The Netherlands. He has been a lecturer in the mathematical physics group at the Delft Institute of Applied Mathematics (DIAM) since 2006. His work concentrates on dynamical systems in general, translocation of polymers, and the interaction
between dynamics and topology on networks.

Kirk Green holds a PhD in applied bifurcation analysis from the University of Bristol (UK). He is a project leader at the Centre for Mechanical and Maritime Structures, TNO (Delft, The Netherlands). He has particular expertise in the fields of spatial and time-delayed dynamical systems. His areas of research include Aeronautical, Mechanical, Optical and Structural Engineering, Applied Mathematics and Theoretical Physics, and Computer Science.

Daan Lenstra received the PhD degree from Delft University of Technology. Since 1979 he has researched topics in quantum electronics, quantum optics and condensed matter physics. He was chair in theoretical quantum electronics at the Vrije Universiteit in Amsterdam from 1991 to 2006, Scientific Director of COBRA, Eindhoven University, from 2004 to 2006 and since 2006 he is the Dean of the Faculty Electrical Engineering, Mathematics and Computer Science at Delft University of Technology. Prof. Lenstra has (co)authored more than 350 publications in international scientifi c journals and (co)edited 7 books.

Acknowledgements.

List of Contributors.

Introduction.

Part One Applications.

1 Coastal Morphodynamics (Nicholas Dodd).

1.1 1D Theoretical Framework.

1.2 Sediment Transport, Erosion, and Deposition.

1.3 Wave Speeds, Free and Forced Modes, and Timescales.

1.4 Phase-Averaged Morphodynamics: Crescentic Bars.

1.5 Physical Mechanisms.

1.6 Concluding Remarks.

References.

2 Long-Lived Transients in Transitional Pipe Flow (Jerry Westerweel and Dirk Jan Kuik).

References.

3 Dynamics of Patterns in Lasers with Delayed Feedback (Kirk Green and Bernd Krauskopf).

3.1 Introduction.

3.2 Single-Mode Laser with COF.

3.3 VCSEL with Optical Feedback.

3.4 Numerical Bifurcation Analysis of the Two-Mode ECM Structure.

3.5 Stability and Bifurcations of Periodic Solutions.

3.6 Discussion.

References.

4 Optical Delay Dynamics and Its Applications (Laurent Larger and Ingo Fischer).

4.1 Introduction.

4.2 Experimental Setups.

4.3 Dynamics: Modeling, Numerics, and Experiments.

4.4 Applications.

4.5 Conclusion and Outlook.

References.

5 Symbolic Dynamics in Genetic Oscillation Patterns (Simone Pigolotti, Sandeep Krishna, and Mogens H. Jensen).

5.1 Introduction.

5.2 The Method.

5.3 The Negative Feedback Loop.

5.4 Multiple Loops.

5.5 Negative Feedback Loops on a Lattice.

5.6 Conclusions.

References.

6 Translocation Dynamics and Randomness (Johan Dubbeldam, Vakhtang Rostiashvili, Andrey Milchev, and Thomas Vilgis).

6.1 Introduction.

6.2 Anomalous Diffusion Model.

6.3 Statistical Moments <s>i and <s²> versus Time.

6.4 Discussion.

References.

Part Two Fundamental Aspects.

7 Entropy Production, the Breaking of Detailed Balance, and the Arrow of Time (Christian Van den Broeck).

7.1 Introduction.

7.2 Detailed Balance.

7.3 Stochastic Thermodynamics.

7.4 Microscopic Expression of Entropy Production.

7.5 Discussion.

References.

8 Monodromy and Complexity of Quantum Systems (Boris Zhilinskii).

8.1 Introduction.

8.2 Hamiltonian Monodromy.

8.3 Classical–Quantum Correspondence.

8.4 Lattices and Defects.

8.5 Multicomponent Energy–Momentum Map, Bidromy, and Others.

8.6 Time Evolution and Monodromy.

8.7 Perspectives.

References.

9 Dynamics in Materials Science (Gérard A. Maugin and Martine Rousseau).

9.1 Introduction.

9.2 Essentials of Elasticity.

9.2.1 Finite Strain Elasticity.

9.3 The Boussinesq Paradigm and Akin Nonlinear Dispersive Systems.

9.4 A Basic Problem of Materials Science: Phase Transition Front Propagation.

9.5 Dynamic Materials.

9.6 Further Extensions: Propagation in Metamaterials and Others.

References.

10 Synchronization on the Circle (Alain Sarlette and Rodolphe Sepulchre).

10.1 Introduction.

10.2 Consensus Algorithms on Vector Spaces.

10.3 Consensus Algorithms on the Circle.

10.4 Convergence Properties.

10.5 Obstacles to Global Synchronization.

10.6 Algorithms for Global Synchronization.

10.7 Generalizations on Compact Homogeneous Manifolds.

10.8 Conclusions.

References.

Conclusion and Outlook.

Index.