Verfügbarkeit: Complexity science | Technische Universität München

Complexity science: an introduction

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Weitere beteiligte Personen:	Peletier, Mark (HerausgeberIn), Santen, Rutger A. van 1945- (HerausgeberIn), Steur, Erik (HerausgeberIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New Jersey ; London ; Singapore ; Beijing ; Shanghai ; Hong Kong ; Taipei ; Chennai ; Tokyo World Scientific Publishing Co. Pte. Ltd. [2019]
Schlagwörter:	Philosophie Wissenschaft Komplexität Complexity (Philosophy) Aufsatzsammlung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031288014&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xviii, 409 Seiten 24 cm
ISBN:	9789813239593

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Datensatz im Suchindex

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adam_text	Contents Preface v List of Contributors vii Part A. Basic concepts 1 1. 3 The many facets of complexity............................................................. Grégoire Nicolis 2. 1. Introduction...................................................................................... 3 2. Phenomenology of complexity........................................................ 4 3. Formulation....................................................................................... 9 3.1. Deterministic view.................................................................. 10 3.2. Probabilistic approach............................................................. 15 4. Emergence....................................................................................... 17 5. Complexity and Information............................................................. 19 6. Predicting under Uncertainty........................................................ 24 7. Conclusions...................................................................................... 27 8. Further Reading................................................................................. 28 Disguises of complexity....................................................................... 31 Rutger A. van Santen 1. Introduction....................................................................................... 2. Founding complexity science principles......................................... 31 37 2.1. Macroscopic order parameters, microscopic fluctuations . 37 2.2. Percolation and symmetrybreaking..................................... 40 2.3. Self-organization.................................................................. 43 xi Contents xii 2.4. Collective behavior, synchronization and self similarity . 2.5. Connectivity and networks............................................. 50 2.6. Evolutionary dynamics................................................... 53 2.7. Self organized criticality; punctuated equilibrium ... 2.8. Adaptation and hierarchical organization.................... 59 2.9. Multiscale systems in physics and chemistry............... 62 2.10. Summary............................................................................ 64 56 3. Complexity science and biology................................................... 65 3.1. The origin of life.................................................................. 65 3.2. Cognition and consciousness................................................... 69 4. The world view that complexity science suggests......................... 72 4.1. Can we predict?....................................................................... 72 4.2. Resilience................................................................................. 73 References................................................................................................. 76 Part B. Tools 3. 47 Complex dynamics of deterministic nonlinear systems 81 .... 83 1. Introduction...................................................................................... 83 2. Deterministic nonlinear dynamical systems and their analysis . . 85 2.1. The phase portrait.................................................................. 86 2.2. Stability theory....................................................................... 90 2.3. Bifurcations............................................................................ 96 2.4. Stability of feedback systems.............................................. 98 3. Networked dynamical systems and collective dynamics .... 100 Erik Steur and Henk Nijmeijer 3.1. An example of collective dynamics: synchronization. . . 102 3.2. Another example of collective dynamics: emergent oscillations..................................................................106 4. Analysis of collective dynamics.............................................................109 4.1. A network dynamical system is a feedback system . . . 109 4.2. Synchrony subspaces..................................................................112 4.3. Synchrony feedback-gain.............................................................115 xiii Contents 4.4. Bounded solutions....................................................................... 117 4.5. Conditions for synchrony............................................................. 118 4.6. Conditions for emergent oscillations........................................ 121 5. Concluding remarks............................................................................ 124 6. Suggested reading................................................................................. 125 References..................................................................................................... 125 4. Pattern formation in reaction-diffusion systems — an explicit approach................................................................................. 129 Arjen Doelman 1. Introduction........................................................................................... 129 2. The onset of pattem formation: the Turing bifurcation .... 132 2.1. Spectral analysis: the Turing destabilization.............................. 132 2.2. Nonlinear effects: the derivation of the Ginzburg-Landau equation...................................................................................... 136 2.3. The validity of the Ginzburg-Landau approximation . . . 140 2.4. Ginzburg-Landau dynamics and the Turing bifurcation . . 142 2.5. Alternative pattem generating mechanisms near equilibrium 146 3. Bridging the gap: spatially periodic patterns and the Busse balloon 148 3.1. Symmetric spatially periodic patterns........................................ 149 3.2. The Busse balloon.......................................................................152 4. Far from equilibrium: localized structures.........................................154 4.1. Some a priori observations........................................................155 4.2. The existence of stationary pulse solutions.............................. 160 4.3. The stability of stationary pulse solutions.............................. 165 5. Complex pattem dynamics..................................................................172 5.1. In Ä1 ............................................................................................173 5.2. Pattern formation in M2.............................................................175 5.3. Beyond reaction-diffusion systems..............................................177 References..................................................................................................... 178 Contents 5. A primer on stochastic processes........................................................183 Mark A. Peletier 1. Introduction.......................................................................................183 2. Two basic stochastic processes: Random walks and stochastic differential equations............................................................................ 184 2.1. Random walks............................................................................ 184 2.2. Brownian motion and stochasticdifferential equations . . 187 2.3. Two special SDEs: Langevin and overdamped-Langevin equations...................................................................................... 189 3. Numerically simulating random walksand SDEs..............................189 3.1. General remarks.......................................................................189 3.2. Random walks.......................................................................190 3.3. Stochastic differential equations..............................................191 4. Itô’s Lemma and the Fokker-Planck equation .................................... 191 4.1. Itô’s Lemma................................................................................. 191 4.2. The Fokker-Planck equation: evolution of the law . . . 192 4.3. Numerical simulation (again)...................................................193 5. Metastability........................................................................................... 193 5.1. The phenomenon of metastability..............................................193 5.2. Metastability and chemical reactions........................................ 196 6. Comments and extensions..................................................................197 References..................................................................................................... 197 6. Random graphs models for complex networks, and the brain . . 199 Remco van der Hofstad 1. Introduction and motivation................................................................. 199 1.1. Motivation: real-world networks............................................. 200 1.2. Random graphs and real-world networks................................... 206 1.3. Random graph models................................................................. 208 1.4. Related geometries and universality........................................ 219 Contents XV 2. The giant component in random graphs............................................. 219 2.1. Branching processes..................................................................220 2.2. Giant component for the Erdős-Rényi random graph. . . 222 2.3. Giant component for inhomogeneous random graphs. . . 223 2.4. Giant component for the configuration model.................... 223 3. Small-world random graphs..................................................................226 3.1. Logarithmic distances in random graphs with finite-variance weights..................................................................227 3.2. Distances in random graphs with infinite-variance degrees . 227 4. Random graphs and the brain............................................................ 232 4.1. Networks for the brain..................................................................232 4.2. Stochastic processes on random graphs and network functionality..................................................................236 4.3. Stochastic models for the brain: some final speculations. . 239 References..................................................................................................... 241 7. Mesoscale simulations of complex fluids...................................................247 Johan T. Padding 1. Introduction........................................................................................... 247 2. Simple and complex fluids..................................................................248 2.1. Simple fluids.................................................................................248 2.2. Complex fluids............................................................................249 3. Coarse graining and Brownian motion............................................. 250 3.1. Coarse graining............................................................................250 3.2. Langevin equation for a single colloidal particle .... 252 3.3. The fluctuation-dissipation theorem........................................ 253 3.4. The Einstein and Stokes-Einstein equations..............................254 3.5. When can Brownian motion be neglected?..............................255 3.6. When can hydrodynamic interactions be neglected? . . . 256 3.7. Langevin equations for multiple colloidal particles . . 257 . 3.8. Brownian dynamics of overdampedsystems.......................... 258 Contents XVI 4. Mesoscale simulations with hydrodynamic interactions .... 4.1. Implicit inclusion of hydrodynamic interactions .... 259 259 4.2. Particle-based mesoscale simulations methods.................... 260 4.3. Multi-particle collision dynamics.........................................262 5. Example: pattern formation in sedimenting binary colloidal particles................................................................................. 266 6. Conclusion........................................................................................... 267 References..................................................................................................... 268 Part C. Applications 8. 271 Biorhythms and the brain..................................................................273 Jos H. T. Rohling and Johanna H. Meijer 1. General introduction in brain networks — setting the scene . . 273 2. Introduction to the mammalian biological clock.............................. 277 3. A heterogeneous population of neurons............................................. 282 4. A network property of the clock: jet lag............................................. 283 5. A second network property of the clock: seasonality.........................285 6. Why is the SCN a unique model to investigate brain networks? . 287 7. Network measures in the SCN............................................................ 288 8. Inferring the SCN network................................................................. 290 9. Conclusion...........................................................................................293 References.....................................................................................................294 9. Modelling of collective motion................................................................. 305 Barry W. Fitzgerald, Rutger A. van Santen and Johan T. Padding 1. Introduction.......................................................................................... 305 2. Measuring collective behaviour............................................................ 306 3. Modelling collective behaviour............................................................ 308 3.1. The Vicsek model...................................................................... 309 3.2. Modelling pedestrians dynamics............................................. 313 3.3. Collective motion in fish............................................................ 321 xvii Contents 4. Conclusion........................................................................................... 324 References..................................................................................................... 325 10. Path-integral representation of diluted pedestrian dynamics . . 329 Alessandro Corbetta and Federico Toschi 1. Introduction........................................................................................... 329 2. Microscopic modeling of pedestrian dynamics in the diluted limit 333 3. Path-integral representation for pedestrian dynamics.........................334 4. Langevin dynamics in a narrow corridor............................................. 336 4.1. Path-integral for the longitudinal dynamics.............................. 341 5. Discussion................................................................................................343 References.....................................................................................................344 11. Chemical reaction kinetic perspective with mesoscopic nonequilibrium thermodynamics....................................................... 347 Hong Qian 1. Introduction...........................................................................................347 1.1. Mechanics and chemistry............................................................ 349 2. Chemical kinetics and chemical thermodynamics.............................. 350 2.1. A single chemical reaction as an emergent phenomenon. . 350 2.2. Chemical kinetics and elementary reactions.............................. 350 2.3. Mesoscopic description of chemical kinetics.........................351 3. Nonequilibrium՛ thermodynamics (NET)............................................. 351 3.1. Gibbs’chemical thermodynamics............................................. 353 3.2. The source of complexity............................................................ 353 3.3. Macroscopic NET of continuous media................................... 354 3.4. Mesoscopic NET.......................................................................355 3.5. Mesoscopic NET as a foundation of stochastic dynamics . 355 3.6. Stochastic Liouville dynamics.................................................. 357 4. Mesoscopic stochastic NET and Hill’s cycle kinetics.........................358 4.1. Stationary distribution generates an entropie force. . . . 358 4.2. Two mesoscopic laws and three nonnegative quantities . . 359 4.3. The significance of free energy balance equation .... 360 xviii Contents 4.4. Kinetic cycles and cycle kinetics..............................................361 4.5. Nonlinear force-flux relation........................................................361 4.6. Comparison with macroscopic NET........................................ 362 5. Further development and applications..................................................362 5.1. Nonequilibrium steady state and dissipative structure. . . 362 5.2. Macroscopic limit: Gibbs’ chemical thermodynamics . . 363 5.3. Applications: biochemical dynamics in single cells . . . 364 5.4. Complex systems and symmetry breaking.............................. 367 References..................................................................................................... 369 12. Metabolic pathways and optimisation...................................................375 Robert Planqué and Josephus Hulshof 1. Introduction........................................................................................... 375 2. Modelling metabolic pathways............................................................ 376 2.1. The seminal example: Michaelis-Menten kinetics. . . . 376 2.2. General rate laws.......................................................................378 3. Steady-state metabolism, using only stoichiometry: flux balance analysis............................................................................379 3.1. EFMs as base vectors of the flux cone........................................ 380 3.2. Decomposing the fluxcone.........................................................381 3.3. EFMs as maximisers of steady state specific flux .... 382 4. An introduction to adaptive control: running a car economicaly . 383 5. Dynamically changing from one optimal metabolic state to another................................................................................................385 5.1. An alternative to adaptive control: optimal control . . . 389 References.....................................................................................................390 13. Particle-based modelling of flows through obstacles......................... 393 Emilio N. M. Cirillo, Adrian Muntean and Rutger A. van Santen 1. Introduction.......................................................................................... 393 2. Dynamics with an exclusion rule........................................................ 395 2.1. Obstacle free case...................................................................... 396 2.2. Presence of obstacles................................................................. 400 3. The case of a simple randomwalker................................................... 404 References.................................................................................................... 408
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title	Complexity science an introduction
title_auth	Complexity science an introduction
title_exact_search	Complexity science an introduction
title_full	Complexity science an introduction editors: Mark A Peletier (Eindhoven University of Technology,, The Netherlands), Rutger A van Santen (Eindhoven University of technology, The Netherlands), Erik Steur (Delft University of technology, The Netherlands)
title_fullStr	Complexity science an introduction editors: Mark A Peletier (Eindhoven University of Technology,, The Netherlands), Rutger A van Santen (Eindhoven University of technology, The Netherlands), Erik Steur (Delft University of technology, The Netherlands)
title_full_unstemmed	Complexity science an introduction editors: Mark A Peletier (Eindhoven University of Technology,, The Netherlands), Rutger A van Santen (Eindhoven University of technology, The Netherlands), Erik Steur (Delft University of technology, The Netherlands)
title_short	Complexity science
title_sort	complexity science an introduction
title_sub	an introduction
topic	Philosophie (DE-588)4045791-6 gnd Wissenschaft (DE-588)4066562-8 gnd Komplexität (DE-588)4135369-9 gnd
topic_facet	Philosophie Wissenschaft Komplexität Aufsatzsammlung
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