ebook ebooks e-book e-books downloaden bei MyEbooks.ch downloaden

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

:	Alexander N. Gorban, Ioannis G. Kevrekidis, Constantinos Theodoropoulos, Nikolaos K. Kazantzis, Hans
:	Alexander N. Gorban, Nikolas Kazantzis, Yannis G. Kevrekidis, Hans Christian Öttinger, Konstantinos
:	Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
:	Springer-Verlag
:	9783540358886
:	1
:	CHF 132.90
:

:	Allgemeines, Lexika
:	English

:	560
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.

	Preface	5
	References	8
	Contents	9
	Computation of Invariant Manifolds	12
	A New Model Reduction Method for Nonlinear Dynamical Systems Using Singular PDE Theory	13
	1 Introduction	13
	2 Mathematical Preliminaries	15
	3 Main Results	16
	4 Conclusions	23
	References	23
	A Versatile Algorithm for Computing Invariant Manifolds	26
	1 Introduction	26
	2 Invariant Manifolds	28
	3 Discrete Sections	33
	4 The Discrete Graph Transform	36
	5 Numerical Implementation	40
	6 An Application	43
	References	44
	Covering an Invariant Manifold with Fat Trajectories	47
	1 Introduction	47
	2 Basic Definitions	49
	3 Fat Trajectories	51
	4 Flying Disks	52
	5 Interpolation	56
	6 Example	57
	References	61
	Ghost ILDM-Manifolds and Their Identification	63
	1 Introduction	63
	2 Theoretical Background	64
	3 Ghost ILDM-Manifolds Examples	75
	4 Criteria for Ghost -Manifolds Identification	82
	5 Conclusions	85
	References	85
	Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays	88
	1 Introduction	88
	2 Dynamic Fast-Slow Decomposition: Underlying Philosophy	90
	3 Decomposition of the System of Equations	92
	4 Choice of Decomposition	95
	5 Application	97
	6 Conclusions	102
	References	102
	Model Reduction of Multiple Time Scale Processes in Non- standard Singularly Perturbed Form	105
	1 Introduction	105
	2 Standard Singularly Perturbed Form	107
	3 Nonstandard Singularly Perturbed Form	109
	4 Application	114
	5 Conclusion	118
	References	118
	Coarse-Graining and Ideas of Statistical Physics	120
	Basic Types of Coarse-Graining	121
	1 Introduction	121
	2 The Ehrenfests’ Coarse-Graining	127
	3 Coarse-Graining by Filtering	153
	4 Errors of Models, e-trajectories and Stable Properties of Structurally Unstable Systems	166
	5 Conclusion	173
	References	175
	Renormalization Group Methods for Coarse- Graining of Evolution Equations	181
	1 Introduction and Basic Formalism	181
	2 RSRG for the Selection of Relevant Degrees of Freedom	186
	3 DMRG and the Time-Evolution of Strongly Correlated Many- Body Systems	194
	4 Conclusions	207
	References	207
	A Stochastic Process Behind Boltzmann’s Kinetic Equation and Issues of Coarse Graining	211
	1 Motivation and Problem	211
	2 Markov Processes	214
	3 Nonlinear Fokker-Planck Equations	215
	4 Boltzmann’s Kinetic Equation	217
	5 Boltzmann Process	218
	6 Gaussian Boltzmann Process	220
	7 Application: Diffusion Coefficient	223
	8 Perspectives	225
	References	226
	Finite Difference Patch Dynamics for Advection Homogenization Problems	229
	1 Introduction	229
	2 Model Problems	233
	3 Patch Dynamics	234
	4 Convergence Results	237
	5 Numerical Results for Advection Problems	241
	6 Conclusions	248
	References	248
	Coarse-Graining the Cyclic Lotka-Volterra Model: SSA and Local Maximum Likelihood Estimation	251
	1 Introduction	251
	2 The Lattice Lotka-Volterra Model	252
	3 Equation Free Computation	253
	4 Estimation Procedure	254
	5 Illustrations of Equation-Free Computation	258
	6 Discussion	263
	References	268
	Relations Between Information Theory, Robustness and Statistical Mechanics of Stochastic Uncertain Systems via Large Deviation Theory	272
	1 Introduction	272
	2 Thermodynamics and Statistical Mechanics	276
	3 Robustness of Stochastic Uncertain Systems: General Setting	279
	4 Robustness of Stochastic Uncertain Systems: an Energy Constraint Formulation	281
	5 Robustness of Stochastic Uncertain Systems: a Relative Entropy Constraint Formulation	286
	6 The Large Deviations Principle Applied to Diffusion Processes	291
	7 Conclusion	293
	References	293
	Kinetics and Model Reduction	296
	Exactly Reduced Chemical Master Equations	297
	1 Introduction	297
	2 Stochastic Population Modeling and the Chemical Master Equation	300
	3 Methods and Results	307
	4 Conclusions	314
	References	315
	Model Reduction in Kinetic Theory	318
	1 Introduction	318
	2 Basic Kinetic Theory	319
	3 Chapman-Enskog Method	321
	4 Grad Moment Method	323
	5 Combining the Chapman-Enskog and Grad Methods	325
	6 Order of Magnitude Method	327
	7 Relations Between the Various Sets of Equations	330
	8 Applications	331
	9 Conclusions and Outlook	337
	References	339
	Novel Trajectory Based Concepts for Model and Complexity Reduction in ( Bio) Chemical Kinetics	343
	1 Introduction	343
	2 Model Reduction: Constrained Relaxation of Chemical Forces and Minimal Entropy Production Trajectories	345
	3 Complexity Reduction of Biochemical Reaction Networks	352
	References	362
	Dynamics of the Plasma Sheath	365
	1 Introduction	365
	2 The Euler Equations with Planar, Radical, and Spherical symmetry	366
	3 Collisional and Collisionless Plasmas	366
	4 Dynamics of the Plasma Sheath	367
	5 Generalization to Non-Symmetric Case	369
	References	371
	Mesoscale and Multiscale Modeling	372
	Construction of Stochastic PDEs and Predictive Control of Surface Roughness in Thin Film Deposition	373
	1 Introduction	373
	2 Preliminaries	375
	3 Model Construction	381
	4 Predictive Control	388
	5 Conclusions	397