Non-Linear Dynamics Near and Far from Equilibrium (eBook)
X, 304 Seiten
Springer Netherlands (Verlag)
978-1-4020-5388-7 (ISBN)
This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group, and self-consistent mode coupling.
We will be concerned mainly with systems with in?nite degrees of freedom which can however, be described by a few variables. These variables must necessarily be ?elds i. e. functions of space and time. A typical example would be to try to describethe?owofairaroundus. Thevariablesthatwouldbenecessarytodescribe the state of air would certainly be its density, its temperature and its velocity. All these variables (density, temperature and velocity) are, in general, functions of space and time. They are mesoscopic variables. They do not re?ect the variations occurring at the molecular level. To de?ne a density, it should be recalled, we take a small volume (small compared to the total system size, yet large compared to atomic dimensions) and consider the mass of this small volume. The ratio of mass tovolumeremainsconstantforareasonablylargevariationinthesizeofthevolume chosen and de?nes the density of the system. It fails to be a constant if the volume becomessosmallthatitcontainsonlyafewmolecules. Inthatcaseourdescription in terms of a density fails. All the systems that we will talk about can be described in terms of a coarse grained ?eld like the density. Because of the smallness (at the macroscopic level) of the volume used in de?ning density it can be considered a local variable. This is what makes it a ?eld. Similarly we can talk about the local temperature and local velocity. The local velocity is not the velocity of an individual molecule but the velocity associated with a macroscopically small, yet microscopicallylargevolumeofair.
1: Introduction
2: Models of Dynamics. 2.1. Introduction. 2.2. Langevin Picture. 2.3. Fokker-Planck Description. 2.4. Dynamics of a Magnet near its Critical Point. 2.5. Systems not in Equilibrium. 2.6. Models of Growth. 2.7. Turbulence.
3: The Renormalization Group. 3.1. Introduction. 3.2. Renormalization Group: General Framework. 3.3. Dynamics of Model A. 3.4. Inclusion of Reversible Terms. 3.5. Field Theoretic Form.
4: Mode Coupling Theories. 4.1. Introduction. 4.2. Self-Consistent Mode Coupling. 4.3. Spherical Limit.
5: Critical Dynamics in Fluids. 5.1. Introduction. 5.2. Equations for Transport Coefficients. 5.3. One-Loop Perturbation Theory. 5.4. Diagrammatic Perturbation Theory. 5.5. Self-Consistent Perturbation Theory. 5.6. Sound Propagation. 5.7. The Lambda Transition. 5.8. Generalized n-Vector Model.
6: Systems far from Equilibrium. 6.1. Introduction. 6.2. Ginzburg-Landau Model. 6.3. Phase Ordering Kinetics. 6.4. Topological Defects. 6.5. The Structure Factor. 6.6. Approximate Tehcniques. 6.7. Renormalization Group for Late Stage Behaviour.
7: Surface Growth. 7.1. Intorduction. 7.2. Edwards-Wilkinson (EW) Model. 7.3. Kardar-Parisi-Zhang (KPZ) Model. 7.4. KPZ Equation and the Renormalization Group. 7.5. KPZ Equation and Mode Coupling Theories. 7.6. Growth with Surface Diffusion. 7.7. Discrete Models. 7.8. Growth Models with Correlated Noise. 7.9. Growth Models with Non-Locality. 7.10. Roughening Transition. 7.11. Quenched Noise. 7.12. Coupled Growth Models.
8: Turbulence. 8.1. Description of the Turbulent State. 8.2. Kolmogorov Phenomenology. 8.3. The Correlation Function. 8.4. Randomly Stirred Model. 8.5. Advection of a Passive Scalar. 8.6. Intermittency Phenomenology. 8.7. Perturbation Theory. 8.8. Dynamical Systems and Turbulence.
9: Polymer Dynamics. 9.1. Introduction.
Appendix A – Functional Integration
Appendix B – Field Theoretic RG
Subject Index
| Erscheint lt. Verlag | 27.12.2007 |
|---|---|
| Zusatzinfo | X, 304 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| Technik | |
| Schlagworte | Critical Phenomena • growth models • perturbation theory • phase ordering • phase transitions • Renormalization Group • Turbulence |
| ISBN-10 | 1-4020-5388-6 / 1402053886 |
| ISBN-13 | 978-1-4020-5388-7 / 9781402053887 |
| Haben Sie eine Frage zum Produkt? |
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