Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction and Motivation: Are Birds Smarter Than Nerds?
- 2 Dynamical Derivation (and a More Conventional One) of the Mermin–Wagner–Hohenberg Theorem; or, Why We Can’t All Point the Same Way
- 3 The Dynamical Renormalization Group; or, WhyWe Can Do Physics, Illustrated by the KPZ Equation
- 4 Formulating the Hydrodynamic Model for Flocking
- 5 The Dynamical Renormalization Group Applied to the Flocking Problem
- 6 Incompressible Polar Active Fluids in the Moving Phase in Dimensions d > 2: the “Canonical” Exponents
- 7 Heuristic Argument for the Canonical Exponents (“20-20 Hindsight Hand-Waving Argument”)
- 8 Incompressible Flocks in Spatial Dimensions d = 2: Mapping to the KPZ Equation
- 9 “Malthusian” Flocks (Flocks with Birth and Death)
- Bibliography
- Index
2 - Dynamical Derivation (and a More Conventional One) of the Mermin–Wagner–Hohenberg Theorem; or, Why We Can’t All Point the Same Way
Published online by Cambridge University Press: 16 May 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction and Motivation: Are Birds Smarter Than Nerds?
- 2 Dynamical Derivation (and a More Conventional One) of the Mermin–Wagner–Hohenberg Theorem; or, Why We Can’t All Point the Same Way
- 3 The Dynamical Renormalization Group; or, WhyWe Can Do Physics, Illustrated by the KPZ Equation
- 4 Formulating the Hydrodynamic Model for Flocking
- 5 The Dynamical Renormalization Group Applied to the Flocking Problem
- 6 Incompressible Polar Active Fluids in the Moving Phase in Dimensions d > 2: the “Canonical” Exponents
- 7 Heuristic Argument for the Canonical Exponents (“20-20 Hindsight Hand-Waving Argument”)
- 8 Incompressible Flocks in Spatial Dimensions d = 2: Mapping to the KPZ Equation
- 9 “Malthusian” Flocks (Flocks with Birth and Death)
- Bibliography
- Index
Summary
I present a purely dynamical derivation of the Mermin–Wagner–Hohenberg theorem, and compare it with the standard equilibrium derivation. This also provides an opportunity to introduce diffusion equations and gradient expansions, both of which play a large role in what follows.
- Type
- Chapter
- Information
- The Physics of FlockingBirth, Death, and Flight in Active Matter, pp. 9 - 29Publisher: Cambridge University PressPrint publication year: 2024