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Notes
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 251-272
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Preface
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp xi-xiv
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Part II - Tangles in Different Contexts
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 31-32
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Part IV - Applying Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 185-186
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Acknowledgments
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp xv-xvi
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13 - Applying tangles in the social sciences
from Part IV - Applying Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

Published online:

16 May 2024

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23 May 2024, pp 203-214
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Index
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 277-282
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Part III - The Mathematics of Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 73-74
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5 - The Dynamical Renormalization Group Applied to the Flocking Problem
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp 117-120
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Summary

This chapter applies the dynamical renormalization group introduced in Chapter 4 to the flocking problem, and uses it to show that nonlinear terms in the dynamics are “relevant,” and change the dynamics in precisely the way needed to circumvent the Mermin–Wagner–Hohenberg theorem.

1 - Introduction and Motivation: Are Birds Smarter Than Nerds?
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp 1-8
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Summary

I introduce the problem of “dry active matter” more precisely, describing the symmetries (both underlying, and broken) of the state I wish to consider, and also discuss how shocking it is that such systems can exhibit long-ranged order – that is, all move together – even in d = 2.

Contents
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp vii-x
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Bibliography
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp 231-237
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3 - The two main tangle theorems: an informal preview
from Part I - Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 27-30
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12 - Applying tangles in the natural sciences
from Part IV - Applying Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 187-202
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2 - The notion of a tangle
from Part I - Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 15-26
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9 - “Malthusian” Flocks (Flocks with Birth and Death)
John Toner, University of Oregon
Book:

The Physics of Flocking

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16 May 2024

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23 May 2024, pp 164-230
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Summary

The final chapter treats “Malthusian” flocks; that is, flocks with birth and death. Here, a full dynamical renormalization group calculation must be done; specifically, it can only be done using a d = 4-epsilon expansion.

6 - Examples from data science
from Part II - Tangles in Different Contexts
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 53-72
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1 - The idea behind tangles
from Part I - Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 3-14
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4 - Examples from the natural sciences
from Part II - Tangles in Different Contexts
Reinhard Diestel, Universität Hamburg
Book:

Tangles

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16 May 2024

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23 May 2024, pp 33-40
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10 - Choosing the feature system
from Part III - The Mathematics of Tangles
Reinhard Diestel, Universität Hamburg
Book:

Tangles

Published online:

16 May 2024

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23 May 2024, pp 157-168
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Notes

Preface

Part II - Tangles in Different Contexts

Part IV - Applying Tangles

Acknowledgments

13 - Applying tangles in the social sciences

Index

Part III - The Mathematics of Tangles

5 - The Dynamical Renormalization Group Applied to the Flocking Problem

Summary

1 - Introduction and Motivation: Are Birds Smarter Than Nerds?

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Contents

Bibliography

3 - The two main tangle theorems: an informal preview

12 - Applying tangles in the natural sciences

2 - The notion of a tangle

9 - “Malthusian” Flocks (Flocks with Birth and Death)

Summary

6 - Examples from data science

1 - The idea behind tangles

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10 - Choosing the feature system

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