Minimal Models of Flocking Open Access

Abstract

Living systems provide an abundance of fascinating examples of non-equilibrium collective motion, from microscopic vortices of swimming bacteria to macroscopic murmurations in flocks of starlings. Understanding the mechanics of how simple interactions between biological agents can give rise to rich, complex patterns of behavior is one of the central concerns of the field of active matter. A cornerstone of this field is the collection of flocking models which, although initially formulated to study the behavior of flocks of birds, have had their application extended to a diverse range of biological and synthetic systems across many orders of magnitude in length scale. My contributions to this sub-field that I present in this dissertation include: (1) resolving contradictory observations within the literature about the fundamental nature of the flocking transition, (2) discovering a flocking model which neatly connects disparate avenues of research on the effect of time-delayed interactions and non-reciprocal field theory, and (3) revealing a new regime of low-Reynolds-number systems that flocking models can be applied to. I conclude by discussing my preliminary work on systems of cooperatively interacting follower and leader cancer cells, and introduce computational pipeline for inferring models of their interactions. A series of theoretical and experimental studies that one can do build upon this preliminary work are outlined.

Table of Contents

1 Introduction

1.1 The Surprising Usefulness of Simplistic Models of Complex Systems

1.2 Minimal Agent-Based Models of Flocking

1.3 Minimal Field Theory Models of Flocking

1.4 Coarse-Graining Agent-Based Models Into Field Theories

1.5 High-Complexity, Deep-Learning Models of Flocking

1.6 Structure of Dissertation

2 Banded Phases In Topological Flocks

2.1 Introduction

2.1.1 Order-Disorder Transition In Metric Flocks

2.1.2 Hydrodynamic Theory of Traveling Waves

2.1.3 Topological Field Theory

2.2 Results

2.2.1 Model

2.2.2 Coarse-Grained Fields Statistics

2.2.3 Shape of Propagating Bands

2.3 Conclusion

3 Flocks With Hierarchical Reaction Times

3.1 Introduction

3.1.1 Measurements of Time-Delayed Interactions in Flocks

3.1.2 Time-Delay Models

3.2 Results

3.2.1 Hierarchical Time Delay Model

3.2.2 Emergence of PT Symmetry Phase

3.2.3 Phase Separation In the PT-Symmetric State

3.2.4 Self-Assembled Spatial Organization of Agents

3.3 Conclusion

4 Flocking and Vortex Phases In Bos Taurus Sperm Cells

4.1 Introduction

4.1.1 Hydrodynamics of Micro-swimmers

4.1.2 Collective Sperm Motility

4.1.3 Pulse-Induced Vortex and Flocking States

4.2 Results

4.2.1 Inferring A Density-Dependent Transition Via Machine Learning

4.2.2 Density Fluctuation Statistics

4.2.3 Persistent Turning Particle Model

4.2.4 Vortex-Flocking Phase Diagram

4.3 Conclusion

5 Deep Learning the Heterogeneous Dynamics and Morphology of Follower/Leader Cancer Cells

5.1 Introduction

5.1.1 Follower and Leader Cell Heterogeneity

5.1.2 Minimal Models of Monolayer Migration

5.2 Methods

5.2.1 Force Inference Graph Neural Network

5.2.2 Trajectory Extraction

5.2.3 Proof of Concept

5.2.4 Application To Heterogeneous Follower and Leader Cell Populations

5.3 Phenotypic Heterogeneity of Follower and Leader Cells

5.3.1 Population Statistics

5.3.2 Image-Based Classification

5.4 Conclusion

6 Conclusions

Appendix A Hidden Non-Reciprocity In The Vicsek Model

Appendix B Coarse-Graining The Vicsek Model

Appendix C Non-Reciprocal Fluctuation Renormalization

C.1 Introduction

C.2 Perturbation expansion of equations of motion

C.3 Renormalized field dynamics

C.4 Renormalized free energy

C.5 Fluctuation expansion of non-reciprocal hydrodynamic corrections

C.6 Non-reciprocal corrections to renormalized hydrodynamics

C.6.1 Computation of correlators near the critical point

Bibliography

About this Dissertation

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School	Laney Graduate School
Department	Physics
Degree	Ph.D.
Submission	Dissertation
Language	English
Research Field	Physics, Theory
Keyword	Active Matter
Committee Chair / Thesis Advisor	Daniel Sussman, Emory University
Committee Members	Luiz Santos, Emory University Alessandro Veneziani, Emory University Gordon Berman, Emory University Justin Burton, Emory University

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