ruben van drongelen idemalab.tudelft faculteit/afdelingen... · flocking behaviour: vicsek model...
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Moving without a leader
Kessin et al. Nature 2003
Ruben van Drongelen Idemalab.tudelft.nl
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Population models
Flocking behaviour: Vicsek model
• Vicsek Model (1995) – Point-particles with
velocity �⃗�0 – Align with velocity of
local environment – Noise on direction
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Population models
Flocking behaviour: Vicsek model
High density: Jamming
Active (overdamped) soft matter
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Interaction rules
• Forces – Repulsive when
overlapping – Self-propulsion
• Torques – Alignment with
neighbours – Noise
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Interaction rules
• Forces – Repulsive when
overlapping – Self-propulsion
• Torques – Alignment with
neighbours – Noise
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Interaction rules
• Forces – Repulsive when
overlapping – Self-propulsion
• Torques – Alignment with
neighbours – Noise
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Interaction rules
• Forces – Repulsive when
overlapping – Self-propulsion
• Torques – Alignment with
neighbours – Noise
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Interaction rules
• Forces – Repulsive when
overlapping – Self-propulsion – Outsiders want in
• Torques – Alignment with
neighbours – Noise – Outsiders want in
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State diagram
RvD et al. PRE 91, 032706/arXiv: 1411.4821
alignment
self- propulsion
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State diagram
alignment
self- propulsion
RvD et al. PRE 91, 032706/arXiv: 1411.4821
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Order parameter:
State diagram
𝜙 ≡1𝑁 �𝜓�𝑖
𝑖
alignment
self- propulsion
RvD et al. PRE 91, 032706/arXiv: 1411.4821
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State diagram
alignment
self- propulsion
Order parameter:
𝜙 ≡1𝑁 �𝜓�𝑖
𝑖
RvD et al. PRE 91, 032706/arXiv: 1411.4821
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State diagram
alignment
self- propulsion
Order parameter:
𝜙 ≡1𝑁 �𝜓�𝑖
𝑖
RvD et al. PRE 91, 032706/arXiv: 1411.4821
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Moving without a leader • Collective global dynamics
from local interactions: – Migration – Rotation – ‘Run-and-tumble’
RvD et al. PRE 91, 032706/arXiv: 1411.4821
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Social / geometric alignment
Image from TansLab (AMOLF)
How can cells align without eyes?
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Anisotropic interaction rules
• Forces – Self-propulsion – Repulsive when
overlapping
• Torques – Noise – Steric repulsion
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Anisotropic interaction rules
• Forces – Self-propulsion – Repulsive when
overlapping
• Torques – Noise – Steric repulsion
Aligned
Anti-aligned
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Rotating state?
But, unstable
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States of eliptical particles
Jammed “Slug” Random
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Preliminary state diagram
Jammed
Break
Is polar alignment or geometry responsible for collective dynamics?
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Thanks
Ruben van Drongelen idemalab.tudelft.nl
• Timon Idema (Delft) • Carl Goodrich (UPenn) • Anshuman Pal (UPenn)
• Brian Tighe (Delft) • Doris Heinrich (Leiden) • Gerard Barkema
(Utrecht/Leiden) • Shashi Thutupalli
(Princeton)