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生物集団に見られる相転移現象と�超一様性に対する理論的研究�Theoretical Study of Phase Transitions and Hyperuniformity Observed in Biological Populations

Ayana Ezoe (Department of Physics, Chuo University, Tokyo)

Joint work with M. Katori (Chuo) and H. Nishimori (Meiji)

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Physica A 643 (2024) 129798.

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1 November 2024

修士論文中間発表会

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Outline

  • Introductions
  • Model
  • Numerical Analysis
  • Summary and Future Problems
  • Other Research

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Introductions

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Switching of Cues by Foraging Ants

Foraging Ants

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  • Collective behavior and swarm intelligence have been studied.

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  • Ants reach food and come back to the nest by following pheromones dropped by other ants.

https://mas.kke.co.jp/

Edward O. Wilson and Bert Holldobler : `The Ants’, Belknap Press (1990), pp.265-279

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Switching of Cues by Foraging Ants

Nishimori’s group experiments

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Ogihara, Yamanaka, Akino, Izumi, Awazu, Nishimori : in `Mathematical Approaches to Biological Systems’, Springer (2015), pp.119-137

  1. In a box, put a food source separated from the nest.

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  • The preliminarily extracted recruit pheromone was applied along the white line.

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  • Trajectories of ants in 10 minutes were recorded.

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Ants perform not only

pheromone-mediated walks but also visual-cues-mediated walks.

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Switching Particle Systems

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Two-layer model (Switching interacting particle systems)

Floreani, Giardina, den Hollander, Nandan, Redig : J. Stat. Phys. 186 (2022) 33 (pp.45)

 

fast particles

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Model

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Stochastic Models for Foraging Path Selection

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Two types of particles, two types of walks

Two-layer model

Our model

slow particles

pheromone-mediated walks

fast particles

visual-cues-mediated walks

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Stochastic Models for Foraging Path Selection

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Two types of particles, two types of walks

Two-layer model

Our model

slow particles

pheromone-mediated walks

fast particles

visual-cues-mediated walks

(When ants are moving from nest to food.)

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Stochastic Models for Foraging Path Selection

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Two types of particles, two types of walks

Two-layer model

Our model

slow particles

pheromone-mediated walks

fast particles

visual-cues-mediated walks

(When ants are moving from food to nest.)

 

 

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Stochastic Models for Foraging Path Selection

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Stochastic Models for Foraging Path Selection

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Pheromone field (Time evolution)

 

 

 

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Stochastic Models for Foraging Path Selection

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Pheromone-mediated walks

 

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Stochastic Models for Foraging Path Selection

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Visual-cues-mediated walks

 

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Extreme Cases

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Slow particle Fast particle

 

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Numerical Analysis

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Definition of Nearly Optimal Paths

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The size dependence seems to be small.

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Data collapse in statistical mechanics.

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1/L-plots

 

 

 

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Continuous Phase Transitions

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The critical values of order parameters.

 

 

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Evaluation of Critical Exponents

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Evaluation of Critical Exponents

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Summary

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  • A new stochastic model on a lattice for the group behavior of foraging ants is proposed and numerically studied.

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  • A new application of switching interacting particle systems studied in probability theory is shown.

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  • Global changes observed in experiments in path selections of ants are realized as continuous phase transitions in the model.

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  • Order parameters are introduced to characterize path selections of ants and new types of phase transitions and critical phenomena are clarified.

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Future Problems

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We want to know the following.

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  • Mathematical description of interactions between ants through the pheromone field which the ants generated in the past.

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  • Mathematical theory for the phase transitions and critical phenomena in path selection for foraging ants.

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Other Research

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超一様性に対する理論的研究

アルゼンチンの砂漠の衛星写真　by Google Maps

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Other Research

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超一様性に対する理論的研究

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  •  

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藪点過程

藪点過程

(massの重みつき)

massの重みなし　　　　超一様でない

massの重みつき　　　　超一様である

Other Research

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Other Research

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mass

大

中

小

超一様性に対する理論的研究

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Other Research

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超一様性に対する理論的研究

密度が等しい独立なポアソン分布から始め、得られた20個の定常分布のサンプル平均

※エラーバーは標準偏差を表す

Class Iの超一様性を持つ重みつきの点過程が生成できた。

 

 

S. Torquato, Hyperuniform states of matter, Physics Reports (2018) 745, 1-95

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Thank you very much for your attention!

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Supplement (Scaling argument)

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Supplement (Scaling argument)

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