Active Flows using Multi-Particle Collision Dynamics

DSFD 2023

Timofey Kozhukhov, Benjamin Loewe, Tyler N. Shendruk (t.shendruk@ed.ac.uk)
$\definecolor{saphire}{RGB}{0, 50, 95}$ $\definecolor{crimson}{RGB}{193, 0, 67}$ $\definecolor{capri}{RGB}{0, 196, 223}$ $\definecolor{amber}{RGB}{244, 170, 0}$ $\definecolor{plum}{RGB}{129, 2, 98}$ $\definecolor{cerulean}{RGB}{0, 145, 181}$ $\definecolor{ruby}{RGB}{212, 0, 114}$ $\definecolor{cardinal}{RGB}{172, 0, 64}$ $\definecolor{ccinnamon}{RGB}{205, 90, 19}$ $\definecolor{climegreen}{RGB}{41, 188, 41}$ $\definecolor{cgold}{RGB}{141, 116, 74}$ $\definecolor{ctaupe}{RGB}{110, 80, 72}$ $\definecolor{cteal}{RGB}{69, 126, 129}$ $\definecolor{cforestgreen}{RGB}{0, 70, 49}$ $\definecolor{cmahogany}{RGB}{106, 51, 40}$ $\definecolor{csilver}{RGB}{194, 211, 223}$ $\definecolor{coldrose}{RGB}{184, 133, 141}$ $\definecolor{curry}{RGB}{156, 154, 0}$ $\definecolor{cobalt}{RGB}{0, 80, 114}$ $\definecolor{rubydarker}{RGB}{197, 0, 99}$ $\definecolor{purple}{RGB}{56, 6, 92}$ $\definecolor{cardinaldarker}{RGB}{97, 0, 36}$ $\definecolor{ceruleandarker}{RGB}{0, 113, 140}$ $\definecolor{amberlighter}{RGB}{240, 191, 79}$ $\definecolor{amberbrighter}{RGB}{245, 242, 88}$ $\definecolor{onyx}{RGB}{15, 15, 15}$

Active matter ranges across scales

  • Individual "active" units
  • Absorb energy from environment
  • Energy used to locomote
But what about the mesoscale?

Youtube: Wonders in the sky (2015)
Henkes S, et al., Phys. Rev. E, 2011
Rivas D, et al., Soft Matter, 2020
Sokolov A, et al., Phys. Rev. X, 2019

Active matter at the mesoscale is numerically under-explored

Thijssen K, Khaladj D, et al., PNAS, 2021
Drechsler M, et al., Mol Biol Cell, 2020
Ray S, et al., Phys. Rev. Lett., 2023

Why?

Multi-Particle Collision Dynamics (MPCD)


Streaming: $\vec{x}_i(t+\delta t) = \vec{x}_i(t) + \vec{v}_i(t)\delta t$

Collision: $\vec{v}_i(t+\delta t) = \vec{v}_{CM}(t) + \vec\Xi_i(\vec{r}_\mathrm{CM}, t)$
  • Shendruk T, Yeomans J M, Soft Matter, 2015

A planar collision rule induces local force dipoles

$\Xi_i^\mathrm{Active} = \Xi_i^{N}$ ${\color{ruby} {+ \alpha_C \delta t \left( \frac{\kappa_i}{m_i} - \langle \frac{\kappa_j}{m_j} \rangle_C \right) \vec{n}_C} ; \quad \alpha_C = \sum_i^{\rho_C}\alpha_i} $
  • Kozhukhov T, Shendruk T, Sci. Adv., 2022

Active-Nematic MPCD Reproduces Active Turbulence

Rivas D, et al., Soft Matter, 2020
$\alpha = 0.1$. Turbulence regime: $\alpha > 0.025$
  • Kozhukhov T, Shendruk T, Sci. Adv., 2022

Strategy: Modulate local activity

$\Xi_i^{Active} = \Xi_i^{N}+ {\alpha_C} \delta t \left( \frac{\kappa_i}{m_i} - \langle \frac{\kappa_j}{m_j} \rangle_C \right) \vec{n}_C $

  • Active Sum: $\alpha_C^\mathrm{S} = \alpha \rho_C$
  • Active Average: $\alpha_C^\mathrm{A} = \alpha$

  • $\mathcal{S}_C(\rho_C; \sigma_p, \sigma_w) = \frac{1}{2} \left( 1 - \tanh \left( \frac{\rho_C - \av{\rho_C} \left( 1 + \sigma_p \right)}{\av{\rho_C} \sigma_w} \right) \right)$
  • Sigmoidal Av.: $\alpha_C^\mathrm{S-A}(\rho_C) = \alpha_C^\mathrm{A} \mathcal{S}_C(\rho_C)$
  • Sigmoidal Sum: $\alpha_C^\mathrm{S-S}(\rho_C) = \alpha_C^\mathrm{S} \mathcal{S}_C(\rho_C)$
  • Kozhukhov T, Shendruk T, Sci. Adv., 2022
  • Kozhukhov T, Loewe B, Shendruk T, in prep.
Active Sum
Active Av.
Sigmoid Sum ($\sigma_p=0.4, \sigma_w=0.5$)
Sigmoid Av. ($\sigma_p=0.4, \sigma_w=0.5$)
$\alpha = 0.1$
Active Sum
Active Av.
Sigmoid Sum ($\sigma_p=0.4, \sigma_w=0.5$)
Sigmoid Av. ($\sigma_p=0.4, \sigma_w=0.5$)
$\alpha = 0.1$

Modulated AN-MPCD reproduces active turbulence


$\ell_d = \rho_d^{-1/2}$; Theory: $\ell_d \propto \alpha^{-1/2}$

Theory: $v \propto \alpha^{1/2}$

Modulations reduce density-induced drift

Fick's law: Density-induced drift $\propto \left| \nabla \rho \right|$


$\alpha=0.1$

$\chi_\mathrm{NGM}=\frac{d}{d+2} \frac{\Delta r^4}{|\Delta r^2|^2}-1$

Applications of mesoscale AN-MPCD


Louise Head
Related: arXiv:2306.05328, Submitted 2023
Active Av.

Applications of mesoscale AN-MPCD


Ryan Keogh
Keogh R, et al., Submitted 2023
Active Av.

Applications of mesoscale AN-MPCD


Zahra Valei
Valei Z, et al., In prep. 2023
Sigmoidal Av.

Applications of mesoscale AN-MPCD


Benjamín Loewe
Active Sum

Applications of mesoscale AN-MPCD


Kira Koch
Sigmoidal Av.

Conclusions

  • A force dipole is sufficient to reproduce active turbulence in MPCD
  • Density dependent activity modulation reduces density fluctuations
  • AN-MPCD is a strong framework to simulate out of equilibrium mesoscale systems

Contacts: t.shendruk@ed.ac.uk, t.kozhukhov@sms.ed.ac.uk

View this talk online at www.Kozhukhov.co.uk/


Acknowledgements

Tyler N. Shendruk
Benjamín Loewe
Kristian Thijssen
Ryan Keogh
Jack Paget
Louise Head
Zahra Valei
François de Tournemire
Oleksandr Baziei
Kira Koch

Appendix Slides

Sig-Av. Sig-Sum very similar. Chosen params are $\sigma_p=0.4, \sigma_w=0.5$

Modulations reduce density fluctuations

Modulations reduce density band width

Giant number fluctuations analysis reveal algorithm regimes

Central Limit Theorem: $\sigma_{N_C}\propto \langle N_C \rangle^{1/2}$


$\sigma_{N_C}=A\langle N_C \rangle^\nu$
$A=\sigma_{N_C}|_{\langle N_C \rangle=1}$