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Variational methods and deep Ritz method for active elastic solids.

Haiqin Wang1,2, Boyi Zou3, Jian Su1

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This summary is machine-generated.

This study applies variational methods based on minimum free energy to active elastic solids, using deep learning for enhanced solutions. It investigates active plate bending and contraction, offering insights into cell monolayer morphogenesis and gravity

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Area of Science:

  • Soft matter physics
  • Active matter physics
  • Solid mechanics

Background:

  • Variational methods, including minimum free energy (MFEVP) and Onsager's variational principle (OVP), are crucial in soft matter physics.
  • Previous work explored OVP for active matter dynamics.
  • This study focuses on MFEVP for static problems in active elastic solids.

Purpose of the Study:

  • To apply MFEVP-based variational methods to static problems in active elastic solids.
  • To develop and enhance approximate solution methods, such as the Ritz method, using deep learning.
  • To investigate the spontaneous bending and contraction of active circular plates and understand morphogenesis in cell monolayers.

Main Methods:

  • Utilizing the variational principle of minimum free energy (MFEVP) for active solid statics.
  • Applying the Ritz method with deep neural networks (Deep Ritz method) for approximate solutions.
  • Analyzing the bending and contraction of a thin active circular plate under internal asymmetric active contraction.

Main Results:

  • MFEVP successfully derives equilibrium equations and enables approximate solutions for active solid statics.
  • The Deep Ritz method enhances the accuracy of variational solutions.
  • Active circular plates bend towards the contracting side, and an 'activogravity' length scale is introduced to quantify the influence of gravity.

Conclusions:

  • MFEVP-based variational methods, enhanced by deep learning, provide a powerful framework for active solid statics.
  • The findings offer insights into the morphogenesis of solid-like confluent cell monolayers.
  • Gravitaxis behaviors at multicellular scales are significant for tissue development and symmetry breaking.