Lagrangian mechanics of active systems

Area of Science:

• Fluid dynamics
• Biophysics
• Computational modeling

Background:

• Modeling low-Reynolds number hydrodynamics of shape-changing objects like microswimmers is computationally challenging.
• Existing methods often struggle to efficiently incorporate complex internal dynamics driving shape changes.

Purpose of the Study:

• To introduce a novel multi-scale modeling and simulation framework for low-Reynolds number hydrodynamics.
• To enable efficient simulation of shape-changing immersed objects, including biological microswimmers and active surfaces.

Main Methods:

• The framework treats principal shape changes as generalized coordinates and defines conjugate generalized hydrodynamic friction forces.
• Generalized friction coefficients are pre-computed for rapid reuse in solving equations of motion.
• Extends Lagrangian mechanics to active systems where shape dynamics are driven by internal forces.

Main Results:

• The framework successfully models the hydrodynamics of shape-changing objects.
• It enables fast computation of dynamic equations of motion.
• Demonstrated prediction of in-phase and anti-phase synchronization in pairs of cilia using an experimentally measured beat pattern.

Conclusions:

• The presented framework offers an efficient and versatile tool for studying microscale hydrodynamics.
• It provides a robust method for analyzing synchronization phenomena in biological microswimmers and active surfaces.
• This approach facilitates the understanding of complex fluid-structure interactions in micro-environments.