Modal analysis and optimization of swimming active filaments.

Area of Science:

• Fluid dynamics
• Biophysics
• Mathematical modeling

Background:

• Active flexible filaments, like flagella, are crucial for biological locomotion (spermatozoa, algae).
• Existing models quantify the relationship between internal forces and external motion (shape, speed).
• This framework extends to artificial microswimmers.

Purpose of the Study:

• To model and optimize the locomotion of isolated active filaments as a mathematical problem.
• To reduce computational complexity by using a reduced set of eigenmodes.
• To analyze the governing dynamics of artificial swimmers with monophasic forcing.

Main Methods:

• Formulating filament locomotion as a mathematical optimization problem.
• Utilizing eigenmode decomposition to represent filament dynamics.
• Analyzing swimmers with monophasic forcing.

Main Results:

• Swimming dynamics can be accurately described and optimized using a limited number of eigenmodes.
• Monophasic forcing in artificial swimmers is governed by four forcing eigenmodes.
• Two of these four eigenmodes are independent, simplifying control.
• Optimizations under various constraints were presented.

Conclusions:

• Eigenmode analysis offers a computationally efficient method for studying and optimizing active filament locomotion.
• This approach provides insights into the design and control of artificial microswimmers.
• The findings simplify the understanding of complex fluid dynamics in microscale propulsion.