Frenet algorithm for simulations of fluctuating continuous elastic filaments.

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding the behavior of continuous elastic filaments is crucial in various scientific fields.
• Fluctuations and spontaneous curvature significantly influence filament configurations.
• Incorporating volume interactions is essential for accurate modeling.

Purpose of the Study:

• To develop an algorithm for generating equilibrium configurations of fluctuating continuous elastic filaments.
• To calculate the end-to-end distance distribution for filaments with spontaneous curvature.
• To investigate the effect of volume interactions on filament behavior.

Main Methods:

• Combining statistical mechanics and differential geometry principles.
• Developing a novel algorithm for simulating filament equilibrium.
• Calculating distribution functions and analyzing temperature-dependent behavior.

Main Results:

• An algorithm for generating equilibrium configurations of fluctuating elastic filaments was developed.
• A specific temperature range was identified where filaments with nonvanishing spontaneous curvature become nearly completely stretched.
• The algorithm successfully incorporated volume interactions, showing their effect on filament end-to-end distance.

Conclusions:

• The developed algorithm provides a robust framework for studying elastic filaments.
• The findings highlight a unique phase behavior in filaments under specific conditions.
• The inclusion of volume interactions enhances the predictive power of the model for real-world applications.