On dispersion curve coloring for mechanical metafilters

Area of Science:

• Computational mathematics
• Applied physics
• Materials science

Background:

• Curve identification with intersections is challenging.
• Existing methods can be computationally expensive.

Purpose of the Study:

• Formalize smooth curve coloring as an optimization problem.
• Develop a novel, efficient automatic technique for curve identification.
• Investigate the properties of the optimal solution.

Main Methods:

• Formulated as minimizing total variation of curve derivatives.
• Employs first-order finite difference approximation.
• Uses prediction/correction steps with Euclidean bipartite matching.

Main Results:

• The proposed algorithm efficiently solves the curve identification problem.
• Demonstrated successful application to elastic periodic metamaterials.
• Achieved excellent agreement with smoothness and periodicity properties for metafilter dispersion curves.

Conclusions:

• The novel algorithm provides an effective solution for smooth curve coloring with intersections.
• The method is suitable for high-performance mechanical metafilter design.
• Future work may incorporate machine learning techniques for further development.