On dispersion curve coloring for mechanical metafilters
Abstract This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formal...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2022-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-23491-4 |
| _version_ | 1811211882486300672 |
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| author | Andrea Bacigalupo Maria Laura De Bellis Giorgio Gnecco Federico Nutarelli |
| author_facet | Andrea Bacigalupo Maria Laura De Bellis Giorgio Gnecco Federico Nutarelli |
| author_sort | Andrea Bacigalupo |
| collection | DOAJ |
| description | Abstract This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, written as functions of a scalar parameter. The algorithm is based on a first-order finite difference approximation of the curves and a sequence of prediction/correction steps. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving an Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming technique is presented. The proposed algorithm is applied with success to elastic periodic metamaterials for the realization of high-performance mechanical metafilters. Its output is shown to be in excellent agreement with desirable smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out. |
| first_indexed | 2024-04-12T05:20:55Z |
| format | Article |
| id | doaj.art-0de5b00b311041d58b18743b25880458 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-12T05:20:55Z |
| publishDate | 2022-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-0de5b00b311041d58b18743b258804582022-12-22T03:46:28ZengNature PortfolioScientific Reports2045-23222022-11-0112111310.1038/s41598-022-23491-4On dispersion curve coloring for mechanical metafiltersAndrea Bacigalupo0Maria Laura De Bellis1Giorgio Gnecco2Federico Nutarelli3DICCA – University of GenoaINGEO – University of Chieti-PescaraAXES – IMT School for Advanced StudiesICRIOS – Bocconi UniversityAbstract This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, written as functions of a scalar parameter. The algorithm is based on a first-order finite difference approximation of the curves and a sequence of prediction/correction steps. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving an Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming technique is presented. The proposed algorithm is applied with success to elastic periodic metamaterials for the realization of high-performance mechanical metafilters. Its output is shown to be in excellent agreement with desirable smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out.https://doi.org/10.1038/s41598-022-23491-4 |
| spellingShingle | Andrea Bacigalupo Maria Laura De Bellis Giorgio Gnecco Federico Nutarelli On dispersion curve coloring for mechanical metafilters Scientific Reports |
| title | On dispersion curve coloring for mechanical metafilters |
| title_full | On dispersion curve coloring for mechanical metafilters |
| title_fullStr | On dispersion curve coloring for mechanical metafilters |
| title_full_unstemmed | On dispersion curve coloring for mechanical metafilters |
| title_short | On dispersion curve coloring for mechanical metafilters |
| title_sort | on dispersion curve coloring for mechanical metafilters |
| url | https://doi.org/10.1038/s41598-022-23491-4 |
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