Coexistence of Defect Morphologies in Three-Dimensional Active Nematics Article Swipe
Pasquale Digregorio
,
C. Rorai
,
Ignacio Pagonabarraga
,
Federico Toschi
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevlett.132.258301
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1103/physrevlett.132.258301
We establish how active stress globally affects the morphology of disclination lines of a three-dimensional active nematic liquid crystal under chaotic flow. Thanks to a defect detection algorithm based on the local nematic orientation, we show that activity selects a crossover length scale in between the size of small defect loops and that of long and tangled defect lines of fractal dimension 2. This length scale crossover is consistent with the scaling of the average separation between defects as a function of activity. Moreover, on the basis of numerical simulation in a 3D periodic geometry, we show the presence of a network of regular defect loops, contractible onto the 3-torus, always coexisting with wrapping defect lines. While the length of regular defects scales linearly with the emerging active length scale, it verifies an inverse quadratic dependence for wrapping defects. The shorter the active length scale, the more the defect lines wrap around the periodic boundaries, resulting in extremely long and buckled structures.
Related Topics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1103/physrevlett.132.258301
- OA Status
- gold
- Cited By
- 7
- References
- 55
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399775314
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4399775314Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1103/physrevlett.132.258301Digital Object Identifier
- Title
-
Coexistence of Defect Morphologies in Three-Dimensional Active NematicsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-06-18Full publication date if available
- Authors
-
Pasquale Digregorio, C. Rorai, Ignacio Pagonabarraga, Federico ToschiList of authors in order
- Landing page
-
https://doi.org/10.1103/physrevlett.132.258301Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://research.tue.nl/en/publications/810e7a7e-83fa-403e-bca2-2e7376fa30dfDirect OA link when available
- Concepts
-
Materials science, Active matter, Condensed matter physics, Physics, Biology, Cell biologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
7Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 4, 2024: 3Per-year citation counts (last 5 years)
- References (count)
-
55Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4399775314 |
|---|---|
| doi | https://doi.org/10.1103/physrevlett.132.258301 |
| ids.doi | https://doi.org/10.1103/physrevlett.132.258301 |
| ids.pmid | https://pubmed.ncbi.nlm.nih.gov/38996247 |
| ids.openalex | https://openalex.org/W4399775314 |
| fwci | 3.17837574 |
| type | article |
| title | Coexistence of Defect Morphologies in Three-Dimensional Active Nematics |
| awards[0].id | https://openalex.org/G216686704 |
| awards[0].funder_id | https://openalex.org/F4320338438 |
| awards[0].display_name | |
| awards[0].funder_award_id | 75446 |
| awards[0].funder_display_name | HORIZON EUROPE Marie Sklodowska-Curie Actions |
| awards[1].id | https://openalex.org/G3348101162 |
| awards[1].funder_id | https://openalex.org/F4320321505 |
| awards[1].display_name | |
| awards[1].funder_award_id | 2021SGR-673 |
| awards[1].funder_display_name | Generalitat de Catalunya |
| awards[2].id | https://openalex.org/G1482387628 |
| awards[2].funder_id | https://openalex.org/F4320331518 |
| awards[2].display_name | |
| awards[2].funder_award_id | s1194 |
| awards[2].funder_display_name | Centro Svizzero di Calcolo Scientifico |
| awards[3].id | https://openalex.org/G4311146116 |
| awards[3].funder_id | https://openalex.org/F4320315062 |
| awards[3].display_name | |
| awards[3].funder_award_id | PID2021-126570NB-100 |
| awards[3].funder_display_name | Ministerio de Ciencia, Innovación y Universidades |
| awards[4].id | https://openalex.org/G882274831 |
| awards[4].funder_id | https://openalex.org/F4320331518 |
| awards[4].display_name | |
| awards[4].funder_award_id | s1079 |
| awards[4].funder_display_name | Centro Svizzero di Calcolo Scientifico |
| biblio.issue | 25 |
| biblio.volume | 132 |
| biblio.last_page | 258301 |
| biblio.first_page | 258301 |
| topics[0].id | https://openalex.org/T11486 |
| topics[0].field.id | https://openalex.org/fields/31 |
| topics[0].field.display_name | Physics and Astronomy |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/3104 |
| topics[0].subfield.display_name | Condensed Matter Physics |
| topics[0].display_name | Micro and Nano Robotics |
| topics[1].id | https://openalex.org/T12784 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.9968000054359436 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2210 |
| topics[1].subfield.display_name | Mechanical Engineering |
| topics[1].display_name | Modular Robots and Swarm Intelligence |
| topics[2].id | https://openalex.org/T11187 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9757000207901001 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1705 |
| topics[2].subfield.display_name | Computer Networks and Communications |
| topics[2].display_name | Nonlinear Dynamics and Pattern Formation |
| funders[0].id | https://openalex.org/F4320315062 |
| funders[0].ror | |
| funders[0].display_name | Ministerio de Ciencia, Innovación y Universidades |
| funders[1].id | https://openalex.org/F4320321505 |
| funders[1].ror | https://ror.org/01bg62x04 |
| funders[1].display_name | Generalitat de Catalunya |
| funders[2].id | https://openalex.org/F4320323868 |
| funders[2].ror | https://ror.org/05sd8tv96 |
| funders[2].display_name | Barcelona Supercomputing Center |
| funders[3].id | https://openalex.org/F4320331518 |
| funders[3].ror | |
| funders[3].display_name | Centro Svizzero di Calcolo Scientifico |
| funders[4].id | https://openalex.org/F4320332999 |
| funders[4].ror | https://ror.org/00k4n6c32 |
| funders[4].display_name | Horizon 2020 Framework Programme |
| funders[5].id | https://openalex.org/F4320338438 |
| funders[5].ror | |
| funders[5].display_name | HORIZON EUROPE Marie Sklodowska-Curie Actions |
| is_xpac | False |
| apc_list.value | 3750 |
| apc_list.currency | USD |
| apc_list.value_usd | 3750 |
| apc_paid.value | 3750 |
| apc_paid.currency | USD |
| apc_paid.value_usd | 3750 |
| concepts[0].id | https://openalex.org/C192562407 |
| concepts[0].level | 0 |
| concepts[0].score | 0.5582037568092346 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[0].display_name | Materials science |
| concepts[1].id | https://openalex.org/C2775993382 |
| concepts[1].level | 2 |
| concepts[1].score | 0.434621125459671 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q4677565 |
| concepts[1].display_name | Active matter |
| concepts[2].id | https://openalex.org/C26873012 |
| concepts[2].level | 1 |
| concepts[2].score | 0.38732069730758667 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q214781 |
| concepts[2].display_name | Condensed matter physics |
| concepts[3].id | https://openalex.org/C121332964 |
| concepts[3].level | 0 |
| concepts[3].score | 0.2678072452545166 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[3].display_name | Physics |
| concepts[4].id | https://openalex.org/C86803240 |
| concepts[4].level | 0 |
| concepts[4].score | 0.0 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q420 |
| concepts[4].display_name | Biology |
| concepts[5].id | https://openalex.org/C95444343 |
| concepts[5].level | 1 |
| concepts[5].score | 0.0 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q7141 |
| concepts[5].display_name | Cell biology |
| keywords[0].id | https://openalex.org/keywords/materials-science |
| keywords[0].score | 0.5582037568092346 |
| keywords[0].display_name | Materials science |
| keywords[1].id | https://openalex.org/keywords/active-matter |
| keywords[1].score | 0.434621125459671 |
| keywords[1].display_name | Active matter |
| keywords[2].id | https://openalex.org/keywords/condensed-matter-physics |
| keywords[2].score | 0.38732069730758667 |
| keywords[2].display_name | Condensed matter physics |
| keywords[3].id | https://openalex.org/keywords/physics |
| keywords[3].score | 0.2678072452545166 |
| keywords[3].display_name | Physics |
| language | en |
| locations[0].id | doi:10.1103/physrevlett.132.258301 |
| locations[0].is_oa | False |
| locations[0].source.id | https://openalex.org/S24807848 |
| locations[0].source.issn | 0031-9007, 1079-7114, 1092-0145 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0031-9007 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | Physical Review Letters |
| locations[0].source.host_organization | https://openalex.org/P4310320261 |
| locations[0].source.host_organization_name | American Physical Society |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310320261 |
| locations[0].source.host_organization_lineage_names | American Physical Society |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Physical Review Letters |
| locations[0].landing_page_url | https://doi.org/10.1103/physrevlett.132.258301 |
| locations[1].id | pmid:38996247 |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306525036 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | PubMed |
| locations[1].source.host_organization | https://openalex.org/I1299303238 |
| locations[1].source.host_organization_name | National Institutes of Health |
| locations[1].source.host_organization_lineage | https://openalex.org/I1299303238 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | publishedVersion |
| locations[1].raw_type | |
| locations[1].license_id | |
| locations[1].is_accepted | True |
| locations[1].is_published | True |
| locations[1].raw_source_name | Physical review letters |
| locations[1].landing_page_url | https://pubmed.ncbi.nlm.nih.gov/38996247 |
| locations[2].id | pmh:oai:pure.tue.nl:openaire/810e7a7e-83fa-403e-bca2-2e7376fa30df |
| locations[2].is_oa | True |
| locations[2].source | |
| locations[2].license | cc-by |
| locations[2].pdf_url | |
| locations[2].version | publishedVersion |
| locations[2].raw_type | info:eu-repo/semantics/publishedVersion |
| locations[2].license_id | https://openalex.org/licenses/cc-by |
| locations[2].is_accepted | True |
| locations[2].is_published | True |
| locations[2].raw_source_name | Digregorio, P, Rorai, C, Pagonabarraga, I & Toschi, F 2024, 'Coexistence of Defect Morphologies in Three-Dimensional Active Nematics', Physical Review Letters, vol. 132, no. 25, 258301. https://doi.org/10.1103/PhysRevLett.132.258301 |
| locations[2].landing_page_url | https://research.tue.nl/en/publications/810e7a7e-83fa-403e-bca2-2e7376fa30df |
| locations[3].id | pmh:oai:ricerca.uniba.it:11586/553583 |
| locations[3].is_oa | False |
| locations[3].source.id | https://openalex.org/S4377196296 |
| locations[3].source.issn | |
| locations[3].source.type | repository |
| locations[3].source.is_oa | False |
| locations[3].source.issn_l | |
| locations[3].source.is_core | False |
| locations[3].source.is_in_doaj | False |
| locations[3].source.display_name | CINECA IRIS Institutional Research Information System (University of Bari Aldo Moro) |
| locations[3].source.host_organization | https://openalex.org/I5561750 |
| locations[3].source.host_organization_name | University of Bari Aldo Moro |
| locations[3].source.host_organization_lineage | https://openalex.org/I5561750 |
| locations[3].license | |
| locations[3].pdf_url | |
| locations[3].version | submittedVersion |
| locations[3].raw_type | info:eu-repo/semantics/article |
| locations[3].license_id | |
| locations[3].is_accepted | False |
| locations[3].is_published | False |
| locations[3].raw_source_name | |
| locations[3].landing_page_url | https://hdl.handle.net/11586/553583 |
| indexed_in | crossref, pubmed |
| authorships[0].author.id | https://openalex.org/A5006965375 |
| authorships[0].author.orcid | https://orcid.org/0000-0001-6567-9382 |
| authorships[0].author.display_name | Pasquale Digregorio |
| authorships[0].countries | ES |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I71999127 |
| authorships[0].affiliations[0].raw_affiliation_string | Universitat de Barcelona |
| authorships[0].affiliations[1].institution_ids | https://openalex.org/I71999127 |
| authorships[0].affiliations[1].raw_affiliation_string | Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain |
| authorships[0].institutions[0].id | https://openalex.org/I71999127 |
| authorships[0].institutions[0].ror | https://ror.org/021018s57 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I71999127 |
| authorships[0].institutions[0].country_code | ES |
| authorships[0].institutions[0].display_name | Universitat de Barcelona |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Pasquale Digregorio |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | Universitat de Barcelona, Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain |
| authorships[1].author.id | https://openalex.org/A5032996261 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-6309-4652 |
| authorships[1].author.display_name | C. Rorai |
| authorships[1].countries | CH |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I5124864 |
| authorships[1].affiliations[0].raw_affiliation_string | École Polytechnique Fédérale de Lausanne (EPFL) |
| authorships[1].institutions[0].id | https://openalex.org/I5124864 |
| authorships[1].institutions[0].ror | https://ror.org/02s376052 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I2799323385, https://openalex.org/I5124864 |
| authorships[1].institutions[0].country_code | CH |
| authorships[1].institutions[0].display_name | École Polytechnique Fédérale de Lausanne |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Cecilia Rorai |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | École Polytechnique Fédérale de Lausanne (EPFL) |
| authorships[2].author.id | https://openalex.org/A5004099682 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-6187-5025 |
| authorships[2].author.display_name | Ignacio Pagonabarraga |
| authorships[2].countries | ES |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I71999127 |
| authorships[2].affiliations[0].raw_affiliation_string | Universitat de Barcelona |
| authorships[2].affiliations[1].institution_ids | https://openalex.org/I71999127 |
| authorships[2].affiliations[1].raw_affiliation_string | Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain |
| authorships[2].institutions[0].id | https://openalex.org/I71999127 |
| authorships[2].institutions[0].ror | https://ror.org/021018s57 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I71999127 |
| authorships[2].institutions[0].country_code | ES |
| authorships[2].institutions[0].display_name | Universitat de Barcelona |
| authorships[2].author_position | middle |
| authorships[2].raw_author_name | Ignacio Pagonabarraga |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | Universitat de Barcelona, Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain |
| authorships[3].author.id | https://openalex.org/A5061447676 |
| authorships[3].author.orcid | https://orcid.org/0000-0001-5935-2332 |
| authorships[3].author.display_name | Federico Toschi |
| authorships[3].countries | NL |
| authorships[3].affiliations[0].raw_affiliation_string | CNR-IAC, I-00185 Rome, Italy |
| authorships[3].affiliations[1].institution_ids | https://openalex.org/I83019370 |
| authorships[3].affiliations[1].raw_affiliation_string | Department of Applied Physics and Science Education, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, Netherlands |
| authorships[3].institutions[0].id | https://openalex.org/I83019370 |
| authorships[3].institutions[0].ror | https://ror.org/02c2kyt77 |
| authorships[3].institutions[0].type | education |
| authorships[3].institutions[0].lineage | https://openalex.org/I83019370 |
| authorships[3].institutions[0].country_code | NL |
| authorships[3].institutions[0].display_name | Eindhoven University of Technology |
| authorships[3].author_position | last |
| authorships[3].raw_author_name | Federico Toschi |
| authorships[3].is_corresponding | False |
| authorships[3].raw_affiliation_strings | CNR-IAC, I-00185 Rome, Italy, Department of Applied Physics and Science Education, Eindhoven University of Technology, Den Dolech 2, 5600 MB Eindhoven, Netherlands |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://research.tue.nl/en/publications/810e7a7e-83fa-403e-bca2-2e7376fa30df |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Coexistence of Defect Morphologies in Three-Dimensional Active Nematics |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11486 |
| primary_topic.field.id | https://openalex.org/fields/31 |
| primary_topic.field.display_name | Physics and Astronomy |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/3104 |
| primary_topic.subfield.display_name | Condensed Matter Physics |
| primary_topic.display_name | Micro and Nano Robotics |
| related_works | https://openalex.org/W4372239356, https://openalex.org/W3127679539, https://openalex.org/W2754312467, https://openalex.org/W2738371553, https://openalex.org/W4294877867, https://openalex.org/W4246450666, https://openalex.org/W4388998267, https://openalex.org/W2898370298, https://openalex.org/W2137437058, https://openalex.org/W4306824620 |
| cited_by_count | 7 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 4 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 3 |
| locations_count | 4 |
| best_oa_location.id | pmh:oai:pure.tue.nl:openaire/810e7a7e-83fa-403e-bca2-2e7376fa30df |
| best_oa_location.is_oa | True |
| best_oa_location.source | |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | info:eu-repo/semantics/publishedVersion |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Digregorio, P, Rorai, C, Pagonabarraga, I & Toschi, F 2024, 'Coexistence of Defect Morphologies in Three-Dimensional Active Nematics', Physical Review Letters, vol. 132, no. 25, 258301. https://doi.org/10.1103/PhysRevLett.132.258301 |
| best_oa_location.landing_page_url | https://research.tue.nl/en/publications/810e7a7e-83fa-403e-bca2-2e7376fa30df |
| primary_location.id | doi:10.1103/physrevlett.132.258301 |
| primary_location.is_oa | False |
| primary_location.source.id | https://openalex.org/S24807848 |
| primary_location.source.issn | 0031-9007, 1079-7114, 1092-0145 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0031-9007 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | Physical Review Letters |
| primary_location.source.host_organization | https://openalex.org/P4310320261 |
| primary_location.source.host_organization_name | American Physical Society |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310320261 |
| primary_location.source.host_organization_lineage_names | American Physical Society |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Physical Review Letters |
| primary_location.landing_page_url | https://doi.org/10.1103/physrevlett.132.258301 |
| publication_date | 2024-06-18 |
| publication_year | 2024 |
| referenced_works | https://openalex.org/W4388376074, https://openalex.org/W2519211786, https://openalex.org/W2022227344, https://openalex.org/W2065592901, https://openalex.org/W2110990313, https://openalex.org/W3170743020, https://openalex.org/W2953795337, https://openalex.org/W2056707942, https://openalex.org/W2554468600, https://openalex.org/W2892001986, https://openalex.org/W2913413126, https://openalex.org/W2965116788, https://openalex.org/W2123543343, https://openalex.org/W2021187668, https://openalex.org/W2767776190, https://openalex.org/W1683737216, https://openalex.org/W2074574519, https://openalex.org/W3005821439, https://openalex.org/W4309466671, https://openalex.org/W4200324242, https://openalex.org/W3012562395, https://openalex.org/W2612799535, https://openalex.org/W3115139999, https://openalex.org/W2950245548, https://openalex.org/W2037169654, https://openalex.org/W2345621746, https://openalex.org/W1999617370, https://openalex.org/W1992084946, https://openalex.org/W2798033522, https://openalex.org/W3048978708, https://openalex.org/W3010259520, https://openalex.org/W4328130284, https://openalex.org/W3177065778, https://openalex.org/W3094296995, https://openalex.org/W3008773947, https://openalex.org/W2965514916, https://openalex.org/W4390975707, https://openalex.org/W4388395150, https://openalex.org/W1528590971, https://openalex.org/W3211931796, https://openalex.org/W1844978518, https://openalex.org/W1973343935, https://openalex.org/W2087722380, https://openalex.org/W2094705424, https://openalex.org/W2340194477, https://openalex.org/W3102912952, https://openalex.org/W2501502571, https://openalex.org/W3099867946, https://openalex.org/W3103108796, https://openalex.org/W3118565451, https://openalex.org/W3101500626, https://openalex.org/W2976683398, https://openalex.org/W3104289385, https://openalex.org/W3105946182, https://openalex.org/W3098086261 |
| referenced_works_count | 55 |
| abstract_inverted_index.a | 13, 24, 39, 79, 91, 100 |
| abstract_inverted_index.2. | 62 |
| abstract_inverted_index.3D | 92 |
| abstract_inverted_index.We | 0 |
| abstract_inverted_index.an | 132 |
| abstract_inverted_index.as | 78 |
| abstract_inverted_index.in | 43, 90, 156 |
| abstract_inverted_index.is | 67 |
| abstract_inverted_index.it | 130 |
| abstract_inverted_index.of | 9, 12, 47, 53, 59, 72, 81, 87, 99, 102, 119 |
| abstract_inverted_index.on | 29, 84 |
| abstract_inverted_index.to | 23 |
| abstract_inverted_index.we | 34, 95 |
| abstract_inverted_index.The | 139 |
| abstract_inverted_index.and | 51, 55, 159 |
| abstract_inverted_index.for | 136 |
| abstract_inverted_index.how | 2 |
| abstract_inverted_index.the | 7, 30, 45, 70, 73, 85, 97, 108, 117, 125, 141, 145, 147, 152 |
| abstract_inverted_index.This | 63 |
| abstract_inverted_index.long | 54, 158 |
| abstract_inverted_index.more | 146 |
| abstract_inverted_index.onto | 107 |
| abstract_inverted_index.show | 35, 96 |
| abstract_inverted_index.size | 46 |
| abstract_inverted_index.that | 36, 52 |
| abstract_inverted_index.with | 69, 112, 124 |
| abstract_inverted_index.wrap | 150 |
| abstract_inverted_index.While | 116 |
| abstract_inverted_index.based | 28 |
| abstract_inverted_index.basis | 86 |
| abstract_inverted_index.flow. | 21 |
| abstract_inverted_index.lines | 11, 58, 149 |
| abstract_inverted_index.local | 31 |
| abstract_inverted_index.loops | 50 |
| abstract_inverted_index.scale | 42, 65 |
| abstract_inverted_index.small | 48 |
| abstract_inverted_index.under | 19 |
| abstract_inverted_index.Thanks | 22 |
| abstract_inverted_index.active | 3, 15, 127, 142 |
| abstract_inverted_index.always | 110 |
| abstract_inverted_index.around | 151 |
| abstract_inverted_index.defect | 25, 49, 57, 104, 114, 148 |
| abstract_inverted_index.length | 41, 64, 118, 128, 143 |
| abstract_inverted_index.lines. | 115 |
| abstract_inverted_index.liquid | 17 |
| abstract_inverted_index.loops, | 105 |
| abstract_inverted_index.scale, | 129, 144 |
| abstract_inverted_index.scales | 122 |
| abstract_inverted_index.stress | 4 |
| abstract_inverted_index.affects | 6 |
| abstract_inverted_index.average | 74 |
| abstract_inverted_index.between | 44, 76 |
| abstract_inverted_index.buckled | 160 |
| abstract_inverted_index.chaotic | 20 |
| abstract_inverted_index.crystal | 18 |
| abstract_inverted_index.defects | 77, 121 |
| abstract_inverted_index.fractal | 60 |
| abstract_inverted_index.inverse | 133 |
| abstract_inverted_index.nematic | 16, 32 |
| abstract_inverted_index.network | 101 |
| abstract_inverted_index.regular | 103, 120 |
| abstract_inverted_index.scaling | 71 |
| abstract_inverted_index.selects | 38 |
| abstract_inverted_index.shorter | 140 |
| abstract_inverted_index.tangled | 56 |
| abstract_inverted_index.3-torus, | 109 |
| abstract_inverted_index.activity | 37 |
| abstract_inverted_index.defects. | 138 |
| abstract_inverted_index.emerging | 126 |
| abstract_inverted_index.function | 80 |
| abstract_inverted_index.globally | 5 |
| abstract_inverted_index.linearly | 123 |
| abstract_inverted_index.periodic | 93, 153 |
| abstract_inverted_index.presence | 98 |
| abstract_inverted_index.verifies | 131 |
| abstract_inverted_index.wrapping | 113, 137 |
| abstract_inverted_index.Moreover, | 83 |
| abstract_inverted_index.activity. | 82 |
| abstract_inverted_index.algorithm | 27 |
| abstract_inverted_index.crossover | 40, 66 |
| abstract_inverted_index.detection | 26 |
| abstract_inverted_index.dimension | 61 |
| abstract_inverted_index.establish | 1 |
| abstract_inverted_index.extremely | 157 |
| abstract_inverted_index.geometry, | 94 |
| abstract_inverted_index.numerical | 88 |
| abstract_inverted_index.quadratic | 134 |
| abstract_inverted_index.resulting | 155 |
| abstract_inverted_index.coexisting | 111 |
| abstract_inverted_index.consistent | 68 |
| abstract_inverted_index.dependence | 135 |
| abstract_inverted_index.morphology | 8 |
| abstract_inverted_index.separation | 75 |
| abstract_inverted_index.simulation | 89 |
| abstract_inverted_index.boundaries, | 154 |
| abstract_inverted_index.structures. | 161 |
| abstract_inverted_index.contractible | 106 |
| abstract_inverted_index.disclination | 10 |
| abstract_inverted_index.orientation, | 33 |
| abstract_inverted_index.three-dimensional | 14 |
| cited_by_percentile_year.max | 98 |
| cited_by_percentile_year.min | 96 |
| countries_distinct_count | 3 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/2 |
| sustainable_development_goals[0].score | 0.5899999737739563 |
| sustainable_development_goals[0].display_name | Zero hunger |
| citation_normalized_percentile.value | 0.91789404 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |