Os nós são usados de todas as maneiras, todos os dias. Eles garantem a segurança tanto em ambientes internos quanto em atividades ao ar livre, como passeios de barco ou vela, são usados como suturas cirúrgicas, como decoração e podem até...
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Crédito: École Polytechnique Federale de Lausanne
Os nós são usados de todas as maneiras, todos os dias. Eles garantem a segurança tanto em ambientes internos quanto em atividades ao ar livre, como passeios de barco ou vela, são usados como suturas cirúrgicas, como decoração e podem até ser encontrados em nanoescala na natureza, por exemplo, em moléculas de DNA.
Nós elásticos são aqueles que voltam à sua forma original na ausência de atrito. Existem nós elásticos abertos amarrados com um único pedaço de fio com duas pontas, que voltam a ser uma linha reta , e nós elásticos fechados em que as pontas do fio usado para amarrá-los foram unidas. Estes tendem a voltar a ter uma forma curva .
Com foco em nós fechados, pesquisadores do Laboratório de Computação Geométrica da Ecole Polytechnique Federale de Lausanne, liderados pelo professor Mark Pauly, juntamente com colegas no Canadá e nos Estados Unidos, descobriram milhares de novos nós transformáveis, incluindo três novas formas que a humilde figura -oito nós podem assumir, dobrando o número documentado até o momento na literatura científica.
As descobertas foram publicadas na revista ACM Transactions on Graphics .
Para fazer essas descobertas, a equipe primeiro desenvolveu um pipeline computacional que combina amostragem espacial aleatória e simulação física para encontrar com eficiência os estados de equilíbrio estáveis dos nós elásticos. Aproveitando os resultados da teoria dos nós , eles executaram seu pipeline em milhares de diferentes tipos de nós topológicos para criar um extenso conjunto de dados de nós multiestáveis.
“Ao aplicar uma série de filtros a esses dados, descobrimos novos nós transformáveis com propriedades físicas interessantes e belas formas geométricas”, explicou a assistente de doutorado Michele Vidulis, autora principal do artigo “Exploração Computacional de Nós Elásticos Multiestáveis”.
"Este rico conjunto de formas fascinantes pode ser criado simplesmente amarrando um fio elástico, e notamos como esses objetos aparentemente simples podem às vezes exibir dezenas ou até centenas de formas estáveis diferentes. Os novos padrões geométricos que identificamos foram às vezes surpreendentes. Por exemplo , descobrimos que a maioria - mas não todas - das formas preferidas dos nós elásticos são planas e planas, enquanto poucos deles assumem formas tridimensionais", continuou Vidulis.
A equipe conduziu análises adicionais entre tipos de nós que revelaram novos padrões geométricos e topológicos com princípios construtivos não vistos em tipos de nós previamente tabulados, mostrando como nós elásticos multiestáveis podem ser usados para projetar novas estruturas.
"Como resultado de nossa pesquisa, podemos ver nós elásticos sendo usados no processo de projeto de estruturas auto-desdobráveis, como tendas pop-up ou abrigos de emergência leves. Novos metamateriais podem ser projetados que combinam vários elementos com nós elásticos para construir uma rede com comportamento mecânico complexo", explicou Vidulis.
A equipe também criou quebra-cabeças recreativos envolventes com o desafio de deformar um nó elástico e encontrar manualmente algumas das formas geométricas interessantes que calcularam com seus algoritmos.
Por mais satisfatórias que sejam essas novas descobertas, Vidulis e a equipe acreditam que o trabalho abre caminho para várias outras possíveis novas direções de pesquisa.
"Queremos explorar o projeto de estruturas autodesdobráveis e considerar o acoplamento de hastes elásticas com materiais de tecido. Além disso, apesar de simular milhares de nós diferentes, nossa exploração apenas arranhou a superfície dos milhões de nós que são conhecidos. Também planejamos estudar conjuntos mais complexos de sistemas com nós, nos quais novas propriedades mecânicas podem emergir da maneira como os componentes individuais estão interligados", concluiu.
Mais informações: Michele Vidulis et al, Exploração Computacional de Nós Elásticos Multiestáveis, Transações ACM em Gráficos (2023). DOI: 10.1145/3592399
GitHub: github.com/EPFL-LGG/ElasticKnots
Informações do diário: Transações ACM em Gráficos