Materials inspired by mathematics

Kotani, Masahiro; Ikeda, Susumu

doi:10.1080/14686996.2016.1180233

Cited by 18 publications

(13 citation statements)

References 27 publications

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“…Those changes resulted in the impact factor rising from 1.267 in 2008 to 4.787 in 2017making STAM the world's leading open access journal focused on materials science. Further changes were initiated in 2016 by the former STAM Editor-in-Chief Shu Yamaguchi, including the launch of 'Vision' [2], 'Materials Informatics' [3] and 'Historical Review' [4] article categories; a materials informatics forum [5]; and an open-access publication network based at leading universities in Japan.…”

Section: Editorialmentioning

confidence: 99%

Looking to the future as STAM celebrates its 20th anniversary

Hashimoto

2019

Science and Technology of Advanced Materials

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Section: Editorialmentioning

confidence: 99%

Looking to the future as STAM celebrates its 20th anniversary

Hashimoto

2019

Science and Technology of Advanced Materials

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“…Homogenised behaviour of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenisation is the basis for computational topology optimisation (Allaire 2002;Bendsøe and Sigmund 2004;Guest and Prévost 2006;Challis et al 2008;Vicente et al 2016;Salonitis et al 2017;Asadpoure et al 2017;Khakalo and Niiranen 2017;Wang et al 2017) which will give rise to the next generation of architectured materials as it can already be seen in the works of (Laszczyk et al 2009;Andreassen et al 2014;Körner and Liebold-Ribeiro 2015;Hopkins et al 2016;Kotani and Ikeda 2016;Ghaedizadeh et al 2016;Ren et al 2016;Liu et al 2016;Dalaq et al 2016).…”

Section: Architectured Materialsmentioning

confidence: 99%

From Architectured Materials to Large-Scale Additive Manufacturing

Dirrenberger¹

2018

Springer Series in Adaptive Environments

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The classical material-by-design approach has been extensively perfected by materials scientists, while engineers have been optimising structures geometrically for centuries. The purpose of architectured materials is to build bridges across the microscale of materials and the macroscale of engineering structures, to put some geometry in the microstructure. This is a paradigm shift. Materials cannot be considered monolithic anymore. Any set of materials functions, even antagonistic ones, can be envisaged in the future. In this paper, we intend to demonstrate the pertinence of computation for developing architectured materials, and the not-so-incidental outcome which led us to developing large-scale additive manufacturing for architectural applications.

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“…Connectivity beyond standard pairwise interactions can be described by simplexes (cliques) of different orders; they constitute, for example, of groups of the system's elements or vertices of the underlying network that join together to make organised complexes at a larger scale. These higher-order structures are found and are increasingly recognised as responsible for the performance of complex materials [1][2][3] and many complex systems from the brain [4][5][6] to large-scale social dynamics [7,8].…”

Section: Introductionmentioning

confidence: 99%

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

Tadić

Andjelković²,

Šuvakov³

et al. 2020

Entropy

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Functional designs of nanostructured materials seek to exploit the potential of complex morphologies and disorder. In this context, the spin dynamics in disordered antiferromagnetic materials present a significant challenge due to induced geometric frustration. Here we analyse the processes of magnetisation reversal driven by an external field in generalised spin networks with higher-order connectivity and antiferromagnetic defects. Using the model in (Tadić et al. Arxiv:1912.02433), we grow nanonetworks with geometrically constrained self-assemblies of simplexes (cliques) of a given size n, and with probability p each simplex possesses a defect edge affecting its binding, leading to a tree-like pattern of defects. The Ising spins are attached to vertices and have ferromagnetic interactions, while antiferromagnetic couplings apply between pairs of spins along each defect edge. Thus, a defect edge induces n − 2 frustrated triangles per n-clique participating in a larger-scale complex. We determine several topological, entropic, and graph-theoretic measures to characterise the structures of these assemblies. Further, we show how the sizes of simplexes building the aggregates with a given pattern of defects affects the magnetisation curves, the length of the domain walls and the shape of the hysteresis loop. The hysteresis shows a sequence of plateaus of fractional magnetisation and multiscale fluctuations in the passage between them. For fully antiferromagnetic interactions, the loop splits into two parts only in mono-disperse assemblies of cliques consisting of an odd number of vertices n. At the same time, remnant magnetisation occurs when n is even, and in poly-disperse assemblies of cliques in the range n ∈ [ 2 , 10 ] . These results shed light on spin dynamics in complex nanomagnetic assemblies in which geometric frustration arises in the interplay of higher-order connectivity and antiferromagnetic interactions.

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Materials inspired by mathematics

Cited by 18 publications

References 27 publications

Looking to the future as STAM celebrates its 20th anniversary

Looking to the future as STAM celebrates its 20th anniversary

From Architectured Materials to Large-Scale Additive Manufacturing

Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques

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