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Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity. 

Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity. 

ABSTRACT The fission yeastSchizosaccharomyces pombedivides via closed mitosis, meaning that spindle elongation and chromosome segregation transpire entirely within the closed nuclear envelope. Both the spindle and nuclear envelope must undergo shape changes and exert varying forces on each other during this process. Previous work has demonstrated that nuclear envelope expansion (Yam, He, Zhang, Chiam, & Oliferenko, 2011; Mori & Oliferenko, 2020) and spindle pole body (SPB) embedding in the nuclear envelope are required for normalS. pombemitosis, and mechanical modeling has described potential contributions of the spindle to nuclear morphology (Fang et al., 2020; Zhu et al., 2016). However, it is not yet fully clear how and to what extent the nuclear envelope and mitotic spindle each directly shape each other during closed mitosis. Here, we investigate this relationship by observing the behaviors of spindles and nuclei in live mitotic fission yeast following laser ablation. First, we characterize these dynamics in mitoticS. pombenuclei with increased envelope tension, finding that nuclear envelope tension can both bend the spindle and slow elongation. Next, we directly probe the mechanical connection between spindles and nuclear envelopes by ablating each structure. We demonstrate that envelope tension can be relieved by severing spindles and that spindle compression can be relieved by rupturing the envelope. We interpret our experimental data via two quantitative models that demonstrate that fission yeast spindles and nuclear envelopes are a mechanical pair that can each shape the other's morphology.