Structures currently used for energy absorption include foams, composites, and honeycombs. Recent studies have indicated the potential of triply periodic minimal surfaces (TPMS) for energy absorption applications as well as weight reduction. This study presents three TPMS lattice structures, namely the Gyroid, Fischer‐Koch S, and PMY, which are fabricated in uniform and graded densities. These structures, created in the MSLattice software are 3D printed using polylactic acid. Subsequently, the 3D‐printed structures undergo a gas foaming process to investigate benefits of higher porosity on energy absorption. The structures are then characterized for porosity, compressive properties, energy absorption, and thermal properties. The results show that the uniform and graded density structures have similar energy absorption values as long as the structures have a similar average density with the PMY structure exhibiting the highest energy absorption value, both in unfoamed and foamed conditions, respectively. The foaming process increased the porosity by 50% but did not improve the energy absorption characteristics of any of the structures with the foamed PMY structures exhibiting the least deviation compared to the unfoamed samples. These foamed TPMS structures are suitable for applications in the automotive and aerospace industry that demand lightweight structures for energy absorption.
We study two agent based models of opinion formation -one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models -notably the convergence rates -which are explored through analytical arguments and several numerical experiments.
A generic feature of bounded confidence type models is the formation of clusters of agents. We propose and study a variant of bounded confidence dynamics with the goal of inducing unconditional convergence to a consensus. The defining feature of these dynamics which we name the No one left behind dynamics is the introduction of a local control on the agents which preserves the connectivity of the interaction network. We rigorously demonstrate that these dynamics result in unconditional convergence to a consensus. The qualitative nature of our argument prevents us quantifying how fast a consensus emerges, however we present numerical evidence that sharp convergence rates would be challenging to obtain for such dynamics. Finally, we propose a relaxed version of the control. The dynamics that result maintain many of the qualitative features of the bounded confidence dynamics yet ultimately still converge to a consensus as the control still maintains connectivity of the interaction network.
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