Hello @Windy_Skies , I see you are interested about Kagome lattice within Dave’s topic title.
I don’t know enough about this subject, although certain connections with these publications seem obvious, for example concerning triangles and their beginnings in realization, as well as the text itself.
Maybe this is an opportunity to reinstate Dave. Indeed:“Suspension can be appealed after completing an academic writing course”. The mentioned references in his text reproduced below could be assimilated to academic sources, and the connections between the text and the references look to show some level of coherence, and could lead to later academic publications about the topic Dave is raising.
And in a field as complex and fragile as AWE research where the results can be not quite apparent, we cannot afford the luxury of closing a path, here for a kite network generation methodology, even if it seems narrow.
Now the task of moderation can be a difficult, if not impossible, task. Perhaps, if you intend to reinstate Dave, you could somehow try to contract with him (or vice versa) on what he can edit, if of course this does not give rise to oppositions.
Dave Santos’ text:
" Kite Networks is a disruptive paradigm in AWE, with periodic topological ordering under many-unit metamaterial dynamics as the governing mathematics, subsuming classical equations of motion at unit and meta-unit scale. This post reviews static kite network order, with dynamical energy harvesting by Spin-Network physics as the follow-on subject for another post. Attached slides provide a panoramic view of the ideas. Two papers linked relate state-of-the-art metamaterial molecular science to kite metamaterial concepts, under scale-invariance.
While Classic Kites take countless fantastic forms, highly effective most-common forms are primitive geometric shapes like circles, triangles, and rectangles. These unit primitives are traditionally periodically-ordered into various basic network topologies of kite trains, arches, and meshes. Modern empirical and heuristic kite network rigging emerges from Bell’s Cellular Kites of triangular fabric cells, which led to fully soft “Rogallo Lattices”.
Remarkably, these same basic topological orders hold across multiple engineering scales, from molecular polymer scale to scales of twisting, weaving, and braiding of polymer fibers into kite lines and fabrics, and ultimately to overall rigging design of GW-class kite networks. As Metamaterial engineering science flourishes, the AWE paradigm of energy-harvesting “KiteMatter” is co-evolving within the broader conceptual framework.
A particularly iconic topological motif is the Kagome Lattice, a triangular pattern basic to graphene and to current state-of-the-art kite network concepts (SpiderMill). Ongoing design refinement converges rather exactly with molecular models like “Kagome Lattice in Low-Angle Twisted Bilayer Graphene”.
“Overlaying two graphene layers with a small twist angle 𝜃 can create a moiré superlattice to realize exotic phenomena that are entirely absent in a graphene monolayer.”
“…an artificial kagome potential to generate and control multiple Dirac bands of graphene…unique high-order potential…natural multiperiodic components, enabling…band structures through different potential contributions…band components, each characterized by distinct dispersions, shift in energy at different velocities in response to the variation of artificial potential…significant spectral weight redistribution of the multiple Dirac peaks.”
Multiple GPTs affirm the basic soundness of the analogies being drawn and concur on the vast potential.
Attached are selected kite network diagrams showing emergence of bilayer kagome ordering over the last century of kite science.