Applied Math Seminar

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Topological floppy modes in aperiodic networks and a mechanical duality theorem

Speaker: Xiaoming Mao, University of Michigan

Location: TBA

Date: Friday, December 4, 2020, 3:55 p.m.

Synopsis:

Topological states of matter have been intensively studied in crystals, leading to fascinating phenomena such as scattering-free edge current in topological insulators. However, the power of topological protection goes well beyond ordered crystal lattices. In this talk we explore how topology protects mechanical edge modes in messy, noncrystalline, systems. We will use disordered fiber networks and quasicrystals as our examples, to demonstrate how topological edge floppy modes can be induced in these structures by controlling their geometry. Fiber networks are ubiquitous in nature and especially important in bio-related materials. Establishing topological mechanics in fiber networks may shed light on understanding robust processes in mechanobiology. Quasicrystals show unusual orientational order with quasiperiodic translational order. We found that a bulk topological polarization can be defined for mechanics of quasicrystals that is unique to their non-crystallographic orientational symmetry.

 

References: (1) Di Zhou, Leyou Zhang, Xiaoming Mao, "Topological Edge Floppy Modes in Disordered Fiber Networks", Phys. Rev. Lett. 120, 068003 (2018); (2) Di Zhou, Leyou Zhang, Xiaoming Mao, "Topological Boundary Floppy Modes in Quasicrystals", Phys. Rev. X 9, 021054 (2019).  

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