# On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph

@inproceedings{Ettehad2021OnTS, title={On the Spectra of Periodic Elastic Beam Lattices: Single-Layer Graph}, author={Mahmood Ettehad and Burak Hat.inouglu}, year={2021} }

We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued self-adjoint operator, which is also known as the fourth order Schrödinger operator, equipped with a real periodic symmetric potential. In contrast to the second order Schrödinger operator commonly applied in quantum graph literature, here vertex matching conditions encode geometry of the underlying…

## 3 Citations

### On Vertex Conditions In Elastic Beam Frames: Analysis on Compact Graphs

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- 2021

We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which…

### Three‐dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

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We consider three‐dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The…

### Topics on Fermi varieties of discrete periodic Schrödinger operators

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This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schrödinger operators.

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