# Mechanical Properties of Warped Membranes

 Title: Mechanical Properties of Warped Membranes Author: Kosmrlj, Andrej; Nelson, David R. Note: Order does not necessarily reflect citation order of authors. Citation: Kosmrlj, Andrej, and David R. Nelson. 2013. "Mechanical Properties of Warped Membranes." Physical Review E 88 (1): 012136. Full Text & Related Files: 1306.5941v1.pdf (882.9Kb; PDF) Abstract: We explore how a frozen background metric affects the mechanical properties of planar membranes with a shear modulus. We focus on a special class of “warped membranes” with a preferred random height profile characterized by random Gaussian variables h(q) in Fourier space with zero mean and variance $$⟨| h(q)|^2〉\sim q^{−d_h}$$ and show that in the linear response regime the mechanical properties depend dramatically on the system size L for $$d_h\geq 2$$. Membranes with $$d_h=4$$ could be produced by flash polymerization of lyotropic smectic liquid crystals. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases as $$\kappa R\sim L^{(d_h−2)/2}$$ for membranes of size L, while the Young and shear moduli decrease according to $$Y_R,\mu R \sim L^{−(d_h−2)/2}$$ resulting in a universal Poisson ratio. Numerical results show good agreement with analytically determined exponents. Published Version: doi:10.1103/PhysRevE.88.012136 Other Sources: http://arxiv.org/pdf/1306.5941v1.pdf Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:13457880 Downloads of this work: