Anomalous elasticity, fluctuations and disorder in elastic membranes

@article{Doussal2017AnomalousEF,
  title={Anomalous elasticity, fluctuations and disorder in elastic membranes},
  author={Pierre Le Doussal and Leo Radzihovsky},
  journal={arXiv: Soft Condensed Matter},
  year={2017}
}

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References

SHOWING 1-10 OF 109 REFERENCES

Structure of physical crystalline membranes within the self-consistent screening approximation.

  • D. Gazit
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
TLDR
The anomalous exponents governing the long-wavelength behavior of the flat phase of physical crystalline membranes are calculated within a self-consistent screening approximation (SCSA) applied to second order expansion in 1/dC, and the prediction of SCSA applied to first order expansion for the Poisson ratio is shown to be exact to all orders.

Rippling and crumpling in disordered free-standing graphene

Graphene is a famous realization of elastic crystalline 2D membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range order in the system. Such fluctuations are stabilized by

Fluctuations and lower critical dimensions of crystalline membranes

We study flexible D-dimensional fixed-connectivity crystalline membranes fluctuating in a d-dimensional embedding space. We address both the crumpling transition and fluctuations around the flat

The Flat Phase of Crystalline Membranes

We present the results of a high-statistics Monte Carlo simulation of a phantorn crystalline (fixed-connectivity) membrane with free boundary. We verify trie existence of a fiai phase by exarnining

Anomalous Hooke’s law in disordered graphene

The discovery of graphene, a single monolayer of graphite, has provided an experimental demonstration of stability of 2D crystals. Although thermal fluctuations of such crystals tend to destroy the

Curvature disorder in tethered membranes: A new flat phase at T=0.

  • MorseLubensky
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
TLDR
The presence of random spontaneous curvature is found to stiffen the long-wavelength bending rigidity, giving rise at temperature T=0 to a disordered flat phase associated with a new fixed point of the renormalization group.

Elasticity, shape fluctuations, and phase transitions in the new tubule phase of anisotropic tethered membranes

We study the shape, elasticity, and fluctuations of the recently predicted [L. Radzihovsky and J. Toner, Phys. Rev. Lett. 75, 4752 (1995)] and subsequently observed (in numerical simulations) [M.

Thermal crumpling of perforated two-dimensional sheets

TLDR
A mechanism to tune the onset of the crumpling transition by altering the geometry and topology of the sheet itself by simply altering their geometries is proposed.

Defects in flexible membranes with crystalline order.

  • SeungNelson
  • Materials Science
    Physical review. A, General physics
  • 1988
TLDR
Computer simulation of buckled defects confirms predictions of the disclination energies and gives evidence for a finite dislocation energy.
...