Anomalous elasticity, fluctuations and disorder in elastic membranes

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

Figures from this paper

Thermal ripples in bilayer graphene

We study thermal fluctuations of a free-standing bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum

Thermal Buckling Transition of Crystalline Membranes in a Field.

Through a detailed analysis, it is shown that the transition of two-dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant, e.g., for graphene, is in a new universality class.

Thermalized buckling of isotropically compressed thin sheets

The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations

Thermal buckling transition of crystalline membranes

Two dimensional crystalline membranes in isotropic embedding space exhibit a flat phase with anomalous elasticity, relevant e.g., for graphene. Here we study their thermal fluctuations in the absence

Statistical Mechanics of Freely Fluctuating Two-Dimensional Elastic Crystals

In this paper, some facts related Joel L. Lebowitz are mentioned. In addition, some of the known theory concerning the statistical physics of freely fluctuating two-dimensional crystals subject to a

Spontaneous Tilt of Single-Clamped Thermal Elastic Sheets.

Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here, we use

Geometrically induced localization of flexural waves on thin warped physical membranes.

This work considers the propagation of flexural waves across a nearly flat, thin membrane, whose stress-free state is curved, and shows that at long times and lengths, the undulation intensity obeys a diffusion equation.

Perturbative renormalization and thermodynamics of quantum crystalline membranes

We analyze the statistical mechanics of a free-standing quantum crystalline membrane within the framework of a systematic perturbative renormalization group (RG). A power-counting analysis shows that



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

  • D. Gazit
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
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
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

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
Computer simulation of buckled defects confirms predictions of the disclination energies and gives evidence for a finite dislocation energy.