Statistical mechanics of membranes and surfaces

  title={Statistical mechanics of membranes and surfaces},
  author={David R. Nelson and Tsvi Piran and Steven Weinberg},
The Statistical Mechanics of Membranes and Interfaces (D Nelson) Interfaces: Fluctuations, Interactions and Related Transitions (M E Fisher) Equilibrium Statistical Mechanics of Fluctuating Films and Membranes (S Leibler) The Physics of Microemulsions and Amphiphilic Monolayers (D Andelman) Properties of Tethered Surfaces (Y Kantor) Theory of the Crumpling Transition (D Nelson) Geometry and Field Theory of Random Surfaces and Membranes (F David) Statistical Mechanics of Self-Avoiding Crumpled… 

Thermal Fluctuations in Fluid Membranes 8.334 Final Project

A brief review of mean field theory and differential geometry concepts to introduce models for (fluid) elastic membranes and their fluctuations from nearly-flat or curved zero-temperature

Statistical mechanics of bilayer membrane with a fixed projected area.

The equilibrium and fluctuation methods for determining the surface tension, sigma, and bending modulus, kappa, of a bilayer membrane with a fixed projected area are discussed. In the fluctuation

Shapes of hydrophobic thick membranes

The binding/unbinding transition of a membrane to a wall that serves to shield the membrane from the solvent is discussed and spontaneous symmetry breaking with the membrane folding along a preferential axis is demonstrated.

Dynamics of vesicle self-assembly and dissolution.

Hydrodynamic interactions are found to speed up the dynamics in both fluid membranes with bending energy and with boundaries-line tension, and makes vesicle more spherical in the membrane-closure process.

Mechanics of Fluctuating Elastic Plates and Fiber Networks

Lipid membranes and fiber networks in biological systems perform important mechanical functions at the cellular and tissue levels. In this thesis I delve into two detailed problems -thermal

Mechanical properties of warped membranes.

  • A. KošmrljD. Nelson
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
This work focuses 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 and finds that in the linear response regime the mechanical properties depend dramatically on the system size L for d(h)≥2.

Structure, dynamics, and phase transitions of tethered membranes: a Monte Carlo simulation study.

A systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions of a coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination is presented.

Thermal fluctuations of vesicles and nonlinear curvature elasticity--implications for size-dependent renormalized bending rigidity and vesicle size distribution.

The statistical mechanics of closed membranes (vesicles) incorporating both constitutive and geometrical nonlinearities are discussed and results for the renormalized bending rigidity of small vesicles are derived and it is shown that significant stiffening may occur for sub-20 nm vesicle sizes.

A continuous mechanobiological model of lateral inhomogeneous biological surfaces

Thin elastic surfaces containing molecules influencing the mechanical properties of the surface itself are wide spreaded structures of dierent scales in biological systems. Prominent examples are