Dynamical scaling of polymerized membranes

Self-avoiding Polymerized Membranes

Recent progresses in the understanding of the scaling behavior of self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed (joint works with B. Duplantier and E. Guitter, and with K. Wiese). They rely on a new general renormalization group approach for a class of models with non-local singular interactions. This approach allows to prove the existence of a ǫ-expansion for t...

Thermodynamical behavior of polymerized membranes

Scaling relations in dynamical evolution of star clusters

We have carried out a series of small scale collisional N-body calculations of single-mass star clusters to investigate the dependence of the lifetime of star clusters on their initial parameters. Our models move through an external galaxy potential with a logarithmic density profile and they are limited by a cut-off radius. In order to find scaling relations between the lifetime of star cluste...

Anisotropic and Heterogeneous Polymerized Membranes

In these lectures I describe long scale properties of fluctuating polymerized membranes in the presence of network anisotropy and random heterogeneities. Amazingly, even infinitesimal amount of these seemingly innocuous but physically important ingredients in the membrane’s internal structure leads to a wealth of striking qualitatively new phenomena. Anisotropy leads to a “tubule” phase that is...

Self-consistent theory of polymerized membranes.

We study D-dimensional polymerized membranes embedded in d dimensions using a selfconsistent screening approximation. It is exact for large d to order 1/d, for any d to order ǫ = 4−D and for d = D. For flat physical membranes (D = 2, d = 3) it predicts a roughness exponent ζ = 0.590. For phantom membranes at the crumpling transition the size exponent is ν = 0.732. It yields identical lower crit...