Validation of EDQNM for subgrid and supergrid models

From preliminary calculations it was concluded that the two-point Eddy Damping Quasi-Normal Markovian (EDQNM) closure accurately describes the behavior of second order moments. This closure can be applied as subgrid and supergrid models for Large Eddy Simulations at higher Reynolds numbers. In the case of homogeneous anisotropic turbulence, when the nonlinear terms are introduced the calculation becomes quite onerous but is still considerably less expensive than the calculation of a DS. The major merit of two-point closure models is that they can be easily applied to flows at Reynolds numbers that are unreachable by a DS. Work is in progress to derive expressions for the nonlinear terms that give good global conservation properties

Quantum Harmonic Black Holes

Inspired by the recent conjecture that black holes are condensates of gravitons, we investigate a simple model for the black hole degrees of freedom that is consistent both from the point of view of Quantum mechanics and of General Relativity. Since the two perspectives should "converge" into a unified picture for small, Planck size, objects, we expect our construction is a useful step for understanding the physics of microscopic, quantum black holes. In particular, we show that a harmonically trapped condensate gives rise to two horizons, whereas the extremal case (corresponding to a remnant with vanishing Hawking temperature) naturally falls out of its spectrum.Comment: 7 pages, no figures. Clarifications and comments adde

Continuous interfaces with disorder: Even strong pinning is too weak in 2 dimensions

We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta-pinning at height zero. There is a detailed mathematical understanding of the depinning transition in 2 dimensions without disorder. Then the variance of the interface height w.r.t. the Gibbs measure stays bounded uniformly in the volume for any positive pinning force and diverges like the logarithm of the pinning force when it tends to zero. How does the presence of a quenched disorder term in the Hamiltonian modify this transition? We show that an arbitarily weak random field term is enough to beat an arbitrarily strong delta-pinning in 2 dimensions and will cause delocalization. The proof is based on a rigorous lower bound for the overlap between local magnetizations and random fields in finite volume. In 2 dimensions it implies growth faster than the volume which is a contradiction to localization. We also derive a simple complementary inequality which shows that in higher dimensions the fraction of pinned sites converges to one when the pinning force tends to infinity.Comment: 8 page

A simple fluctuation lower bound for a disordered massless random continuous spin model in d=2

We prove a finite volume lower bound of the order of the squareroot of log N on the delocalization of a disordered continuous spin model (resp. effective interface model) in d = 2 in a box of size N . The interaction is assumed to be massless, possibly anharmonic and dominated from above by a Gaussian. Disorder is entering via a linear source term. For this model delocalization with the same rate is proved to take place already without disorder. We provide a bound which is uniform in the configuration of the disorder, and so our proof shows that randomness will only enhance fluctuations