Transition to coarsening for confined one-dimensional interfaces with bending rigidity

Transition to coarsening for confined one-dimensional interfaces with bending rigidity.

We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimensional hydrodynamic model, where membranes are effectively one-dimensional objects. In a previous work [T. Le Goff et al., Phys. Rev. E 90, 032114 (2014)], we ha...

Marked length rigidity for one dimensional spaces

In a compact geodesic metric space of topological dimension one, the minimal length of a loop in a free homotopy class is well-defined, and provides a function l : π1(X) −→ R+ ∪ ∞ (the value ∞ being assigned to loops which are not freely homotopic to any rectifiable loops). This function is the marked length spectrum. We introduce a subset Conv(X), which is the union of all non-constant minimal...

On Rigidity of One-Dimensional Maps

The regularity of the conjugacy between two onedimensional maps with singular points is considered. We prove that the conjugacy between two nice and mixing quasi-hyperbolic one-dimensional maps is a diffeomorphism if it is an absolutely continuous homeomorphism and the exponents and the asymmetries of these two maps at all corresponding singular points are the same. We also discuss the applicat...

Transition to chaos in a confined two-dimensional fluid flow.

For a two-dimensional fluid in a square domain with no-slip walls, new direct numerical simulations reveal that the transition from steady to chaotic flow occurs through a sequence of various periodic and quasiperiodic flows, similar to the well-known Ruelle-Takens-Newhouse scenario. For all solutions beyond the ground state, the phenomenology is dominated by a domain-filling circulation cell, ...

A one dimensional nearest neighbor model of coarsening