Cylinder morphology of a stretched and twisted ribbon

A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a transverse instability of the helicoid. Here, we propose a simple description for this cylindrical shape. By comparing its energy to the energy of other configurations, we are able to determine its location on the phase diagram. The theoretical predictions are in good agreement with our experimental results

A new stability results for the backward heat equation

In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1).Comment: 13 page