We present Bistable Auxetic Surface Structures , a novel deployable material system based on optimized bistable auxetic cells. Such structure can be flat-fabricated from elastic sheet material, then deployed towards desired double-curved target shape by activating the mechanism of its component A unique feature is that model design in stable state. This facilitates deployment without need compl...

A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. [Phys. Rev. Lett. 112, 038101 (2014)]. They have computed the mean switching time for such a system using a continuous Fokker-Planck equation derived from the Taylor expansion of the master equation to estimate the parameter of such a system from experiment. In this article, we provide t...

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODE’s) for the dynamics of the governing advection–reaction–diffusion partial differential equation (PDE), for pulse-like and for plateau-like solutions, based on a nonperturbative approach. This reduction allow...

We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analyti...

We study reaction-diffusion equations in one spatial dimension and with general (spaceor time-) inhomogeneous mixed bistable-ignition reactions. For those satisfying a simple quantitative hypothesis, we prove existence and uniqueness of transition fronts, as well as convergence of “typical” solutions to the unique transition front (the existence part even extends to mixed bistable-ignition-mono...