We study the one-dimensional asymmetric simple exclusion process on lattice $\{1, \dots,N\}$ with creation/annihilation at boundaries. The boundary rates are time dependent and change a slow scale $N^{-a}$ $a>0$. prove that $N^{1+a}$ system evolves quasi-statically macroscopic density profile given by entropy solution of stationary Burgers equation densities changing in time, determined corresp...

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during propagation. As such, study deformations is key to rationalize effective failure properties micro-structured solids interfaces. Yet, impact localized dissipation in finite region behind front, called process zone, has ...