https://www.selleckchem.com/products/sirpiglenastat.html We study periodic arrays of impurities that create localized regions of expansion, embedded in two-dimensional crystalline membranes. These arrays provide a simple elastic model of shape memory. As the size of each dilational impurity increases (or the relative cost of bending to stretching decreases), it becomes energetically favorable for each of the M impurities to buckle up or down into the third dimension, thus allowing for of order 2^M metastable surface configurations corresponding to different impurity "spin" configurations. With both discrete simulations and the nonlinear continuum theory of elastic plates, we explore the buckling of both isolated dilations and dilation arrays at zero temperature, guided by analogies with Ising antiferromagnets. We conjecture ground states for systems with triangular and square impurity superlattices, and comment briefly on the possible behaviors at finite temperatures.The phenomenology of Landau theory with spatial coupling through diffusion has been widely used in the study of phase transitions and patterning. Here we follow this theory and apply it to study theoretically and numerically continuous and discontinuous transitions to periodic spatial cellular patterns driven by lateral inhibition coupling. As opposed to diffusion, lateral inhibition coupling drives differences between adjacent cells. We analyze the appearance of errors in these patterns (disordered metastable states) and propose mechanisms to prevent them. These mechanisms are based on a temporal-dependent lateral inhibition coupling strength, which can be mediated, among others, by gradients of diffusing molecules. The simplicity and generality of the framework used herein is expected to facilitate future analyses of additional phenomena taking place through lateral inhibition interactions in more complex scenarios.We study dynamical signatures of quantum chaos in one of the most relevant models in ma