We perform a systematic study of the characteristics of shear transformation zones (STZs) that nucleate at free surfaces of two-dimensional amorphous solids subject to tensile loading using two different atomistic simulation methods, the standard athermal, quasistatic (AQ) approach and our recently developed self-learning metabasin escape (SLME) method, to account for the finite temperature and...

For general non-linear parametrized partial differential equations (PDEs), the standard Galerkin projection is no longer efficient to generate reduced-order models. This is because the evaluation of the integrals involving the non-linear terms has a high computational complexity and cannot be pre-computed. This situation also occurs for linear equations when the parametric dependence is nonaffi...

We present reduced basis approximations and associated a posteriori error bounds for nonaffine linear time-varying parabolic partial differential equations. We employ the Empirical Interpolation Method in order to construct “affine” coefficient-function approximations of the “nonaffine” parametrized functions. To this end, we extend previous work on time-invariant functions to time-varying func...

We propose a terminal sliding mode control (SMC) law based on adaptive fuzzy-neural observer for nonaffine nonlinear uncertain system. First, a novel nonaffine nonlinear approximation algorithm is proposed for observer and controller design. Then, an adaptive fuzzy-neural observer is introduced to identify the simplified model and resolve the problem of the unavailability of the state variables...

The mechanical response of solids depends on temperature, because the way atoms and molecules respond collectively to deformation is affected at various levels by thermal motion. This is a fundamental problem of solid state science and plays a crucial role in materials science. In glasses, the vanishing of shear rigidity upon increasing temperature is the reverse process of the glass transition...