Polymeric materials display distinguished characteristics which stem from the interplay of
phenomena at various length and time scales. Further development of polymer systems …

The most difficult computational problems nowadays are those of higher dimensions. This
research monograph offers an introduction to tensor numerical methods designed for the …

Abstract Machine-learned interatomic potentials (MLIPs) are typically trained on datasets
that encompass a restricted subset of possible input structures, which presents a potential …

Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …

Machine-learned interatomic potentials (MLIPs) and force fields (ie, interaction laws for
atoms and molecules) are typically trained on limited data-sets that cover only a very small …

The quasicontinuum (QC) method coarse-grains crystalline atomic ensembles in order to
bridge the scales from individual atoms to the micro-and mesoscales. A crucial cornerstone …

Rock is geometrically and mechanically multiscale in nature, and the traditional
phenomenological laws at the macroscale cannot render a quantitative relationship …

We develop and analyze a framework for consistent QM/MM (quantum/classic) hybrid
models of crystalline defects, which admits general atomistic interactions including …

We develop a rigorous framework for modeling the geometry equilibration of crystalline
defects. We formulate the equilibration of crystal defects as a variational problem on a …

We present an efficient a posteriori error control strategy for an energy-based concurrent
multiscale method with sharp interface in molecular mechanics, namely the geometric …