@article{17462,
  abstract     = {We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale l in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a box of diameter L >>l around the support of the charge. We show that the algorithm in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint, arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With overwhelming probability, we obtain a convergence rate in terms of l, L, and the size of the correlations for which optimality is supported with numerical simulations. These estimates are provided for ensembles which satisfy a multiscale logarithmic Sobolev inequality, where our main tool is an extension of the semigroup estimates in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378]. As part of our strategy, we construct sublinear second-order correctors in this correlated setting, which is of independent interest.},
  author       = {Clozeau, Nicolas and Wang, Lihan},
  issn         = {1540-3467},
  journal      = {Multiscale Modeling and Simulation},
  number       = {3},
  pages        = {973--1029},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Artificial boundary conditions for random elliptic systems with correlated coefficient field}},
  doi          = {10.1137/23M1603819},
  volume       = {22},
  year         = {2024},
}

@article{6762,
  abstract     = {We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first step: convert light (photons) into electronic excitations. We formulate various desirable properties of the excitations as mathematical control goals at the Kohn-Sham-DFT level
of theory, with the control being given by the nuclear charge distribution. We prove that nuclear distributions exist which give rise to optimal HOMO-LUMO excitations, and present illustrative numerical simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features such as large electron-hole separation, and a hierarchy of length scales: internal HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the doping profiles < system size.},
  author       = {Friesecke, Gero and Kniely, Michael},
  issn         = {1540-3467},
  journal      = {Multiscale Modeling and Simulation},
  number       = {3},
  pages        = {926--947},
  publisher    = {SIAM},
  title        = {{New optimal control problems in density functional theory motivated by photovoltaics}},
  doi          = {10.1137/18M1207272},
  volume       = {17},
  year         = {2019},
}