Fine-scale substructure 65L20 Ensemble forecasts Two-scale convergence Vlasov equation Modal analysis Highly oscillatory problems Adjoint model Cardiac electrophysiology Eikonal equation Navier-Stokes Equations Chapman-Enskog expansion Density matrix Error estimate Ensemble forecasting Homogenization Boundary layer Conservation laws Numerical simulations Reaction-diffusion system Numerical range DATA ASSIMILATION Global existence Scattering Uncertainty quantification Vlasov-Poisson equation Conduction Degenerate parabolic equations Concrete Large eddy simulation Regularity Helmholtz decomposition Asymptotic Analysis Diffusion limit Turbulence Averaging Stroboscopic averaging Fractured porous media Finite elements Porous media Nonlinear Schrödinger equation Interaction fluide-structure FOS Mathematics Fluid mechanics Schrödinger equation Fluid-structure interaction Binary alloys Entropy Highly-oscillatory B-series Kinetic equations Maximum principle Finite Element Method Asymptotic analysis Navier-Stokes equations Invariant measure Controllability Convergence Finite element method Optimal control Timoshenko beam Diffusion Stability Optimization Markov chain Uniform accuracy Shape optimization Asymptotic preserving schemes Data assimilation Long-time behavior Dislocation dynamics PIV MPCC Existence Level-set approach Spectral set Robust optimization BGK equation Micro-macro decomposition Backward error analysis Turbulence models Oceanography Dynamical system Subdivision Numerical simulation Reaction-diffusion Deconvolution models Lower-bound gradient estimate Population dynamics $L^1-$dependence in time Stochastic partial differential equations Robust control Formal series White noise Viscosity solutions Hamilton-Jacobi equations Asymptotic behavior Nonlocal front propagation Nonlocal Hamilton-Jacobi Equations Elasticity