0000000000427630
AUTHOR
Herbert Egger
Adjoint-based sampling methods for electromagnetic scattering
In this paper we investigate the efficient realization of sampling methods based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of the Green's function for the background medium, and allows us to sample for all points and all dipole directions simultaneously; thus, several limitations of standard sampling methods are relieved. A detailed derivation of the adjoint approach is presented for two electromagnetic model problems, but the framework can be applied to a much wider class of problems. We also discuss a relation of the adjoint sampling method to standard backprojection algorithms, and present numerical tests that illustrate the e…
Systematic derivation of hydrodynamic equations for viscoelastic phase separation
(abridged) We present a detailed derivation of a simple hydrodynamic two-fluid model, which aims at the description of the phase separation of non-entangled polymer solutions, where viscoelastic effects play a role. It is directly based upon the coarse-graining of a well-defined molecular model, such that all degrees of freedom have a clear and unambiguous molecular interpretation. The considerations are based upon a free-energy functional, and the dynamics is split into a conservative and a dissipative part, where the latter satisfies the Onsager relations and the Second Law of thermodynamics. The model is therefore fully consistent with both equilibrium and non-equilibrium thermodynamics.…
Analysis of a viscoelastic phase separation model
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent with the second law of thermodynamics, and we study well-posedness of the model, i.e., existence of weak solutions, a weak-strong uniqueness principle, and stability with respect to perturbations, which are proven by means of relative energy estimates. A good qualitative agreement with mesoscopic simulations is observed in numerical tests.