Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 14: Complex Fluids
DY 14.8: Vortrag
Freitag, 4. März 2005, 17:15–17:30, TU H3010
Free Energy of a Charged Polymer in an Electrolyte — •Stephan Kramer1, Reiner Kree1, and Gert Lube2 — 1Institut f. Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen — 2Institut f. Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16-18, 37083 Göttingen
Many physical issues fit into the context of parameter identification in optimal control problems with constraints given by partial differential equations (PDE). Solving these problems is usually extremely time-consuming. One important issue to make solving such problems feasible is optimizing the discretization of the PDE constraint especially for simulations in three dimensions. This is achieved by employing goal-oriented error estimation in the mesh adaption which minimizes the error of some target functional of the PDE solution rather than the error in the solution itself.
As a sample problem we use the interactions between the electrostatic field in an aqueous solution of a charged, semi-flexible polymer and its conformation. The target quantity is the combined free energy consisting of the free energy of the charge distribution and the elastic energy of the molecular conformation. Now, the optimization process consists of finding a conformation and thus a charge distribution such that the total free energy is minimal.
Besides the good convergence behavior and the need for adaptivity especially in three dimensions our numerical results demonstrate the influence of the electrostatic potential on the relationship between the conformation and the free energy.