Seminar über Theorie der Kondensierten Materie/ Weiche Materie und Statistische Physik

Accurate molecular simulation requires computationally expensive quantum chemistry models that makes simulating complex material phenomena or large molecules intractable. The past decade has seen a revival of interatomic potentials (IPs), fast but traditionally inaccurate surrogate models, re-casting their construction as an approximation and data-fitting problem. I will give an introduction to this problem, from a mixed modelling / data / mathematics perspective. In particular I want to show how it can be formalised as a high-dimensional approximation problem, with many structures that can be exploited to make it tractable. I will introduce two approximation schemes, both using different symmetric polynomials, targeting in particular efficiency and transferability, some preliminary simulation results, and the beginnings of a rigorous numerical analysis. Joint work with Geneviève Dusson (CNRS Besançon), Markus Bachmayr (Mainz), Gabor Csanyi and Cas van der Oord (Cambridge), Simon Etter (NU Singapur).

I will present the practical construction of interatomic potentials for materials and molecules based on a body-order expansion (ANOVA, HDRM), each body order being represented by polynomials satisfying the rotation and permutation symmetry of the "exact" potential energy surface. These polynomials are determined in a data-driven fashion from linear fits trained with ab initio data. I will report convergence tests on training sets for materials and molecules, illustrating the accuracy, the low computational cost, and the systematic improvability of the potential. I will then outline a range of the regularisation procedures that we incorporate into the polynomial fits to achieve transferability of the potentials. Finally, I will outline a testing framework to stress-test the generalisation capabilities of new potentials far from the training set. Joint work with Alice Allen (Cambridge), Gbor Csnyi (Cambridge), Christoph Ortner (Warwick), and Cas van der Oord (Cambridge).

Phosphatidylcholine (PC) lipids complexed with hyaluronan (HA) have been proposed to form strongly lubricating boundary layers at biosurfaces such as articular cartilage. Depending on the type of PC used, efficient lubrication with friction coefficients down to 10-4 under physiologically high pressures (~100 atm) have been observed. This was attributed to hydration lubrication, acting at the highly hydrated phosphocholine headgroups of the PC lipids, exposed at the liposome surfaces. Such hydration layers can sustain large compressions without water molecules being squeezed out from the gap between sliding surfaces. At the same time, the hydration shells can relax rapidly, ensuring a fluid like response under applied shear. This combination of low shear stresses while sliding under high normal stresses results in very low friction coefficients, an effect termed hydration lubrication. We use the surface force balance (SFB) to examine interactions between polymer layers, in particular how normal interactions and especially frictional interactions, are modified when PC liposomes are added surface in pure water and in aqueous salt solutions, mimicking the presence of macromolecules on the surface of cartilage.