Thema der Dissertation:
Surface waves, 2D percolation-network elasticity, and tensorial molecular diffusion
Surface waves, 2D percolation-network elasticity, and tensorial molecular diffusion
Abstract: The level of complexity encountered in biological systems often demands the introduction of generalizations and refinements of classical physical models. Spanning a wide range of length scales, we study a few different biologically relevant systems, namely the molecular diffusion of water, the elasticity of the basement membrane, and surface waves on viscoelastic interfaces surrounded by viscoelastic media, where generalizations to existing theoretical models are introduced systematically.
Using molecular dynamics simulations, we study the self-diffusion of water in the laboratory frame as well as in the anisotropic molecular frame via calculations of the water viscosity and the translational and rotational diffusion coefficients. Instead of interpreting the results as deviations from the Stokes-Einstein(-Debye) relations, we describe the diffusivities of water molecules by three models of increasing complexity. We discuss successes and limitations of stick sphere and stick ellipsoid models, and finally show that a heuristic spherical model with tensorial slip lengths and hydrodynamic radii simultaneously describes the isotropic translational and rotational diffusivities in the laboratory frame, as well as, in a restricted viscosity range, the anisotropic molecular-frame diffusivities.
We present a coarse-grained elastic model of the laminin network of the basement membrane to simulate the modulation of the elasticity of the basement membrane under influence of netrin-4, and apply our model to longitudinal and transversal deformation scenarios of the basement membrane. We show that the laminin network with defects due to the presence of netrin-4 has a nonlinear stress-strain relationship, and we further extract from our simulations the relevant elastic parameters. To compare with experiments, we develop a method to associate extracted model parameters with measured elastic moduli of bulk samples, and show that our model yields good agreement with experimental data.
We derive the general dispersion relation for interfacial waves along a planar viscoelastic boundary that separates two viscoelastic bulk media, which unifies and generalizes existing results for surface waves, such as Rayleigh waves, capillary-gravity-flexural waves, Lucassen waves, bending waves in elastic plates, and the standard dispersion-free sound waves. We apply our general theory to study interfacial waves at water-water and air-water interfaces, as well as at interfaces of viscoelastic Kelvin-Voigt and Maxwell media. In all scenarios, we study how material properties determine the crossovers, scaling, and existence regimes of the various interfacial waves.
Using molecular dynamics simulations, we study the self-diffusion of water in the laboratory frame as well as in the anisotropic molecular frame via calculations of the water viscosity and the translational and rotational diffusion coefficients. Instead of interpreting the results as deviations from the Stokes-Einstein(-Debye) relations, we describe the diffusivities of water molecules by three models of increasing complexity. We discuss successes and limitations of stick sphere and stick ellipsoid models, and finally show that a heuristic spherical model with tensorial slip lengths and hydrodynamic radii simultaneously describes the isotropic translational and rotational diffusivities in the laboratory frame, as well as, in a restricted viscosity range, the anisotropic molecular-frame diffusivities.
We present a coarse-grained elastic model of the laminin network of the basement membrane to simulate the modulation of the elasticity of the basement membrane under influence of netrin-4, and apply our model to longitudinal and transversal deformation scenarios of the basement membrane. We show that the laminin network with defects due to the presence of netrin-4 has a nonlinear stress-strain relationship, and we further extract from our simulations the relevant elastic parameters. To compare with experiments, we develop a method to associate extracted model parameters with measured elastic moduli of bulk samples, and show that our model yields good agreement with experimental data.
We derive the general dispersion relation for interfacial waves along a planar viscoelastic boundary that separates two viscoelastic bulk media, which unifies and generalizes existing results for surface waves, such as Rayleigh waves, capillary-gravity-flexural waves, Lucassen waves, bending waves in elastic plates, and the standard dispersion-free sound waves. We apply our general theory to study interfacial waves at water-water and air-water interfaces, as well as at interfaces of viscoelastic Kelvin-Voigt and Maxwell media. In all scenarios, we study how material properties determine the crossovers, scaling, and existence regimes of the various interfacial waves.
Zeit & Ort
19.01.2026 | 16:00
Hörsaal B (0.1.01)
(Fachbereich Physik, Arnimallee 14, 14195 Berlin)