Dynamic self-organization and collective propulsion of active particles
One of the brilliant illustrations of swimming mechanics in microworld (bacteria, living cells) is the scallop theorem by Ed. Purcell (Purcell, spektrumdirekt). This theorem states that a rigid scallop possessing a single hinge would not be able to swim at zero Reynolds number. This statement follows immediately from the time reversibility of motion governed by the Stokes equation. Thus, the propulsion at low Reynolds number is only possible due to geometrical asymmetry of the swimming strokes: the power stroke must dissipate less energy on friction than the recovery stroke. It appears, however, that the motion asymmetry does not have to be a property of a single microswimmer but can be imposed by the presence of other species. For example, a pair of single-hinge scalops can propel themselves if they move accordingly head to tail!
The project will include simple analytical calculations of hydrodynamic interactions between the scallops and computer simulations using the ESPResSo package to predict the collective propulsion efficiency of ensembles of microscallops. Basic knowledge of fluid mechanics and Unix/Linux will be required.
Forces acting between metal surfaces and polymers are of extreme technical importance. For instance in the automotive industry body components are nowadays glued by adhesives, which causes a clear stiffening of the assembly seam. In this project we want to calculate these forces for polymers of practical relevance, using molecular dynamics. Atomic accuracy is necessary to correctly describe the relevant forces. For modeling, the description of image charge effects, caused by the metalsurface is important. Within the framework of the project, these effects shall be implemented in already existing molecular dynamic programs. Afterwards adhesion of different polymers to metal surfaces is investigated. Therefore, the polymer is adsorbed at the surface and subsequently desorbed by a controlled constraining force. The desorption force necessary to due so is measured. Afterwards industrial applications shall be reffered to.
Prerequisites: Strong interest in polymer physics and statistical physics and motivation to investigate physical problems by numerical simualtions. Basic knowledge of a programming language (Fortran, C/C++) is helpful.
Take any wire or string around you, for example, a thin rubber tube or a shoelace. Twist your string several times keeping the two ends apart, then you will feel a buildup of tension in the string. When the ends are brought together without being untwisted, you will observe that the string buckles and winds around itself, just like a snarling of telephone cords.
This exact mechanism is in fact used in biological cell machinery. The interwound structure of a DNA filament is called "plectonemic supercoiling" (J. F. Marko and E. D. Siggia, Phys. Rev. E 52, 2912 (1995)). Negative DNA supercoiling is essential in vivo to compact genome, to relieve torsional strain during replication, and to promote local melting for vital processes such as transcript initiation by RNA polymerase. Coupling between elasticity, topology, viscous hydrodynamic drag, and thermal fluctuation may realize a multitude of stationary conformations of a rotationally-driven DNA filament. Many problems have to be solved in this field, where a combined approach of analytic (e.g., continuum theory, scaling arguments) and numerical (e.g., Brownian dynamics) is necessary (H. Wada and R.R. Netz, EPL 75, 645 (2006) )
Recently, it was shown by computer simulations and field-theoretic calculations that disorder of surfaces-ions has a strong influence on the ion distribution close to the disordered surface and thus on the interaction between charged surfaces (C. Fleck and R.R. Netz, EPL 70, 341 (2005)). The effect originates in a coupling between the fluctuating counterions and the surface-ion disorder, an effect not captured by mean-field theories.
For moderately charged surfaces it could be shown that it does not matter whether the disorder is fixed (quenched disorder) or stems from mobile or dissociable surface charges (annealed disorder). The equivalence of quenched and annealed disorder for weakly charged surfaces has been shown numerically, but an analytic proof of this ergodic property is still waiting for discovery.
Moreover, the numerical and analytical investigations for strongly charged surfaces is missing so far. In this case one expects a difference between the two types of disorder. A spontaneous lateral symmetry break is likely to occur for strongly charged surfaces and multivalent counterions.
In this project a combination of numerical (monte-carlo simulation) and analytical (field-theoretical, density-functional theory) methods will be applied. The work will build on methods and results previously derived in our group.
A solid background in statistical physics and an interest in numerical as well as in analytical calculations are prerequisites.