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In this thesis, dynamical structures and manifolds in closed chaotic flows will be investigated. The knowledge about the dynamical structures (and manifolds) of a system is of importance, since they provide us first information about the dynamics of the system - means, with their help we are able to characterize the flow and maybe even to forecast it`s dynamics. The visualization of such structures in closed chaotic flows is a difficult and often long-lasting process. Here, the so-called 'Leaking-method' will be introduced, in examples of simple mathematical maps as the baker- or sine-map, with which we are able to visualize subsets of the manifolds of the system`s chaotic saddle. Comparisons between the visualized manifolds and structures traced out by chemical or biological reactions superimposed on the same flow will be done in the example of a kinematic model of the Gulf Stream. It will be shown that with the help of the leaking method dynamical structures can be also visualized in environmental systems. In the example of a realistic model of the Mediterranean Sea, the leaking method will be extended to the 'exchange-method'. The exchange method allows us to characterize transport between two regions, to visualize transport routes and their exchange sets and to calculate the exchange times. Exchange times and sets will be shown and calculated for a northern and southern region in the western basin of the Mediterranean Sea. Furthermore, mixing properties in the Earth mantle will be characterized and geometrical properties of manifolds in a 3dimensional mathematical model (ABC map) will be investigated.
The cytoskeletal motor protein kinesin-1 (conventional kinesin) is the fast carrier for intracellular cargo transport along microtubules. So far most studies aimed at investigating the transport properties of individual motor molecules. However, the transport in cells usually involves the collective work of more than one motor. In the present work, we have studied the movement of beads as artificial loads/organelles pulled by several kinesin-1 motors in vitro. For a wide range of motor coverage of the beads and different bead (cargo) sizes the transport parameters walking distance or run length, velocity and force generation are measured. The results indicate that the transport parameters are influenced by the number of motors carrying the bead. While the transport velocity slightly decreases, an increase in the run length was measured and higher forces are determined, when more motors are involved. The effective number of motors pulling a bead is estimated by measuring the change in the hydrodynamic diameter of kinesin-coated beads using dynamic light scattering. The geometrical constraints imposed by the transport system have been taken into account. Thus, results for beads of different size and motor-surface coverage could be compared. In addition, run length-distributions obtained for the smallest bead size were matched to theoretically calculated distributions. The latter yielded an average number of pulling motors, which is in agreement with the effective motor numbers determined experimentally.