## 530 Physik

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- Doctoral Thesis (22)
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#### Keywords

- anomalous diffusion (4)
- nonergodicity (4)
- transport (4)
- Datenanalyse (3)
- data analysis (3)
- Crab Nebula (2)
- Gammastrahlungsastronomie (2)
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- Rekonstruktionsmethoden (2)

We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt, Gunzburger & Lee, Comput. Meth. Appl. Mech. Engng, vol. 196, 2006a, pp. 337-355) and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider, Eckhardt & Vollmer, Phys. Rev. E, vol. 75, 2007, art. 066313). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Second, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e. g. using finite-time Lyapunov exponent (FTLE) and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.

Atmospheric interactions with land surface in the arctic based on regional climate model solutions
(2014)

Scientific inquiry requires that we formulate not only what we know, but also what we do not know and by how much. In climate data analysis, this involves an accurate specification of measured quantities and a consequent analysis that consciously propagates the measurement errors at each step. The dissertation presents a thorough analytical method to quantify errors of measurement inherent in paleoclimate data. An additional focus are the uncertainties in assessing the coupling between different factors that influence the global mean temperature (GMT).
Paleoclimate studies critically rely on `proxy variables' that record climatic signals in natural archives. However, such proxy records inherently involve uncertainties in determining the age of the signal. We present a generic Bayesian approach to analytically determine the proxy record along with its associated uncertainty, resulting in a time-ordered sequence of correlated probability distributions rather than a precise time series. We further develop a recurrence based method to detect dynamical events from the proxy probability distributions. The methods are validated with synthetic examples and
demonstrated with real-world proxy records. The proxy estimation step reveals the interrelations between proxy variability and uncertainty. The recurrence analysis of the East Asian Summer Monsoon during the last 9000 years confirms the well-known `dry' events at 8200 and 4400 BP, plus an additional significantly dry event at 6900 BP.
We also analyze the network of dependencies surrounding GMT. We find an intricate, directed network with multiple links between the different factors at multiple time delays. We further uncover a significant feedback from the GMT to the El Niño Southern Oscillation at quasi-biennial timescales. The analysis highlights the need of a more nuanced formulation of influences between different climatic factors, as well as the limitations in trying to estimate such dependencies.

Untersuchungen zur pro-inflammatorischen Wirkung von Serum-Amyloid A in glatten Gefäßmuskelzellen
(2014)

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion
(2014)

The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion
(2014)

Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.