Despite the crowdedness of the interior of cells, microtubule-based motor proteins are able to deliver cargoes rapidly and reliably throughout the cytoplasm. We hypothesize that motor proteins may be adapted to operate in crowded environments by having molecular properties that prevent them from forming traffic jams. To test this hypothesis, we reconstituted high-density traffic of purified kinesin-8 motor protein, a highly processive motor with long end-residency time, along microtubules in a total internal-reflection fluorescence microscopy assay. We found that traffic jams, characterized by an abrupt increase in the density of motors with an associated abrupt decrease in motor speed, form even in the absence of other obstructing proteins. To determine the molecular properties that lead to jamming, we altered the concentration of motors, their processivity, and their rate of dissociation from microtubule ends. Traffic jams occurred when the motor density exceeded a critical value (density-induced jams) or when motor dissociation from the microtubule ends was so slow that it resulted in a pileup (bottleneck-induced jams). Through comparison of our experimental results with theoretical models and stochastic simulations, we characterized in detail under which conditions densityand bottleneck-induced traffic jams form or do not form. Our results indicate that transport kinesins, such as kinesin-1, may be evolutionarily adapted to avoid the formation of traffic jams by moving only with moderate processivity and dissociating rapidly from microtubule ends.

We present a numerical method to identify regions of phase space that are approximately retained in a mobile compact neighbourhood over a finite time duration. Our approach is based on spatio-temporal clustering of trajectory data. The main advantages of the approach are the ability to produce useful results (i) when there are relatively few trajectories and (ii) when there are gaps in observation of the trajectories as can occur with real data. The method is easy to implement, works in any dimension, and is fast to run.Keywords: coherent sets, Lagrangian coherent structure, spatio-temporal clustering.Coherent features in time-dependent dynamical systems are difficult to identify, and considerable effort has been put into the development of identification algorithms. Most approaches require knowledge of the dynamical system or highresolution trajectory information, which in applications may not be available. We present a trajectory-based method that is aimed squarely at the situation where the available information is poor: there are few trajectories, the available trajectories do not span the full time duration under consideration, and there are missing observations within trajectories. As our method is very simple to implement and fast to run, it also provides a rapid "first cut" coherent structure analysis even in situations where the full dynamical system or high-resolution trajectory data is available.

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Abstract. The detection of regions in the ocean that are coherent over an extended period of time is a fundamental problem in many oceanic applications. For instance such regions are important for studying the transport of marine species and for the distribution of nutrients. In this study we demonstrate the efficacy of transfer operators in detecting and analysing such structures. We focus first on the detection of the Weddell and Ross Gyre for the four seasons spanning December 2003–November 2004 within the 3-D oceanic domain south of 30° S, and show distinct seasonal differences in both the three-dimensional structure and the persistence of the gyres. Further, we demonstrate a new technique based on the discretised transfer operators to calculate the mean residence time of water within parts of the gyres and determine pathways of water leaving and entering the gyres.

Abstract. Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operatorbased schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows -the Bickley jet as well as the Antarctic stratospheric polar vortex.

We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr = 0.7, a Rayleigh number Ra = 10 5 , and an aspect ratio Γ = 16 is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem et al., Phys. Rev. E 93, 063107 (2016), builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τ L and lengths λ L U of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, τ and λU , respectively. This trajectory-based clustering is found to work for times t τ ≈ τ L . Longer time periods t τ L require a change of the analysis method to a density-based trajectory clustering by means of timeaveraged Lagrangian pseudo-trajectories, which is applied in this context for the first time. A small coherent subset of the pseudo-trajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.

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