The idea of 'frozen-in' magnetic field lines for ideal plasmas is useful to explain diverse astrophysical phenomena, for example the shedding of excess angular momentum from protostars by twisting of field lines frozen into the interstellar medium. Frozen-in field lines, however, preclude the rapid changes in magnetic topology observed at high conductivities, as in solar flares. Microphysical plasma processes are a proposed explanation of the observed high rates, but it is an open question whether such processes can rapidly reconnect astrophysical flux structures much greater in extent than several thousand ion gyroradii. An alternative explanation is that turbulent Richardson advection brings field lines implosively together from distances far apart to separations of the order of gyroradii. Here we report an analysis of a simulation of magnetohydrodynamic turbulence at high conductivity that exhibits Richardson dispersion. This effect of advection in rough velocity fields, which appear non-differentiable in space, leads to line motions that are completely indeterministic or 'spontaneously stochastic', as predicted in analytical studies. The turbulent breakdown of standard flux freezing at scales greater than the ion gyroradius can explain fast reconnection of very large-scale flux structures, both observed (solar flares and coronal mass ejections) and predicted (the inner heliosheath, accretion disks, γ-ray bursts and so on). For laminar plasma flows with smooth velocity fields or for low turbulence intensity, stochastic flux freezing reduces to the usual frozen-in condition.

We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can be derived in which the streamlines are most likely to reside. This is achieved by transforming the Gaussian random distributions from the low-dimensional Euclidean space into a streamline distribution that follows the statistical model, and by visualizing confidence regions in this distribution via iso-contours. We further make use of the principal component representation to introduce a new concept of streamline-median, based on existing median concepts in multidimensional Euclidean spaces. We demonstrate the potential of our method in a number of real-world examples, and we compare our results to alternative clustering approaches for particle trajectories as well as curve boxplots.

In this paper we present techniques for the visualization of unsteady flows using streak surfaces, which allow for the first time an adaptive integration and rendering of such surfaces in real-time. The techniques consist of two main components, which are both realized on the GPU to exploit computational and bandwidth capacities for numerical particle integration and to minimize bandwidth requirements in the rendering of the surface. In the construction stage, an adaptive surface representation is generated. Surface refinement and coarsening strategies are based on local surface properties like distortion and curvature. We compare two different methods to generate a streak surface: a) by computing a patch-based surface representation that avoids any interdependence between patches, and b) by computing a particle-based surface representation including particle connectivity, and by updating this connectivity during particle refinement and coarsening. In the rendering stage, the surface is either rendered as a set of quadrilateral surface patches using high-quality point-based approaches, or a surface triangulation is built in turn from the given particle connectivity and the resulting triangle mesh is rendered. We perform a comparative study of the proposed techniques with respect to surface quality, visual quality and performance by visualizing streak surfaces in real flows using different rendering options.

Fig. 1. Visualizations of structures in 1024 3 turbulence data sets on 1024 × 1024 viewports, directly from the turbulent motion field. Left: Close-up of iso-surfaces of the ∆ Chong invariant with direct volume rendering of vorticity direction inside the vortex tubes. Middle: Direct volume rendering of color-coded vorticity direction. Right: Close-up of direct volume rendering of R S . The visualizations are generated by our system in less than 5 seconds on a desktop PC equipped with 12 GB of main memory and an NVIDIA GeForce GTX 580 graphics card with 1.5 GB of video memory.Abstract-Despite the ongoing efforts in turbulence research, the universal properties of the turbulence small-scale structure and the relationships between small-and large-scale turbulent motions are not yet fully understood. The visually guided exploration of turbulence features, including the interactive selection and simultaneous visualization of multiple features, can further progress our understanding of turbulence. Accomplishing this task for flow fields in which the full turbulence spectrum is well resolved is challenging on desktop computers. This is due to the extreme resolution of such fields, requiring memory and bandwidth capacities going beyond what is currently available. To overcome these limitations, we present a GPU system for feature-based turbulence visualization that works on a compressed flow field representation. We use a wavelet-based compression scheme including run-length and entropy encoding, which can be decoded on the GPU and embedded into brick-based volume ray-casting. This enables a drastic reduction of the data to be streamed from disk to GPU memory. Our system derives turbulence properties directly from the velocity gradient tensor, and it either renders these properties in turn or generates and renders scalar feature volumes. The quality and efficiency of the system is demonstrated in the visualization of two unsteady turbulence simulations, each comprising a spatio-temporal resolution of 1024 4 . On a desktop computer, the system can visualize each time step in 5 seconds, and it achieves about three times this rate for the visualization of a scalar feature volume.

Particle tracing has been established as a powerful visualization technique to show the dynamics of 3D flows. Particle tracing in 3D, however, quickly overextends the viewer due to the massive amount of visual information that is typically produced by this technique. In this paper, we present strategies to reduce this amount at the same time revealing important structures in the flow. As an importance measure, we introduce a simple, yet effective clustering approach for vector fields, and we use scalar flow quantities at different scales in combination with user-defined regions of interest. These measures are used to control the shape, the appearance, and the density of particles in such a way that the user can focus on the dynamics in important regions at the same time preserving context information. We also introduce a new focus for particle tracing, so called anchor lines. Anchor lines are used to analyze local flow features by visualizing how much particles separate over time and how long it takes until they have separated to a fixed distance. It is of particular interest if the finite time Lyapunov exponent -a scalar quantity that measures the rate of separation of infinitesimally close particles in the flow -is used to guide the placement of anchor lines. The effectiveness of our approaches for the visualization of 3D flow fields is validated using synthetic fields as well as real simulation data.they generate a representation of the entire field. Even by using advanced visualization options like halos [11], transfer functions and clipping geometries [21], and flow-guided importance measures [31], it has been shown difficult to overcome these limitations without loosing relevant information.