Flow fields are usually visualized relative to a global observer, i.e., a single frame of reference. However, often no global frame can depict all flow features equally well. Likewise, objective criteria for detecting features such as vortices often use either a global reference frame, or compute a separate frame for each point in space and time. We propose the first general framework that enables choosing a smooth trade-off between these two extremes. Using global optimization to minimize specific differential geometric properties, we compute a time-dependent observer velocity field that describes the motion of a continuous field of observers adapted to the input flow. This requires developing the novel notion of an observed time derivative. While individual observers are restricted to rigid motions, overall we compute an approximate Killing field, corresponding to almost-rigid motion. This enables continuous transitions between different observers. Instead of focusing only on flow features, we furthermore develop a novel general notion of visualizing how all observers jointly perceive the input field. This in fact requires introducing the concept of an observation time, with respect to which a visualization is computed. We develop the corresponding notions of observed stream, path, streak, and time lines. For efficiency, these characteristic curves can be computed using standard approaches, by first transforming the input field accordingly. Finally, we prove that the input flow perceived by the observer field is objective. This makes derived flow features, such as vortices, objective as well.

This paper presents several strategies to interactively explore 3D flow. Based on a fast illuminated streamlines algorithm, standard graphics hardware is sufficient to gain interactive rendering rates. Our approach does not require the user to have any prior knowledge of flow features. After the streamlines are computed in a short preprocessing time, the user can interactively change appearance and density of the streamlines to further explore the flow. Most important flow features like velocity or pressure not only can be mapped to all available streamline appearance properties like streamline width, material, opacity, but also to streamline density. To improve spatial perception of the 3D flow we apply techniques based on animation, depth cueing, and halos along a streamline if it is crossed by another streamline in the foreground. Finally, we make intense use of focus+context methods like magic volumes, region of interest driven streamline placing, and spotlights to solve the occlusion problem.

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Reference frame optimization is a generic framework to calculate a spatially-varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field is objective, i.e., it is independent of the initial Euclidean transformation of the observer. To check objectivity, the optimized velocity vectors and the coordinates in which they are defined must both be connected by an Euclidean transformation. In this paper we show that a recent publication [1] applied this definition incorrectly, falsely concluding that reference frame optimizations are not objective. Further, we prove the objectivity of the variational formulation of the reference frame optimization proposed in [1], and discuss how the variational formulation relates to recent local and global optimization approaches to unsteadiness minimization.

The bottom‐up covalent assembly of metallic nanoparticles (NP) represents one of the innovative tools in nanotechnology to build functional heterostructures, with the resulting assemblies showing superior collective properties over the individual NP for a broad range of applications. The ability to control the dimensionality of the assembly is one of the major challenges in designing and understanding these advanced materials. Here, two new organic linkers were used as building blocks in order to guide the organization of Ru NP into two‐ or three‐dimensional covalent assemblies. The use of a hexa‐adduct functionalized C60 leads to the formation of 3D networks of 2.2 nm Ru NP presenting an interparticle distance of 3.0 nm, and the use of a planar carboxylic acid triphenylene derivative allows the synthesis of 2D networks of 1.9 nm Ru NP with an interparticle distance of 3.1 nm. The Ru NP networks were found to be active catalysts for the selective hydrogenation of phenylacetylene, reaching good selectivity toward styrene. Overall, we demonstrated that catalyst performances are significantly affected by the dimensionality (2D vs. 3D) of the heterostructures, which can be rationalize based on confinement effects.