We introduce a new method that identifies and tracks features in arbitrary dimensions using the merge tree—a structure for identifying topological features based on thresholding in scalar fields. This method analyzes the evolution of features of the function by tracking changes in the merge tree and relates features by matching subtrees between consecutive time steps. Using the time-varying merge tree, we present a structural visualization of the changing function that illustrates both features and their temporal evolution. We demonstrate the utility of our approach by applying it to temporal cluster analysis of high-dimensional point clouds.

Bimetallic, nanostructured materials hold promise for improving catalyst activity and selectivity, yet little is known about the dynamic compositional and structural changes that these systems undergo during pretreatment that leads to efficient catalyst function. Here we use ozone-activated silver-gold alloys in the form of nanoporous gold as a case study to demonstrate the dynamic behaviour of bimetallic systems during activation to produce a functioning catalyst. We show that it is these dynamic changes that give rise to the observed catalytic activity. Advanced in situ electron microscopy and X-ray photoelectron spectroscopy are used to demonstrate that major restructuring and compositional changes occur along the path to catalytic function for selective alcohol oxidation. Transient kinetic measurements correlate the restructuring to three types of oxygen on the surface. The direct influence of changes in surface silver concentration and restructuring at the nanoscale on oxidation activity is demonstrated. Our results demonstrate that characterization of these dynamic changes is necessary to unlock the full potential of bimetallic catalytic materials.

Activating pretreatments are used to tune surface composition and structure of bimetallic-alloy catalysts. Herein, the activation-induced changes in material properties of a nanoporous Ag0.03Au0.97 alloy and their subsequent evolution under steady-state CH3OH oxidation conditions are investigated. Activation using O3 results in AgO and Au2O3, strongly enriching the near-surface region in Ag. These oxides reduce in the O2/CH3OH mixture, yielding CO2 and producing a highly Ag-enriched surface alloy. At the reaction temperature (423 K), Ag realloys gradually with Au but remains enriched (stabilized by surface O) in the top few nanometers, producing methyl formate selectively without significant deactivation. At higher temperatures, bulk diffusion induces sintering and Ag redistribution, leading to a loss of activity. These findings demonstrate that material properties determining catalytic activity are dynamic and that metastable (kinetically trapped) forms of the material may be responsible for catalysis, providing guiding principles concerning the activation of heterogeneous catalysts for selective oxidation.