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The article discusses various reports published within the issue, including the study on topological properties, algorithms and computation tools for complex networks; the feature on collective behaviors in global and local identical coupled oscillators; and, the research on the impact of motion on the spreading of disease in dynamical social networks of mobile agents.

We report experimental results on breath figures (BFs) observed on substrates with quenched disorder. The evolution of BFs is found to be primarily influenced by global parameters associated with boundary conditions. We investigate classical statistical measures and explore topological properties using persistent homology techniques based on a modified Vietoris-Rips complex. Our findings reveal that the evolution of the number surface density of condensed droplets plays a crucial role in determining various condensation stages previously considered distinct. This evolution is significantly influenced by the distribution of nucleation sites and the individual growth law governing water droplets when coalescence does not occur. Ultimately, we demonstrate the capability to predict coalescence events based on the topological characteristics of BFs at a given point in time.

Polycrystals of thin colloidal deposits, with thickness controlled by spin-coating speed, exhibit axial symmetry with local 4-fold and 6-fold symmetric structures, termed orientationally correlated polycrystals (OCPs). While spin-coating is a very facile technique for producing large-area colloidal deposits, the axial symmetry prevents us from achieving true long-range order. To obtain true long-range order, we break this axial symmetry by introducing a patterned surface topography and thus eliminate the OCP character. We then examine symmetry-independent methods to quantify order in these disordered colloidal deposits. We find that all the information in the bond-orientational order parameters is well captured by persistent homology analysis methods that only use the centers of the particles as input data. It is expected that these methods will prove useful in characterizing other disordered structures.

Water droplets condensing on solidified phase change materials such as benzene and cyclohexane near their melting point show in-plane jumping and continuous "crawling" motion. The jumping drop motion has been tentatively explained as an outcome of melting and refreezing of the materials surface beneath the droplets and can be thus considered as an inverted Leidenfrost-like effect (in the classical case vapor is generated from a droplet on a hot substrate). We present here a detailed investigation of jumping movements using high-speed imaging and static cross-sectional cryogenic focused ion beam scanning electron microscope imaging. Our results show that drop motion is induced by a thermocapillary (Marangoni) effect. The in-plane jumping motion can be delineated to occur in two stages. The first stage occurs on a millisecond time scale and comprises melting the substrate due to drop condensation. This results in droplet depinning, partial spreading, and thermocapillary movement until freezing of the cyclohexane film. The second stage occurs on a second time scale and comprises relaxation motion of the drop contact line (change in drop contact radius and contact angle) after substrate freezing. When the cyclohexane film cannot freeze, the droplet continuously glides on the surface, resulting in the crawling motion.

Fabricating large single crystals with colloidal spheres as building blocks is challenging and of competitive interest. Spin-coating of colloids offers a robust technique, which is highly reproducible in obtaining colloidal crystals even at fast dynamical regimes; however, these crystals are intrinsically polycrystalline due to the axial symmetry of spin-coating. We report a new method that applies a nonuniform electric field during the spin-coating process. By arranging the field direction to be stationary in the rotating frame, we are able to break the axial symmetry and to orient the colloids along one predefined direction. By regulating the applied field strength, we demonstrate local control over the orientation of the crystallites, and thus, the orientation is determined by the applied field strength.

We probe the local and global structure of spin-coated colloidal crystals via laser diffraction measurements and scanning electron and atomic force microscopies, and find that they are unique three-dimensional orientationally correlated polycrystals, exhibiting short-range positional order but long-range radial orientational correlations, reminiscent of-but distinct from-two-dimensional colloidal hexatic phases. Thickness and symmetries are controllable by solvent choice and spin speed. While the polycrystallinity of these colloidal films limits their applicability to photonics, we demonstrate their feasibility as templates to make crack-free magnetic patterns.