Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low dislocation density III-nitride and III-V materials on lattice-mismatched substrates, and interesting from the fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general assumptions on the solid-like coalescence process within the Kolmogorov crystallization theory, results in a morphological diagram for the asymptotic coverage of a substrate surface. The coverage is presented as a function of two variables, the material collection efficiency on the top nanowire facet a, and the normalized surface diffusion flux of adatoms from the NW sidewalls b. The full coalescence of nanowires is possible only when a=1 regardless of b. At a>1, which is usual for vapor-liquid-solid growth with a catalyst droplet, nanowires can only partly merge but never coalesce into continuous film. These results can be used for predicting and controlling the degree of surface coverage by nanowires and three-dimensional islands by tuning the surface density, droplet size, adatoms diffusivity, and geometry of the initial structures in the vapor-liquid-solid, selective area or self-induced growth processes in different epitaxy techniques.

The stochastic modelling of chemical physical processes is essentially based on a coarse-grained formulation of fluctuations, usually described by means of Wiener processes. By taking the paradigmatic example of chemical reaction kinetics, we propose a simple representation of microscopic stochastic dynamics grounded on the use of distributional derivatives of counting processes that account for elementary reactive events. This approach is consistent with the statistical analysis based on the Chemical Master Equation, and provides the formal setting for the existing algorithmic approaches (Gillespie algorithm). Some practical advantages of this formulation are addressed, and several other examples are discussed in connection with cluster formation, velocity fluctuations in liquid systems, and quantum transitions (radiative interactions) at the molecular level.

The contactless coalescence of a droplet is of paramount importance for physical and industrial applications. This paper describes a coalescence method in mid-air via acoustic levitation using an ultrasonic phased array system. Acoustic levitation using ultrasonic phased arrays provides promising lab-on-a-drop applications, such as transportation, coalescence, mixing, separation, evaporation, and extraction in a continuous operation. The mechanism of droplet coalescence in mid-air may be better understood by experimentally and numerically exploring the droplet dynamics immediately before the coalescence. In this study, water droplets were experimentally levitated, transported, and coalesced by controlling acoustic fields. We observed that the edge of droplets deformed and attracted each other immediately before the coalescence. Through image processing, the radii of curvature of the droplets were quantified and the pressure difference between the inside and outside the droplet was simulated to obtain the pressure and velocity information on the droplet surface. The results revealed that the sound pressure acting on the droplet clearly decreased before the impact of the droplets. This pressure on the droplets was quantitatively analyzed from the experimental data. Our experimental and numerical results provide deeper physical insights into contactless droplet manipulation for futuristic lab-on-a-drop applications.