The coagulation-fragmentation equation describes the concentration fi(t) of particles of size i ∈ N/{0} at time t ≥ 0, in a spatially homogeneous infinite system of particles subjected to coalescence and break-up. We show that when the rate of fragmentation is sufficiently stronger than that of coalescence, (fi(t))i∈N/{0} tends to an unique equilibrium as t tends to infinity. Although we suppos...

Polymeric nanoparticles (NPs) have great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scale...

Most modern population genetics inference methods are based on the coalescence framework. Methods that allow estimating parameters of structured populations commonly insert migration events into the genealogies. For these methods the calculation of the coalescence probability density of a genealogy requires a product over all time periods between events. Data sets that contain populations with ...

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence t...

We analyse two-dimensional clamped parallel elastic sheets which are partially immersed in liquid as a model for elasto-capillary coalescence. In the existing literature this problem is studied via minimal energy analysis of capillary and elastic energies of the post-coalescence state, yielding the maximal stable post-coalescence bundle size. Utilizing modal stability analysis and asymptotic an...

We study the coalescence of a drop with its bulk phase in fluid–fluid demixing colloid–polymer mixtures. Such mixtures show behaviour analogous to molecular fluid–fluid systems, but the interfacial tension is between 10 to 10 times smaller than in the molecular case. Such an ultralow interfacial tension has several important consequences and offers significant advantages in the study of droplet...

The distributions of coalescence times and ancestral lineage numbers play an essential role in coalescent modeling and ancestral inference. Both exact distributions of coalescence times and ancestral lineage numbers are expressed as the sum of alternating series, and the terms in the series become numerically intractable for large samples. More computationally attractive are their asymptotic di...

Real-time budding dynamics of multicomponent, tubular lipid vesicles was investigated. By using a fluorescence microscope, three typical growth modes of the buds were observed, corresponding, respectively, to bud growth through coalescence between flat patches, a bud and a patch, as well as that of two buds. The spatial and temporal scales measured in the observation were used to estimate the b...

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey functions are given by integrals in which the exponent...

Some industrial processes, in their operations, involve the presence of two immiscible liquid phases. The dispersed drops are surrounded by a continuous phase. The drops tend to coalesce with adjacent drops or to join their mother phase separated by an interface. These kind of phenomena occur in many industrial operations as well as in environmental processes. The liquid-liquid foams behaviour ...