Breaking waves aerate seawater surfaces and form whitecaps in the open ocean. The aerated surface area, or whitecap coverage, has been used to macroscopically parametrize air–sea momentum and gas exchange. However, the microscopic mechanisms of the generation, evolution and attenuation of surface bubbles in whitecaps remain poorly understood. In this study, we examined the size distributions and size-dependent lifetimes of surface bubbles generated by water sheet entry and air injection on a porous plate during the clustering, coalescing and bursting processes, depending on surfactant concentrations and bubble mobility. Mechanisms of coalescence through film thinning of adjacent bubble walls owing to the inter-bubble attraction and Marangoni forces experimentally described the surfactant-dependent bubble growth, finally achieving bubble bursting, which were statistically characterized in a population balance analysis. Lagrangian bubble lifetimes were described by the Weibull distribution, providing that surfactant in seawater extended the probabilistic survival periods of surface bubbles two times longer than those of clean bubbles.

Metathesis poses challenges for a typologically constrained theory of phonology: despite being simple to describe, its distribution is highly restricted, making it difficult to create analyses that make predictions while not overgenerating. Here, I investigate metathesis in Uab Meto (Austronesian; Indonesia), an understudied language with CV metathesis that is synchronic and productive. Drawing on original fieldwork, I argue that metathesis is not transposition, but instead a serial delete-and-spread mechanism (cf. Takahashi 2018, 2019). To support this, I present a deep case study into the language’s phonology, showing that metathesis arises from spreading, deletion and epenthesis patterns. I propose that synchronic metathesis systems like Uab Meto’s can only emerge from the successive application of these mechanisms, and hypothesise that true transposition, if it exists, only arises through morpheme-specific operations. This study thus presents a new look onto the typology of synchronic metathesis, and offers an explanatory account of its typological rarity.

Recent investigations of Morton Village, a Mississippian and Oneota community formed following Oneota migration into the central Illinois River valley around AD 1300, focus on evaluating the social context for the remarkable violence evidenced at the adjacent Norris Farms 36 cemetery. Here, we use the concepts of thirdspace and hybridity to examine three areas of village life: creation of the physical structure of the village, ritual, and foodways. Within these three areas, we identify transformations of Mississippian and Oneota practices that support the interpretation that villagers were engaged in the formation of a coalescent community.

Experimentally revealing dynamic evolution and growth behavior of small solute clusters in alloys remains a technical challenge. To date, the coalescence of the solute clusters has seldom been experimentally addressed. To address the challenge, we used atom probe tomography (APT) to access boundary information of solute clusters and identify those in close contact. By systematically investigating the population and size evolution of the clusters in close contact with aging time, we unveiled important information regarding the clusters in coalescence with the exsitu experimental technique. In this work, the maximum separation method was employed to identify clusters in APT datasets of naturally aged Al–Zn–Mg alloy. Coalescence was found to significantly contribute to the growth of small clusters and remained predominant for the formation and growth of large Guinier–Preston II ${\rm \lpar G}{\rm P}_{{\eta }^{\prime}}\rpar$ zones after 3 months aging.

We introduce an idealised model for overland flow generated by rain falling on a hillslope. Our prime motivation is to show how the coalescence of runoff streams promotes the total generation of runoff. We show that, for our model, as the rate of rainfall increases in relation to the soil infiltration rate there is a distinct phase change. For low rainfall (the subcritical case) only the bottom of the hillslope contributes to the total overland runoff, while for high rainfall (the supercritical case) the whole slope contributes and the total runoff increases dramatically. We identify the critical point at which the phase change occurs, and show how it depends on the degree of coalescence. When there is no stream coalescence the critical point occurs when the rainfall rate equals the average infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the average infiltration rate, and increasing the amount of coalescence increases the total expected runoff.

High fidelity modeling and simulation of moderately dense sprays at relatively low cost is still a major challenge for many applications. For that purpose, we introduce a new multi-fluid model based on a two-size moment formalism in sections, which are size intervals of discretization. It is derived from a Boltzmann type equation taking into account drag, evaporation and coalescence, which are representative of the complex terms that arise in multi-physics environments. The closure of the model comes from a reconstruction of the distribution. A piecewise affine reconstruction in size is thoroughly analyzed in terms of stability and accuracy, a key point for a high-fidelity and reliable description of the spray. Robust and accurate numerical methods are then developed, ensuring the realizability of the moments. The model and method are proven to describe the spray with a high accuracy in size and size-conditioned variables, resorting to a lower number of sections compared to one size moment methods. Moreover, robustness is ensured with efficient and tractable algorithms despite the numerous couplings and various algebra thanks to a tailored overall strategy. This strategy is successfully tested on a difficult 2D unsteady case, which proves the efficiency of the modeling and numerical choices.

Consider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet. In this paper, the limit behaviors of the distributions of the generation number of the most recent common ancestor of any k chosen individuals and of the whole population are studied for both critical and subcritical cases. Also, we investigate the limit distribution of the joint distribution of the generation number and their types.

In this paper we describe a perfect simulation algorithm for the stable M/G/c queue. Sigman (2011) showed how to build a dominated coupling-from-the-past algorithm for perfect simulation of the super-stable M/G/c queue operating under first-come-first-served discipline. Sigman's method used a dominating process provided by the corresponding M/G/1 queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service). The method exploited the fact that the workload process for the M/G/1 queue remains the same under different queueing disciplines, in particular under the processor sharing discipline, for which a dynamic reversibility property holds. We generalise Sigman's construction to the stable case by comparing the M/G/c queue to a copy run under random assignment. This allows us to produce a naïve perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupled M/G/c queues started respectively from the empty state and the state of the M/G/c queue under random assignment. A careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service. We summarise statistical checks of simulation output, and demonstrate that the mean run-time is finite so long as the second moment of the service duration distribution is finite.

Coalescence is a significant pathway for the growth of nanostructures. Here we studied the coalescence of Bi nanoparticles in situ by liquid cell transmission electron microscopy (TEM). The growth of Bi nanoparticles was initiated from a bismuth neodecanoate precursor solution by electron beam irradiation inside a liquid cell under the TEM. A significant number of coalescence events occurred from the as-grown Bi nanodots. Both symmetric coalescence of two equal-sized nanoparticles and asymmetric coalescence of two or more unequal-sized nanoparticles were analyzed along their growth trajectories. Our observation suggests that two mass transport mechanisms, i.e., surface diffusion and grain boundary diffusion, are responsible for the shape evolution of nanoparticles after a coalescence event.

We investigate the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous-time Bienaymé-Galton-Watson process founded t units of time ago. We also obtain limiting distributions as t → ∞ in the subcritical case. We extend our results for two individuals to the joint distribution of coalescence times for any finite number of individuals sampled in the current generation.

Two related aspects of nano-droplet condensation and droplets coalescence are studied for droplets on self-supported thin water films. The experiments are conducted in the environmental scanning electron microscope using wet scanning transmission electron microscopy. Favorable condensation sites are examined and in-situ position-controlled condensation experiments are conducted. The interaction among condensed multi-droplets as well as between a single droplet and the underneath nano-thick water film are dynamically examined with 10nm lateral resolution. The droplet round shape is reshaped to flat-like facets in-between droplets of 30-230 nm separation. Dynamic imaging of a few minutes duration shows a delayed coalescence effect, being explained by increased droplet-droplet electrostatic interaction relative to van der Waals interaction.

In a discrete-time single-type Galton--Watson branching random walk {Zn, ζn}n≤ 0, where Zn is the population of the nth generation and ζn is a collection of the positions on ℝ of the Zn individuals in the nth generation, let Yn be the position of a randomly chosen individual from the nth generation and Zn(x) be the number of points in ζn that are less than or equal to x for x∈ℝ. In this paper we show in the explosive case (i.e. m=E(Z1∣ Z0=1)=∞) when the offspring distribution is in the domain of attraction of a stable law of order α,0 <α<1, that the sequence of random functions {Zn(x)/Zn:−∞<x<∞} converges in the finite-dimensional sense to {δx:−∞<x<∞}, where δx≡ 1{N≤ x} and N is an N(0,1) random variable.

We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t)={at,i: 1≤ i≤ Z(t)}, where at,i is the age of the ith individual alive at time t, 1≤ i≤ Z(t), and Z(t) is the population size of individuals alive at time t. Also, if Z(t)≥ k, k≥2, is a positive integer, we pick k individuals from those who are alive at time t by simple random sampling without replacement and trace their lines of descent backward in time until they meet for the first time. Let Dk(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of Dk(t) and its limit distribution as t→∞.

In a Galton-Watson branching process that is not extinct by the nth generation and has at least two individuals, pick two individuals at random by simple random sampling without replacement. Trace their lines of descent back in time till they meet. Call that generation Xn a pairwise coalescence time. Similarly, let Yn denote the coalescence time for the whole population of the nth generation conditioned on the event that it is not extinct. In this paper the distributions of Xn and Yn, and their limit behaviors as n → ∞ are discussed for both the critical and subcritical cases.

In this paper, we numerically investigate the effects of surfactant on drop-drop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in (Xu et al., J. Comput. Phys., 212 (2006), 590-616). We find that surfactant plays a critical and nontrivial role in drop-drop interactions. In particular, we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number. This non-monotonic behavior, which does not occur for clean drops, is found to be due to the presence of Marangoni forces along the drop interfaces. This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops, as observed in recent experiments of Leal and co-workers. Although our study is two-dimensional, we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

L’expérience a démontré que la fissure fatale n’est pas nécessairement la plus granderelevée à un moment donné de la fatigue d’un matériau et qu’elle peut être la résultanted’autres microfissures. Ainsi, le dommage (par fatigue) est souvent associé audéveloppement et à la croissance de microfissures en surface. L’avantage de considérer unepopulation de fissures comme facteur physique d’endommagement est que les longueurs defissures et leur nombre sont des données quantifiables qui peuvent être mesurées ensurface du matériau. La présente étude est conduite dans ce sens et vise à caractériserl’endommagement et son évolution par la mesure de la densité de fissures en surface. Unmodèle numérique, basé sur des principes aléatoires de génération de fissures, de leurpropagation et de leur interaction mutuelle, est proposé. Il est ensuite appliqué dans lecas du 316L à température ambiante et pour des déformations plastiques égales à8 × 10-3, 4 × 10-3 et 8 × 10-4.