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An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Given that mergers are often invoked to explain many exotic phenomena in massive star evolution, understanding the evolutionary phase directly preceding a merger, the overcontact phase, is of crucial importance. Despite its importance,…
We study the emergence of a giant component in the configuration model subject to additional constraints on the edges. We partition a $d$-dimensional torus into a cubic lattice with a diverging number of compartments containing vertices and…
A joint volume-surface formalism of the Multi-Moment Sectional Method (MMSM) is developed to describe the evolution of soot size distribution in turbulent reacting flows. The bivariate MMSM (or BMMSM) considers three statistical moments per…
Stellar evolution theory is most uncertain for massive stars. For reliable predictions of the evolution of massive stars and their final fate, solid constraints on the physical parameters, and their changes along the evolution and in…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
Recent observations of Type Ia supernovae provide evidence for the acceleration of our universe, which leads to the possibility that the universe is entering an inflationary epoch. We simulate it under a ``big bounce'' model, which contains…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
Observing the stars in our night sky tells us that giant, supergiant and hypergiant stars hold an unique importance in the understanding of stellar populations. Theoretical stellar models predict a rich tapestry of evolved stars. These…
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many models of biological invasion are extensions of the…
Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of…
Wide hot subdwarf B (sdB) binaries with main-sequence companions are outcomes of stable mass transfer from evolved red giants. The orbits of these binaries show a strong correlation between their orbital periods and mass ratios. The origins…
Strongly first-order phase transitions, i.e., those with a large order parameter, are characterized by a considerable supercooling and high velocities of phase transition fronts. A very strong phase transition may have important…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
The study of the phase transition in planar FK-percolation on the square lattice has seen significant recent breakthroughs. The model undergoes a change in the nature of its phase transition at $q = 4$, transitioning from a continuous to a…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for the late evolution and final fate of massive stars. We develop spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven…
Diffusion of atoms can be important during quiescent phases of stellar evolution. Particularly in the very thin inert envelopes of subdwarf B stars, diffusive movements will considerably change the envelope structure and the surface…