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Modeling the internal structure of self-gravitating solid and liquid bodies presents a challenge, as existing approaches are often limited to either overly simplistic constant-density approximations or more complex numerical equations of…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
Most giant exoplanets discovered by radial velocity surveys have much higher eccentricities than those in the solar system. The planet--planet scattering mechanism has been shown to match the broad eccentricity distribution, but the…
We use numerical relativity simulations to describe the spacetime evolution during nonlinear structure formation in $\Lambda$CDM cosmology. Fully nonlinear initial conditions are set at an initial redshift $z\approx 300$, based directly on…
For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of…
The study of our Solar System -- its formation, evolution, and long-term stability -- has been ongoing for centuries and is now a standard part of scientific education. While the formation of other Solar-like exoplanetary systems is…
Active small bodies in extrasolar systems, the extrasolar analogues of Solar System comets, provide insights into the orbital evolution and physical processes shaping planetary systems. Since the discovery of exocomets around $\beta$…
To study how a zygote develops into an embryo with different tissues, large-scale 4D confocal movies of C. elegans embryos have been produced recently by experimental biologists. However, the lack of principled statistical methods for the…
A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The…
We explore the evolution of the eccentricity of an accretion disc perturbed by an embedded planet whose mass is sufficient to open a large gap in the disc. Various methods for representing the orbit-averaged motion of an eccentric disc are…
A baroclinic model for the atmospheric jet at middle-latitudes is used as stochastic generator of non-stationary time series of the total energy of the system. A linear time trend is imposed on the parameter $T_E$, descriptive of the forced…
Research on the birth and evolution of life are reviewed with reference to the maximum entropy production principle (MEPP). It has been shown that this principle is essential for consistent understanding of the birth and evolution of life.…
After hydrogen and helium, oxygen, carbon, and nitrogen - hereinafter, the CNO elements - are the most abundant species in the universe. They are observed in all kinds of astrophysical environments, from the smallest to the largest scales,…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
A test particle in a noncoplanar orbit about a member of a binary system can undergo Kozai-Lidov oscillations in which tilt and eccentricity are exchanged. An initially circular highly inclined particle orbit can reach high eccentricity. We…
One of the most fundamental concepts of evolutionary dynamics is the "fixation" probability, i.e. the probability that a mutant spreads through the whole population. Most natural communities are geographically structured into habitats…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the…
We study the limiting extremal and cluster point processes of branching Brownian motion. The former records the heights of all extreme values of the process, while the latter records the relative heights of extreme values in a genealogical…