Related papers: The coalescing colony model: mean-field, scaling, …
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
This study presents a computational simulation exploring the complex interactions between population density and economic factors over a 100-year period. Inspired by the Keller-Segel model, traditionally applied in biological contexts, my…
Combining global gridded population and fossil fuel based CO2 emission data at 1km scale, we investigate the spatial origin of CO2 emissions in relation to the population distribution within countries. We depict the correlations between…
We investigated the evolution of clusters of galaxies using self-consistent N-body simulations. We varied the initial model of galaxies and clusters, and studied the dependence of evolution on initial conditions. We found that the growth…
Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
[abridged] We extend our analysis of the dynamical evolution of simple star cluster models, in order to provide comparison standards that will aid in interpreting the results of more complex realistic simulations. We augment our previous…
The amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of what really drives the processes behind urbanisation. In this…
We build a model to predict from first principles the properties of major mergers. We predict these from the coalescence of peaks and saddle points in the vicinity of a given larger peak, as one increases the smoothing scale in the initial…
Sweepstakes reproduction refers to a highly skewed individual recruitment success without involving natural selection and may apply to individuals in broadcast spawning populations characterised by Type III survivorship. We consider an…
A coagulation process is studied in a set of random masses, in which two randomly chosen masses and the smallest mass of the set multiplied by some fixed parameter $\omega\in [-1,1]$ are iteratively added. Besides masses (or primary…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…
Knowledge regarding the kinetics of metastatic tumor formation, as related to the growth of the primary tumor, represents a fundamental issue in cancer biology. Using an in vivo mammalian model, we show here that one can obtain useful…
We establish convergence to the Kingman coalescent for the genealogy of a geographically - or otherwise - structured version of the Wright-Fisher population model with fast migration. The new feature is that migration probabilities may…
Consider a structured population consisting of $d$ colonies, with migration rates proportional to a positive parameter $K$. We sample $N_K$ individuals, distributed evenly across the $d$ colonies, and trace their ancestral lineages backward…