Related papers: The coalescing colony model: mean-field, scaling, …
We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r=0, this reduces to the study of a single…
We consider an expanding population on the plane. The genealogy of a sample from the population is modelled by coalescing Brownian motion on the circle. We establish a weak law of large numbers for the site frequency spectrum in this model.…
To understand how the mechanical properties of tissues emerge from interactions of multiple cells, we measure traction stresses of cohesive colonies of 1-27 cells adherent to soft substrates. We find that traction stresses are generally…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
We propose a one-way coupled model that tracks individual primary particles in a conceptually simple cellular flow setup to predict flocculation in turbulence. This computationally efficient model accounts for Stokes drag, lubrication,…
The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical…
The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do…
We use a general circulation model to study the three-dimensional (3-D) flow and temperature distributions of atmospheres on tidally synchronized extrasolar planets. In this work, we focus on the sensitivity of the evolution to the initial…
Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model…
We study the spatial evolutionary dynamics of solid tumors as they obtain additional driver mutations. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
Turbulence in growth of rain droplets and rain formation is studied under an approximating particle system representing aggregation at the level of individuals, depending on their volume and distance in space, of the Smoluchowski…
Many species live in colonies that thrive for a while and then collapse. Upon collapse very few individuals survive. The survivors start new colonies at other sites that thrive until they collapse, and so on. We introduce spatial and…
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a…
Various bacterial strains (e.g. strains belonging to the genera Bacillus, Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns during growth on poor semi-solid substrates. These patterns reflect the bacterial…
Time evolutions of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…