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Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We study the growth of a population of bacteria in a dynamical hostile environment corresponding to the immune system of the colonised organism. The immune cells evolve as subcritical open clusters of oriented percolation and are…
Nutrient gradients and limitations play a pivotal role in the life of all microbes, both in their natural habitat as well as in artificial, microfluidic systems. Spatial concentration gradients of nutrients in densely packed cell…
This paper introduces a reaction-diffusion-chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (J. of Theor.…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
Colonies of rod-shaped bacteria constitute a system of colloidal active matter with nematic properties. As a single initial bacterium multiplies through repeated divisions, the resulting colony quickly loses long-range orientational order,…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape…
Hybrid models of chemotaxis combine agent-based models of cells with partial differential equation models of extracellular chemical signals. In this paper, travelling wave properties of hybrid models of bacterial chemotaxis are…
Models based on surfactant driven instabilities have been employed to describe pattern formation by swarming bacteria. However, by definition, such models cannot account for the effect of bacterial sensing and decision making. Here we…
The diffusion of particles in complex media has gained significant interest due to its dual relevance: probing the viscoelastic properties of materials via microrheology and assessing the extent of particle displacement over time. In this…
Bacterial colonies are abundant on living and nonliving surfaces and are known to mediate a broad range of processes in ecology, medicine, and industry. Although extensively researched, from single cells to demographic scales, a…
Dispersal of species is a fundamental ecological process in the evolution and maintenance of biodiversity. Limited control over ecological parameters has hindered progress in understanding of what enables species to colonise new area, as…
In this article a kinetic model for the dynamics of myxobacteria colonies on flat surfaces is investigated. The model is based on the kinetic equation for collective bacteria dynamics introduced in arXiv:2001.02711, which is based on the…
Directed Percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state (fixation). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect of the initial attractant distribution on bacterial…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular…
We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a…
During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially or simultaneously. These growth patterns are manifested in all types of bacteria and yeasts. The ubiquity of these growth…