Related papers: Proteus mirabilis swarm-colony development with dr…
We study the clustering of a model cyanobacterium \textit{Synechocystis} into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness, and interact with the others by aggregation and detachment. We find that…
A recent experiment [Sadoon AA, Wang Y. 2018 Phys. Rev. E 98, 042411] has revealed that nucleoid associated proteins (i.e., DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion…
We present a mean field model for the phase diagram of a community of micro-organisms, interacting through their metabolism so that they are, in effect, engaging in a cooperative social game. We show that as a function of the concentration…
The concept of cross diffusion is applied to some biological systems. The conditions for persistence and Turing instability in the presence of cross diffusion are derived. Many examples including: predator-prey, epidemics (with and without…
In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the…
Predicting evolution of expanding populations is critical to control biological threats such as invasive species and cancer metastasis. Expansion is primarily driven by reproduction and dispersal, but nature abounds with examples of…
We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than what is required for Holder continuity of the solutions, we…
A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d>1 dimensions the phase diagram displays an extended region where both species coexist,…
Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven…
Propagating interfaces are ubiquitous in nature, underlying instabilities and pattern formation in biology and material science. Physical principles governing interface growth are well understood in passive settings; however, our…
Segregation of populations is a key question in evolution theory. One important aspect is the relation between spatial organization and the population's composition. Here we study a specific example -- sectors in expanding bacterial…
We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type…
It has been experimentally shown that Brownian motion and active forward drift controlled by quorum sensing is sufficient to produce clustering behavior in orientable Janus particles. This paper explores the group formation and cohesion of…
A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
Aerial displays of starlings (Sturnus vulgaris) at their communal roosts are complex: thousands of individuals form multiple flocks which are continually changing shape and density, while splitting and merging. To understand these complex…
We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide…
Predicting Pandemic evolution involves complex modeling challenges, often requiring detailed discrete mathematics executed on large volumes of epidemiological data. Differential equations have the advantage of offering smooth, well-behaved…
In this paper we study the following one-dimensional reaction-diffusion problem $$ u_t+(-\Delta)^s u=f(x-c t, u) \;\:\textrm{ in } \mathbb{R}\times (0,+\infty), $$ where $s>\frac{1}{2}$, $c \in \mathbb{R}$ is a prescribed velocity, and $f$…
Experimental studies of microbial communities routinely reveal that they have multiple stable states. While each of these states is generally resilient, certain perturbations such as antibiotics, probiotics and diet shifts, result in…