Related papers: La ecuaci\'on de Keller-Segel
The Brownian dynamics of a single microorganism coupled by chemotaxis to a diffusing concentration field which is secreted by the microorganism itself is studied by computer simulations in spatial dimensions $d=1,2,3$. Both cases of a…
Cooperative search games are collective tasks where all agents share the same goal of reaching a target in the shortest time while limiting energy expenditure and avoiding collisions. Here we show that the equations that characterize the…
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel model. The model we study has the same entropy as the…
Escherichia coli has long been used as a model organism due to the extensive experimental characterization of its pathways and molecular components. Take chemotaxis as an example, which allows bacteria to sense and swim in response to…
Chemotaxis is the response of a particle to a gradient in the chemical composition of the environment. While it was originally observed for biological organisms, it is of great interest in the context of synthetic active particles such as…
This paper is concerned with a parabolic-elliptic Keller-Segel system where both diffusive and chemotactic coefficients (motility functions) depend on the chemical signal density. This system was originally proposed by Keller and Segel in…
In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for…
In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive…
The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, a new fully discrete scheme for this model was proposed in [46], mass conservation, positivity and energy decay were proved for the proposed scheme,…
Active matter systems comprise self-propelled particles that move on a substrate while leaving chemical trails that influence other particles through chemotaxis (e.g., slime-depositing bacteria). Orientational chemotaxis manifests as a…
Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of…
A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both…
To describe the cellular self-aggregation phenomenon, some strongly coupled PDEs named as Keller-Segel (KS) and Patlak-Keller-Segel (PKS) systems were proposed in 1970s. Since KS and PKS systems possess relatively simple structures but…
The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in…
We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a…
We compare chemotaxis, the migration of cells and higher animals in reaction to a chemical stimulus, and similar phenomena originating within gases from temperature differences. Then we explain two easy mathematical models for handling…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions. One example is the immune system signalling, where infected tissues release chemokines…
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system \begin{equation}\tag{$\ast$} \label{ks0} \left\{ \begin{aligned} u_t =&\; \Delta u - \nabla \cdot(u \nabla v) \quad in {\mathbb R}^2\times(0,\infty),\\ v…
This article studies the aggregation diffusion equation \[ \partial_t\rho = \Delta^\frac{\alpha}{2} \rho + \lambda\,\mathrm{div}((K*\rho)\rho), \] where $\Delta^\frac{\alpha}{2}$ denotes the fractional Laplacian and $K =…
A stochastic walker model is proposed to describe the chemotactic guidance of growth cones, i.e. the tips of developing neurites. The model accounts for the influence of both attractive and repulsive chemical cues, which are emitted by the…