相关论文: Coarsening dynamics of chemotactic aggregates
The Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity $\chi$ of bacteria to the…
Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the "active vertex model" (AVM) exist and yield reasonable agreement with experimental…
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…
The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many instances, processes involving chemical attraction take place in fluids. One of the most studied PDE models of chemotaxis is given by Keller-Segel…
We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and attractant we use a modified Keller-Segel model which accounts attractant absorption. To describe the system we use the chemotaxis…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
The main objective of this article is to study the dynamic transition and pattern formation for chemotactic systems modeled by the Keller-Segel equations. We study chemotactic systems with either rich or moderated stimulant supplies. For…
We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and non-singular) leading to variants of the Keller-Segel model…
The self-diffusion coefficient of a granular gas in the homogeneous cooling state is analyzed near the shearing instability. Using mode-coupling theory, it is shown that the coefficient diverges logarithmically as the instability is…
In micro-swimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
Advection of entities induced by gradients in attractant concentration fields is observed via diffusiophoresis in colloids and via chemotaxis in microorganisms. Mathematically, both diffusiophoresis and chemotaxis follow similar…
A hybrid stochastic individual-based model of proliferating cells with chemotaxis is presented. The model is expressed by a branching diffusion process coupled to a partial differential equation describing concentration of a chemotactic…
We discuss recent progress in the theoretical description of chemotaxis by coupling the diffusion equation of a chemical species to equations describing the motion of sensing microorganisms. In particular, we discuss models for…
We examine coarsening of field-excitation patterns of the sine-Gordon (SG) model, in two and three spatial dimensions, identifying it as universal dynamics near non-thermal fixed points. The SG model is relevant in many different contexts,…
Complex fluids exhibit structure on a wide range of length and time scales, and hierarchical approaches are necessary to investigate all facets of their often unusual properties. The study of idealized coarse-grained models at different…
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…
The simplest prescription for building a patterned structure from its constituents is to add particles, one at a time, to an appropriate template. However, self-organizing molecular and colloidal systems in nature can evolve in much more…
Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange…