Related papers: A full contraction-reaction-diffusion model for pa…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
In this paper the Turing pattern formation mechanism of a two component reaction-diffusion system modeling the Schnakenberg chemical reaction coupled to linear cross-diffusion terms is studied. The linear cross-diffusion terms favors the…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which…
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…
Motor-driven cytoskeletal remodeling in cellular systems can often be accompanied by a diffusive-like effect at local scales, but distinguishing the contributions of the ordering process, such as active contraction of a network, from this…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Organogenesis involves large deformations and complex shape changes that require elaborate mechanical regulation. Models of tissue biomechanics have been introduced to account for the coupling between mechanical response and biochemical…
The bidomain system of degenerate reaction-diffusion equations is a well-established spatial model of electrical activity in cardiac tissue, with "reaction" linked to the cellular action potential and "diffusion" representing current flow…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
We propose a three dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue…
We report new chemoconvective pattern formation phenomena observed in a two-layer system of miscible fluids filling a vertical Hele-Shaw cell. We show both experimentally and theoretically that the concentration-dependent diffusion coupled…
The structure and dynamics of tissue cultures depend strongly on the physical and chemical properties of the underlying substrate. Inspired by previous advances in the context of inorganic materials, the use of patterned culture surfaces…
The mechanosensitivity of cells, which determines how they are able to respond to mechanical signals received from their environment, is crucial for the functioning of all biological systems. In experiments, cells placed on cyclically…