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The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…
Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…
Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered from the point of view of interface motion. A dissipative nonlocal equation of motion for the boundary between high and low…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Diffusion-limited association reactions are ubiquitous in nature. They are particularly important for biological reactions, where the reaction rates are often determined by the diffusive transport of the molecules on two-dimensional…
Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
This paper is concerned with a reaction-diffusion single species model with harvesting on $n$-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a…
Diffusion models excel at generation, but their latent spaces are high dimensional and not explicitly organized for interpretation or control. We introduce ConDA (Contrastive Diffusion Alignment), a plug-and-play geometry layer that applies…