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The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. [2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo. [3]
A Turing bifurcation pattern An example of a natural Turing pattern on a giant pufferfish. The original theory, a reaction–diffusion theory of morphogenesis, has served as an important model in theoretical biology. [6] Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation.
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
Diffusion is of fundamental importance in many disciplines of physics, chemistry, and biology. Some example applications of diffusion: Sintering to produce solid materials (powder metallurgy, production of ceramics) Chemical reactor design; Catalyst design in chemical industry; Steel can be diffused (e.g., with carbon or nitrogen) to modify its ...
The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, statistics, data science, and finance (diffusion of people, ideas, data and price values). The central idea of diffusion, however, is common to all of these: a substance or collection undergoing diffusion ...
Make-A-Video (2022) is a text-to-video diffusion model. [74] [75] CM3leon (2023) is not a diffusion model, but an autoregressive causally masked Transformer, with mostly the same architecture as LLaMa-2. [76] [77] Transfusion architectural diagram. Transfusion (2024) is a Transformer that combines autoregressive text generation and denoising ...
Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems. Brownian motion , reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes.
Possible mechanisms of pattern formation in biological systems include the classical reaction–diffusion model proposed by Alan Turing [10] and the more recently found elastic instability mechanism which is thought to be responsible for the fold patterns on the cerebral cortex of higher animals, among other things.
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