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Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics , probability theory , information theory , neural networks , finance ...
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.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
If there is a change in the potential energy of a system; for example μ 1 >μ 2 (μ is Chemical potential) an energy flow will occur from S 1 to S 2, because nature always prefers low energy and maximum entropy. Molecular diffusion is typically described mathematically using Fick's laws of diffusion.
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 ...
Tracer diffusion describes the motion of individual adparticles on a surface at relatively low coverage levels. At these low levels (< 0.01 monolayer), particle interaction is low and each particle can be considered to move independently of the others. The single atom diffusing in figure 1 is a nice example of tracer diffusion.
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Expansion diffusion: an innovation or idea that develops in a source area and remains strong there, while also spreading outward to other areas. This can include hierarchical, stimulus, and contagious diffusion. Relocation diffusion: an idea or innovation that migrates into new areas, leaving behind its origin or source of the cultural trait.