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In addition, an example with diffusion and chemical removal modelled by a non-linear PDE and three-dimensional diffusion equation is given.
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Numerical examples dealing with diffusion and convection are given.
For example, Chen and Wang [14] studied system (1.3) with diffusion under homogeneous Neumann boundary conditions, while Peng and Wang [15] focused on system (1.3) with diffusion under homogeneous Dirichlet boundary conditions.
As an example, the algorithm is applied to the pair contact process with diffusion (PCPD).
Open image in new window Fig. 1 Example of diffusion maps in an animal with streptozotocin-induced diabetes mellitus (DM) and a control animal.
Abnormal and inadequate vasculature coupled with diffusion limitation results in reduced availability of nutrients, for example glucose and oxygen (Jain, 1988; Vaupel et al, 1989).
For example, it is possible to derive a closed expression for the wavenumber dependency with diffusion constants and the derivative of the linear reaction terms.
In order to demonstrate the learning process of an HMM with diffusion maps, we take a simple HMM with 3 states as an example.
As an example, a diffusion process is approximated by a state space discrete time model with n compartments in the spatial plane and is then reparametrized.
For example, the famous Turing instability was observed in many nature processes, and it was also proved in some mathematical models with diffusion.
8.2 Tube Flows with Diffusion.
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