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While the fractional space derivatives are used to model irregular diffusion or dispersion, where a particle follow spreads at a rate not in agreement with the classical Brownian motion model, and the follow can be asymmetric [1 3].
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Fractional time derivatives are linked with irregular sub-diffusion, where a darken of particles spreads more slowly than a classical diffusion.
We are also able to track the movement of individual grains during deformation and our results show that, in an irregular grain structure, diffusion creep may cause significant grain rotation.
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step.
We present a numerical method for simulating diffusion dominated phenomena on irregular domains and free moving boundaries with Robin boundary conditions on quadtree/octree adaptive meshes.
To reduce computational cost, a modified additive operator splitting (AOS) algorithm is developed to address diffusion equations defined on irregular domains and multi-initial scheme is used to speed up the convergence rate.
The concepts of percolation theory closely coupled with computer constructs and mathematical modelling provide potent tools for understanding the role of irregular morphology in transient reaction and diffusion processes in disordered composites.
Other irregular patterns are observed in local diffusion barriers, such as gaps within the bands forming radial alleys free of precipitate, transition from bands to speckled patterns and links between the bands called anastomoses [26].
The irregular porous structure allowed for the easy diffusion of the electrolyte into the inner region of the electrode.
Further, this approach can be easily adapted to handle complex nonlinear convection-diffusion processes regardless of how irregular the domain geometry might be.
From the perspective of molecular dynamics, gas diffusion is actually the result of irregular thermal motion of gas molecules.
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