The Mathematics of Diffusion¶
Crank, J. (1975). The Mathematics of Diffusion. Oxford University Press.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Asymmetric Flux
- Where a symmetric Fickian diffusion would yield zero net flux at equal concentrations, an asymmetric boundary yields net flux in the favoured direction even at equal concentrations
This sourceCanonical treatment of Fickian diffusion, where flux is proportional to the concentration gradient and net flux vanishes at equal concentrations across a symmetric boundary.
- Where a symmetric Fickian diffusion would yield zero net flux at equal concentrations, an asymmetric boundary yields net flux in the favoured direction even at equal concentrations
- Diffusion
- Crank's
This sourceComprehensive analytical and numerical treatment of linear and nonlinear diffusion equations; standard reference for exact solutions, steady-state, transient, and moving-boundary problems.
- Crank's
- Signal Decay and Fadeout
- These are precisely the parameter-extraction questions Crank (1975) treats systematically in the canonical mathematics-of-diffusion framework, where boundary conditions and characteristic timescales are read directly from the governing decay equations.
This sourceComprehensive analytical and numerical treatment of linear and nonlinear diffusion equations; standard reference for exact solutions and mathematical methods; covers steady-state, transient, and moving-boundary problems. Crank mathematical treatment, diffusion equation methods, analytical solutions, numerical techniques, nonlinear diffusion.
- These are precisely the parameter-extraction questions Crank (1975) treats systematically in the canonical mathematics-of-diffusion framework, where boundary conditions and characteristic timescales are read directly from the governing decay equations.
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