| 7.1 |
One-dimensional formulation |
| 7.1.1 |
Conservation in one dimension |
| 7.1.2 |
Fick's law of diffusion |
| 7.1.3 |
Advection |
| 7.1.4 |
Flux of ions in a field |
| 7.1.5 |
The cable equation |
| 7.1.6 |
Boundary and initial conditions |
| 7.2 |
Important examples with analytic solutions |
| 7.2.1 |
Diffusion through a membrane |
| 7.2.2 |
Ion flux through a channel |
| 7.2.3 |
Voltage clamping |
| 7.2.4 |
Diffusion in a long dendrite |
| 7.2.5 |
Diffusion into a capillary |
| 7.3 |
Numerical solution of the diffusion equation |
| 7.4 |
Multidimensional problems |
| 7.4.1 |
Conservation law in multiple dimensions |
| 7.4.2 |
Fick's law in multiple dimensions |
| 7.4.3 |
Advection in multiple dimensions |
| 7.4.4 |
Boundary and initial conditions for multiple dimensions |
| 7.4.5 |
Diffusion in multiple dimensions: symmetry |
| 7.5 |
Traveling waves in nonlinear reaction-difusion equations |
| 7.5.1 |
Traveling wave solutions |
| 7.5.2 |
Traveling wave in the Fitzhugh-Nagumo equations |
| 7.6 |
Exercises |
