# Stretchable Cells

### Simulation Set-up

- Reflective boundary on the left.
- Absorbing boundary on the right.
- Cells are always connected, cells may stretch and contract.
- The number of cells is varied.
- The amount by which a cell can stretch is varied.
`cellstretch`

refers to the maximum number of additional lattice points a cell may occupy.

- Cells are initialized along the reflective boundary and all only occupy one lattice point.

## Mean First Passage Time

**Hypothesis**

- The mean passage time will increase exponentially as the number of cells in the simulation increases.
- The strength of the exponential will decrease if the cells are allowed to stretch more.

### Results

The box indicates the value of `cellstretch`

for that set of data.

- In the one cell case we recover the same result as the single cell diffusion simulations. The mean passage time is time steps.
- For to our hypothesis seems to be on the right track.
- I am unsure as to the cause of the kink in the exponential increase which occurs at for all cases.
- I believe it has something to do with the fundamental difference between 1 and multiple cell diffusion. When then the cells must stay connected and diffuse together whereas in the 1 cell case there is no such constraint.

- I am unsure as to the cause of the kink in the exponential increase which occurs at for all cases.
- Our hypothesis that increasing
`cellstretch`

will decrease the strength of the exponential increase is incorrect.- I am surprised by how the benefit of being able to stretch more quickly decreases.

Below is the relative decrease in mean passage time with respect to the `cellstretch = 2`

case.

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Written on February 23, 2015