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

wiggle_1

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.
  • 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.

wiggle_2

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Written on February 23, 2015