Diffusion in a polymeric environment

Bachelor thesis (2017)

Authors

P.B. Donkers Electrical Engineering, Mathematics and Computer Science

Contributors

J.L.A. Dubbeldam (supervisor 1)
A.M. Dogterom (supervisor 1)
T. Idema (supervisor 2)
F.H.J. Redig (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Polymer Diffusion Active Boundary conditions
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Published Date

03-07-2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

Cells of the most common organisms like plants and animals are filled with polymeric networks that fulfil important functions of the cell. There is however no analytically solvable model that describes diffusion in such a cell. This thesis presents a model for diffusion in polymeric environments, and some predictions about the behaviour of the model are made and confirmed by simulations.
Furthermore, the Fokker-Planck equation of this problem is studied, in order to solve the problem. Certain approximations are presented and solved, and it is investigated when the approximations are sound. Moreover, a method is described that can derive a solution to an equation with certain boundary conditions, from a solution to the same equation with different boundary conditions. This thesis also shows how this novel method can be applied to this model to find a non-approximated solution to the equation, where this was not
possible without this method. Finally, it is described how a multitude of partial differential equations that are linked to each other via the boundary conditions can be solved, can be solved using the method described.