Biomod/2011/Caltech/DeoxyriboNucleicAwesome/Simulation
Saturday, December 16, 2017

SimulationsOverviewOur proposed sorting mechanism depends very heavily on a particular randomwalking mechanism that has not been demonstrated in literature before. The verification of this mechanism is thus a vital step in our research. Verification of the random walk in one dimension is fairly straightforward: as discussed in <LINK TO THE EXPERIMENTAL DESIGN SECTION>, a onedimensional track is easy to construct, and will behave like a standard 1D random walk, showing an average translation on the order of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n^{\frac{1}{2}}} after n steps. Thus, we should expect the time it takes to get to some specific level of fluorescence to be proportional to the square of the number of steps we start the walker from the irreversible substrate. If we can, in an experiment, record the fluorescence over time when the walker is planted at different starting points and show that that fluorescence varies by this relationship, we'll have fairly certainly verified onedimensional random walking. Our particular case of 2D random walking, however, is not as easily understood, especially considering the mobility restrictions (ability to move to only 4 of 6 surrounding locations at any particular time) of our particular walker. As a control for the verification of 2D random walking, though, we still need to get an idea how long the random walk should take, and how that time will change as we start the walker at different points on the origami. We opt to do this by simulating the system with a set of movement rules derived from our design. We also use the same basic simulation (with a few alterations and extra features) to simulate our entire sorting system in a onecargo, onegoal scenario, to give us some rudimentary numbers on how long sorting should take, with one vs multiple walkers. Basic parameters and assumptions:
MATLAB CodeRandomWalk Simulation 