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We are interested in comparing our computer-generated results with those of an actual experiment. The experimental results are reported in an unpublished paper entitled "Mirror Image Method: A simple technique for tracking 3D motion of a colloidal particle using digital video microscopy" by C.H. Sow, T.S. Sullivan, J. Aizenberg, J.E. Cerise, and C.A. Murray. Our purpose is to verify the method used in the paper to determine the diffusion coefficient Do.

Initially, we altered bsumsci2.c so that its parameters matched those of the experiments. The number of time steps taken was changed from 80,000 to 76,000, and the temperature was decreased to 264 K (The temperature was changed so that the diffusivity of the system would equal to 6.18 x 10-13 m-13, to match the experiment). In the experiment, the cell was so small that hydrodynamic corrections to the theory are expected to be significant. Our simulation does not yet take into account these corrections, so we used the artificial method of changing the temperature to match the simulated and experimental diffusion coefficients. The radius of the colloid particle and the viscosity of fluid remain unchanged from the 'Program Validation' page. bsumsci2.c was then run eight times, each run creating a data set comparable to that obtained in the experiment. Each output file contains particle displacements during a given time interval, from one to eight video frames. The expectation is that these displacements will be normally distributed (see the Theory page). If we then fit these distributions to

we expect that if we plot w2 vs. τ we will get a linear graph since w2=4Doτ. Thus we can get Do from a fit to the slope of these plots.

The following table gives the data produced by bumsci2.c and analyzed by Origin and a portion of the LabTalk script, slopes.ogs for eight displacement files.

τ (s) w (m) w2(τ) (m)2

0.03333

2.9141x10-7

8.49198x10-14
0.06667 4.0339x10-7 1.62723x10-13
0.10000 5.0056x10-7 2.5056x10-13
0.13333 5.7651x10-7 3.32364x10-13
0.16667 6.3348x10-7 4.01297x10-13
0.20000 7.0886x10-7 5.02482x10-13
2.3333 7.5812x10-7 5.74746x10-13
0.26667 8.1447x10-7 6.63361x10-13

The graph below was generated using the above w2 and τ data.

As in the experiments, we see an excellent fit to a linear relationship. The slope of this linear fit is (2.476 +/- 0.02839) x 10-12 (m2), compared to the expected value(4*Do) of 2.472 x 10-12 m2. The intercept of (0.1005 +/- 4.779) x 10-15 is equal to its expected value of zero within its uncertainty as well. Thus, we conclude that this analysis method gives an accurate value for Do. The above process was then repeated five times, with complete results given on the 'Program Results' page.

Two other trials of the same data can also been seen in this section. When fitting our equation to the histograms produced by the delt files, it is necessary to either fix the values of the four variables or allow them to vary. The 'Program Results' section illustrates the results of two variations from analysis done used in the experiment. These results, which attempted to reproduced the experiment, held y0 fixed at zero, while allowing w, A and xc to vary. In running multiple trials while altering variable conditions allows us to determine which method of analysis is best in comparison to the experiment and theory.