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Revision as of 16:06, 24 October 2017
This year, our team creates a mathematical representation of our concrete self-healing system. This representation, or model, constructs a judging scale in which we can utilize to regulate the four main environmental factors affecting our final concrete healing rate (reflected on mineralization activity).
The four factors are:
This modeling process, presented below, can be seen as a feedback between the wet lab (experiment result) and the dry lab(statistic analysis).
The following page shows how we conducted modelling approaches to achieve our goals.To begin with, we make some declaration.
Procedure:
1.Standardizing variables: transformed variables are of the same scale. Here we utilize the z-score standardizing method.
2.Fitting functions of each variable with polynomial function.
3.Getting the overall relationship using linear least square method.
Results:
The graph above depicts the polynomial regression of each 4 factors. In general, they each present a tendency for Mineralization activity of rise first and decline later with the growth of each factor.
Using the iteration of x into each 4 functions above, then fit x with y linealy to get the overall regression equation descrbing each four variables weight.
Overall regression equation:
From this equation, we can see that nitrogen source has the maximum weight, and pH has the minimum weight, which means nitrogen source is the most essential nutrition for B.subtilis spore. Also, the low weight of pH shows the spore is not sensitive to the change of pH, although there is a sharp decline of activity when pH reaches 11.
That is to say, as long as we keep the environment below the boundary high-pH point, it makes no much difference how much we have improved the alkaline resistance of B.subtilis spore. In this way, the modeling instructs us on more appropriate spore micro-environment equipment.
The four factors are:
Based on this model, we can also design the best‘package'– the vesicle shell with adequate nutrition combination.
This modeling process, presented below, can be seen as a feedback between the wet lab (experiment result) and the dry lab(statistic analysis).
The following page shows how we conducted modelling approaches to achieve our goals.To begin with, we make some declaration.
- Variables and nomenclature:
- concentration of spores - c[Spore]
- concentration of carbon source(C3H5O3Na) - c[C3H5O3Na]
- concentration of nitrogen source(NaNO3) - c[NaNO3]
- pH of the media - pH
- Goal of model
- Use preliminary data to guide future experiment conditions and predict results.
1.Standardizing variables: transformed variables are of the same scale. Here we utilize the z-score standardizing method.
2.Fitting functions of each variable with polynomial function.
3.Getting the overall relationship using linear least square method.
Using the iteration of x into each 4 functions above, then fit x with y linealy to get the overall regression equation descrbing each four variables weight.
That is to say, as long as we keep the environment below the boundary high-pH point, it makes no much difference how much we have improved the alkaline resistance of B.subtilis spore. In this way, the modeling instructs us on more appropriate spore micro-environment equipment.
