Using ratio and proportion, I have replicated Onnes' remarkable graph that gave birth to superconductivity.
Figure 1. Superconductivity of mercury [Source]
Figure 2. Pixel conversion. Note the axes offsets. I have normalized the origin to (0,0)
Figure 3. Axes' best-fit lines
From these equations, I have replicated the 6 data points of the original graph. With these, I have obtained the corresponding slopes per division, corresponding to: Normal, Transition and Superconducting (SC) states of the graph.
Figure 4. Linear fitting of the various regions. Normal state is the region with a linear resistance (T>~4.22K), Transition state is the region of greatest resistance change (dashed lines) and the Superconducting state is the region of very low resistance (T<4.2K)
I had problems with the SC region. This is due to the constant in the line equation, which means that my line can have negative values. Rethinking, I have abandoned the use of the line equation and placed a value of zero for temperatures lower than 4.2K in my graph. This decision came from thinking that realistically speaking, resistance values approaches zero for superconductors. The line equation gave erroneous data points at this region due to the limited amount of original data points that I have used to obtain it. Had the original graph been log scaled, this would've been clearer as the actual resolution of the graph is limited by pen and paper.
Figure 5. Overlay of the simulated graph(blue, step size=0.01) with the original graph image (black + points)
The final result is considerably good as we can see from Fig. 5. The Normal state deviation can be attributed to the regression of the line fit. Also, the Transition state is clearly exact due to the fact that it contains only 2 points at that region. Onnes' graph is a very simple scatter plot, as such, I have used linear fit lines to add more points for my replication.
Simple but quite arduous.
Self-Assessment: 10/10
Self-Assessment: 10/10
No comments:
Post a Comment