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I replicated Figure 7 of the paper “Static response of miniature capacitive pressure sensors with square or rectangular silicon diaphragm” by G. Blasquez, Y. Naciri, P. Blondel, N. Ben Moussa and P. Pons. We can conclude from the figure that square sensors are more sensitive devices.

Response of square and rectangular sensors

Figure by LauraMabel	Figure from the paper

I numerically computed the first derivative of the following function at interior points using different methods, in an uniform grid of points. Also, I found the average of the absolute error of the predicted first derivative for all the interior points, providing the best prediction.

• Piecewise quadratic spline functions that represent the function
• 1st order forward scheme
• 2nd central difference
• Padé approximation

Plot of results for each approach along with the exact solution.

I made the following derivation of the two-dimensional (2D) Burgers equation, which is a non-linear model of the convection-diffusion process.

The discretized derivation is done using the second-order central difference (CD) for the spatial derivatives, and Crank-Nicolson (CN) for the time advancement. CN method combine the stability of an implicit method with the accuracy of a method that is second-order both in space and in time, and is achieved by averaging explicit FTCS (Forward-Time-Centered-Space) and implicit BTCS (Backward in Time, Centered in Space) schemes.

Figure by LauraMabel	Figure from the book

I calculated of the thermal conductivity along a copper film with various thicknesses: d = 400, 100 and 50 nm at 300 K. This plot illustrates the size dependence of the effective thermal conductivity, using the size-effect effective conductivity based on Kn number and. The obtained plot is very similar to Figure 5.17 of the book “Nano/Microscale Heat Transfer”, Zhuomin M. Zhang, McGraw-Hill, page 175.

Won Dallas Go Green North America Semi-Finals Schneider Electric.