Chapter 16, Problem 16.31P

Given the following reaction system, where Xo is the input, i.e u(t) = k₁ × Xo: $Xo -> x1; k1*Xo x2; k2*x1 x1 2 x2 ->%; k3*x2^2 x2 ->; k4*x2 Xo 1; k1 = 0.4 k2 4.5; k3 = 0.75 k4= 0.2 a) Build the model in Tellurium and run a simulation. Compute the Jacobian at steady state using the method getFull Jacobian(). Make sure you are at steady state! b) Write out the values for n and p c) Write out the differential equations. d) Write out the state space representation in terms of the rate constants etc. e) Compute the values in the Jacobian matrix from d) by substituting the values of the rate constants etc and any data you need from the simulation. f) Confirm that the Jacobian you get in e) is the same as the one computed from the simulation in a). g) Is the system stable or not? If you find an eigenvalue of zero, that means the system is marginally stable. You can get the eigenvalues using the tellurium method r.getFullEigenvalues()

Solve by Pen and Paper not using chatgpt or AI

You just got a job at Shin-Etsu Chemical growing Si crystals with different dopants. Howmuch Ga needs to be added to 800 kg of Si melt to achieve a 5-10 Ω.cm (measured at midheight) Si CZ crystal with the following characteristics: height: 7 ft, width: 12 inchesdiameter. Assume, angular rotation 10 RPM, melt viscosity 0.1 poise, pull velocity 2mm/min.a. Generate a plot of the doping distribution throughout the length of the crystal (CGa vs. fs ).b. If a second crystal were to be pulled out of the melt without replenishment of silicon nordopant what would be the average resistivity of this crystal (or resistivity at mid height)