Decomposition Modeling

Schrick-Noah_Homework-3.R

@@ -329,7 +329,54 @@ sir.ode.sol.b <- ode45(f = function(t,y){sir.f(t,y,k=sir.params.b)},
 plot.sir(sir.ode.sol.b, "ODE45 with a=3")
 
 ## 6. Decomp of dinitrogen pentoxygen into nitrogen dioxide and molecular oxygen
+decomp.f <- function(t, y, k) {
+  dA <- -k[1]*y[1] + k[2]* y[2]*y[4]
+  dB <- k[1]*y[1] - k[2]*y[2]*y[4] + 2*k[4]*y[4]*y[5]
+  dC <- k[3]*y[2]*y[4]
+  dD <- k[1]*y[1] - k[2]*y[2]*y[4] - k[3]*y[2]*y[4] - k[4]*y[4]*y[5]
+  dE <- k[3]*y[2]*y[4] - k[4]*y[4]*y[5]
+  return(as.matrix(c(dA, dB, dC, dD, dE)))
+}
 
 # a) k1=1.0, k2=0.5, k3=0.2,k4=1.5, [N2O5]o=1, all other IC's=0, t=0 -> 10
+decomp.params <- c(1.0, 0.5, 0.2, 1.5)
+A0 <- 1
+B0 <- 0; C0 <- 0; D0 <- 0; E0 <- 0
+tmin <- 0
+tmax <- 10
 
-# b) Increase k4 to make the intermediate species -> 0
+decomp.ode.sol <- ode45(f = function(t,y){decomp.f(t,y,k=decomp.params)},
+                     y = c(A0, B0, C0, D0, E0),
+                     t0 = tmin, tfinal = tmax)
+
+# plot
+plot.decomp <- function(sol, method){
+  # - pred/prey columns melted to 1 column called "value" 
+  sol.melted <- melt(data.frame(time=sol$t,
+                                N2O5=sol$y[,1],
+                                NO2=sol$y[,2],
+                                O2=sol$y[,3],
+                                NO3=sol$y[,4],
+                                NO=sol$y[,5]),
+                     id = "time") # melt based on time
+  # New column created with variable names, called “variable”
+  colnames(sol.melted)[2] <- "Group" # used in legend  
+  
+  g <- ggplot(data = sol.melted, 
+              aes(x = time, y = value, color = Group))
+  g <- g + geom_point(size=2) 
+  g <- g + xlab("time [seconds]") +  ylab("Concentration") 
+  g <- g + ggtitle(paste("Decomposition Model Using", method))  
+  show(g)
+}
+
+plot.decomp(decomp.ode.sol, "ODE45")
+
+# b) Increase k4 to make the intermediate species -> 0
+k4 <- 10
+decomp.params.b <- c(1.0, 0.5, 0.2, k4)
+decomp.ode.sol.b <- ode45(f = function(t,y){decomp.f(t,y,k=decomp.params.b)},
+                        y = c(A0, B0, C0, D0, E0),
+                        t0 = tmin, tfinal = 100)
+plot.decomp(decomp.ode.sol.b, paste("ODE45 Using k4 =", k4))
+decomp.ode.sol.b$y[,5]