From 392a611d547287920c46edbdaa8c2025596c8edb Mon Sep 17 00:00:00 2001 From: bnewbold Date: Wed, 21 May 2014 00:59:10 -0400 Subject: hw02 first attempt --- assignments/hw02/answers.txt | 18 ++++++ assignments/hw02/euler.jl | 29 +++++++++ assignments/hw02/euler.m | 26 ++++++++ assignments/hw02/euler_mod.jl | 143 ++++++++++++++++++++++++++++++++++++++++++ assignments/hw02/quiz2.pdf | Bin 0 -> 531615 bytes 5 files changed, 216 insertions(+) create mode 100644 assignments/hw02/answers.txt create mode 100644 assignments/hw02/euler.jl create mode 100644 assignments/hw02/euler.m create mode 100644 assignments/hw02/euler_mod.jl create mode 100644 assignments/hw02/quiz2.pdf (limited to 'assignments/hw02') diff --git a/assignments/hw02/answers.txt b/assignments/hw02/answers.txt new file mode 100644 index 0000000..f7a287e --- /dev/null +++ b/assignments/hw02/answers.txt @@ -0,0 +1,18 @@ + +Q1: The concentrations of ATP and Glucose never reach a stable steady-state. +Q2: 20.98, 18.66 +Q3: no, no, yes, no +Q4: second choice is the fastest +Q5: first is fastest +Q6: no, no, yes, no +Q7: the last is the damped one (spiral) +Q8: true, false, false, false ("When is higher than 1 no sustained + oscillations will be observed.") +Q9: false, false (decaying), true, false +Q10: true, false, false, false +Q11: false, false, true, false + + +got 2x wrong: Q7 (forgot to select?) + Q4 (typo? forgot to select?) + diff --git a/assignments/hw02/euler.jl b/assignments/hw02/euler.jl new file mode 100644 index 0000000..a9513bf --- /dev/null +++ b/assignments/hw02/euler.jl @@ -0,0 +1,29 @@ + +# Use Euler's method to integrate simple one variable ODE +# Use program as template for more interesting models + +# Note: produces slightly different output compared with +# example shown in class. Different values of b, dt, tlast + +using Winston + +a = 20 +b = 0.5 +c = 5 + +dt = 0.2 +tlast = 20 + +iterations = integer(round(tlast/dt)) +xall = zeros(Float64, (iterations, 1)) + +x = c +for i = 1:iterations + xall[i] = x + dxdt = a - b*x + x = x + dxdt*dt +end + +time = dt*(0:iterations-1)' +figure +plot(time,xall) diff --git a/assignments/hw02/euler.m b/assignments/hw02/euler.m new file mode 100644 index 0000000..1773e6c --- /dev/null +++ b/assignments/hw02/euler.m @@ -0,0 +1,26 @@ +% % Use Euler's method to integrate simple one variable ODE +% % Use program as template for more interesting models + +% % Note: produces slightly different output compared with +% % example shown in class. Different values of b, dt, tlast + +a = 20 ; +b = 0.5 ; +c = 5 ; + +dt = 0.2 ; +tlast = 20 ; % s + +iterations = round(tlast/dt) ; +xall = zeros(iterations,1) ; + +x = c ; +for i = 1:iterations + xall(i) = x ; + dxdt = a - b*x ; + x = x + dxdt*dt ; +end % of this time step + +time = dt*(0:iterations-1)' ; +figure +plot(time,xall) diff --git a/assignments/hw02/euler_mod.jl b/assignments/hw02/euler_mod.jl new file mode 100644 index 0000000..65446d1 --- /dev/null +++ b/assignments/hw02/euler_mod.jl @@ -0,0 +1,143 @@ + +using Winston + +function doPlot(V_in, k_l, k_p, K_m) + + dt = 0.2 + tlast = 1000 + + iterations = integer(round(tlast/dt)) + ATPall = zeros(Float64, (iterations, 1)) + Gall = zeros(Float64, (iterations, 1)) + + ATP = 4 + G = 3 + for i = 1:iterations + ATPall[i] = ATP + Gall[i] = G + + dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m) + dGdt = V_in - k_l * G * ATP + + ATP = ATP + dATPdt * dt + G = G + dGdt * dt + end + + tall = dt*(0:iterations-1)' + figure() + hold(true) + plot(tall, ATPall, color="red") + plot(tall, Gall, color="blue") + hold(false) + xlabel("Time") + + println("max(G) = ", maximum(Gall)) + println("max(ATP) = ", maximum(ATPall)) + # max(G) = 20.97673324771467 + # max(ATP) = 18.65978074314273 + title("") +end + +doPlot(0.36, 0.02, 6, 12.0) + +function doXY(V_in, k_l, k_p, K_m) + + dt = 0.2 + tlast = 1000 + + iterations = integer(round(tlast/dt)) + ATPall = zeros(Float64, (iterations, 1)) + Gall = zeros(Float64, (iterations, 1)) + + ATP = 4 + G = 3 + for i = 1:iterations + ATPall[i] = ATP + Gall[i] = G + + dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m) + dGdt = V_in - k_l * G * ATP + + ATP = ATP + dATPdt * dt + G = G + dGdt * dt + end + + tall = dt*(0:iterations-1)' + figure() + hold(true) + plot(Gall, ATPall, color="red") + hold(false) + xlabel("G") + ylabel("ATP") +end + +function testStability(V_in, k_l, k_p, K_m) + + dt = 0.05 + tlast = 2000 + + iterations = integer(round(tlast/dt)) + ATPall = zeros(Float64, (iterations, 1)) + Gall = zeros(Float64, (iterations, 1)) + + ATP = 4 + G = 3 + for i = 1:iterations + ATPall[i] = ATP + Gall[i] = G + + dATPdt = 2 * k_l * G * ATP - (k_p * ATP) / (ATP + K_m) + dGdt = V_in - k_l * G * ATP + + ATP = ATP + dATPdt * dt + G = G + dGdt * dt + end + + #deltaATP = maximum(ATPall[length(ATPall)/2:end]) - minimum(ATPall[length(ATPall)/2:end]) + #deltaG = maximum(Gall[length(Gall)/2:end]) - minimum(Gall[length(Gall)/2:end]) + #return (deltaATP, deltaG) + return (maximum(ATPall[length(ATPall)/2:end]), + minimum(ATPall[length(ATPall)/2:end]), + maximum(Gall[length(Gall)/2:end]), + minimum(Gall[length(Gall)/2:end]), ) +end + +function doBistable() + x = 0.1:0.05:1.6 + varATP = zeros(length(x)) + varG = zeros(length(x)) + ATP_h = zeros(length(x)) + ATP_l = zeros(length(x)) + G_h = zeros(length(x)) + G_l = zeros(length(x)) + for i=1:length(x) + (a_h, a_l, g_h, g_l) = testStability(x[i], 0.02, 6, 12.0) + varATP[i] = a_h - a_l + varG[i] = g_h - g_l + ATP_h[i] = a_h + ATP_l[i] = a_l + G_h[i] = g_h + G_l[i] = g_l + println((a_h, g_h)) + end + figure() + hold(true) + plot(x, varG, color="blue") + plot(x, varATP, color="red") + xlabel("V_in") + ylabel("Stability") + hold(false) + title("Stability plot") + + figure() + hold(true) + plot(x, G_h, color="blue") + plot(x, G_l, color="blue") + plot(x, ATP_h, color="red") + plot(x, ATP_l, color="red") + xlabel("V_in") + ylabel("Value") + hold(false) + title("Values plot") +end + diff --git a/assignments/hw02/quiz2.pdf b/assignments/hw02/quiz2.pdf new file mode 100644 index 0000000..d35f763 Binary files /dev/null and b/assignments/hw02/quiz2.pdf differ -- cgit v1.2.3