2 The Concepts Developed In This Course Are Broadly Applicable And Can Be Used To Describe Many Systems Outside Of Chem 1 (67.16 KiB) Viewed 36 times
2 The Concepts Developed In This Course Are Broadly Applicable And Can Be Used To Describe Many Systems Outside Of Chem 2 (67.16 KiB) Viewed 36 times
2 The Concepts Developed In This Course Are Broadly Applicable And Can Be Used To Describe Many Systems Outside Of Chem 3 (67.16 KiB) Viewed 36 times
2. The concepts developed in this course are broadly applicable and can be used to describe many systems outside of chemical reactor design. One famous application is the predator- prey problem developed by Alfred Lotka and Vito Volterra in the mid-1920s. Consider an island (that's our system) with two species, foxes (F; the predator) and rabbits (R; the prey). If the population of foxes grows, the population of rabbits will be affected. Therefore, the rate of change of one species population will depend on the other species population. The predator-prey problem assumes the following: - Rabbits only die by being eaten by foxes Foxes die at a constant rate from natural causes And can be described by the following set of coupled ordinary differential equations: dR = kR-k RF di dF =k,RF-k F dt Where k = constant for growth of rabbits; k2 = constant for death of rabbits, k3 = constant for growth of foxes after eating rabbits, k4 = constant for death of foxes (a) What are the units of ki, k2, k3, and k4? (b) If there are initially 500 rabbits and 200 foxes on the island, use Matlab or any other software to solve the system numerically and plot the concentration of foxes and rabbits as a function of time for up to 800 days. Assume the following values for the rate constants: ki = 0.02, k2 = 0.00004, k3 = 0.00004, k4 = 0.04. (e) Plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do.
2. The concepts developed in this course are broadly applicable and can be used to describe many systems outside of chemical reactor design. One famous application is the predator- prey problem developed by Alfred Lotka and Vito Volterra in the mid-1920s. Consider an island (that's our system) with two species, foxes (F; the predator) and rabbits (R; the prey). If the population of foxes grows, the population of rabbits will be affected. Therefore, the rate of change of one species population will depend on the other species population. The predator-prey problem assumes the following: - Rabbits only die by being eaten by foxes Foxes die at a constant rate from natural causes And can be described by the following set of coupled ordinary differential equations: dR = kR-k RF di dF =k,RF-k F dt Where k = constant for growth of rabbits; k2 = constant for death of rabbits, k3 = constant for growth of foxes after eating rabbits, k4 = constant for death of foxes (a) What are the units of ki, k2, k3, and k4? (b) If there are initially 500 rabbits and 200 foxes on the island, use Matlab or any other software to solve the system numerically and plot the concentration of foxes and rabbits as a function of time for up to 800 days. Assume the following values for the rate constants: ki = 0.02, k2 = 0.00004, k3 = 0.00004, k4 = 0.04. (e) Plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do.
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