上海交通大学python期末大作业题目(姚天昉)(2)

Choose a random molecule (remember, the demon cannot be chosen here)

Generate a random number between -Dv and Dv, where Dv is the velocity corresponding to 10% of the total system energy divided by N. Thus, Dv = sqrt(2 * totalEnergy / N / 10).

Calculate the change in energy. Since we use unit mass (m = 1), the change in energy is deltaEnergy = vNew² / 2 - vOld² / 2.

If the change in energy is valid, then accept the change in velocity for that molecule. Remember that the change in energy is valid as long as the resulting demon energy is non-negative. Because not every change is legal, every iteration may not change N molecules, even though it executes N trials.

The demon and system energies must be updated to use in the next trial. However, since we must generate visuals for the next part of the project, we need to record these values in a list to keep track of the value at each iteration (not trial).

Calculate the average system energy and return it.

Experiments for the Ideal Gas Simulation

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First, write and test the function ideal_gas. Note that in this project you will be handing in the function and the experimental work at the same time. Test the function ideal_gas with small values of N and small values of step. You won't know that you are computing the correct quantities until you generate the plots described next. Test the function with both initial system states.

Your experimental work should consider systems with N= 50 to 500, with an increment of 50. For each N, run the function ideal_gas with steps = 3000 and totalEnergy = 500. Each experiment should be done for each of the two initial system states.

The simulation can use MatPlotLib or VPython. Warning: If you use VPython, you should remove all traces of MatPlotLib from the skeleton code. The two have not been known to play well together. A starting point for the varying values of N is provided in the main of the skeleton code. This part of the project requires you to write code to draw two graphs and two histograms.

The main of the simulation uses the values returned by ideal_gas to generate the graph N_versus_Energy. The value returned by the function ideal_gas represents the average system energy of a simulation with particular value of N. You should graph the average system energy on the y-axis and N on the x-axis. In the same plot, show the total system energy in a different color (in the required experiment it is 500 for every value of N). You can generate the plot after the entire simulation or generate it incrementally after ideal_gas returns a value. Here is an example

plot. nvsenergy1.png

The ideal_gas function should generate two histograms and one graph. Whether and when these plots are generated is determined by the fifth parameter (visuals) of ideal_gas. For example, ideal_gas(N, 500, 3000, 2, N==500) will generate plots only when N=500 and start in initial state

2. Note that omitting the 5th argument will plot every time ideal_gas is called.

Histogram Final_Molecule_Velocity uses the values of the N molecule velocities after steps iterations of ideal_gas (i.e., the values just before ideal_gas returns). Plot the velocities on x-axis and their frequencies on y-axis. You should use the signed velocities and 0 is thus in the center of the x-axis. You should experiment with the most appropriate number of bins. Here is an example plot. velocitydistr1.png

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Histogram Demon_Energy generates a histogram of the observed demon energy. The plot is generated after the steps of ideal_gas are completed. The demon energy is recorded after each simulation step (using a list or array of size step). Show the demon energies on the x-axis and their frequencies on the y-axis. Again, select an appropriate number of bins. Here is an example plot.

demonenergy1.png

Graph Demon_Energy_Time shows the steps demon energies over time. The graph has values from 1 to steps on the x-axis and the corresponding demon energies on the y-axis. Make sure to show these 3000 steps in an effective way.

If you are using VPython, you can show a histogram plot as soon you have data needed. If you are using Matplotlib, the interactive option allows showing results during the computation (See Interactive Matplotlib):

Interactive Matplotlib

Normally, matplotlib will not show plots until you call pylab.show(). However, if you call pylab.ion() before plotting, matplotlib will show the window immediately. For best results, decorate (set title, axis labels, etc) after calling pylab.plot().

Example code:

import pylab

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xs = []

ys = []

pylab.ion()

for x in range(10):

xs.append(x)

ys.append(x ** 2)

pylab.plot(xs, ys, 'b-o')

pylab.pause(1)

pylab.title("curve of x squared")

pylab.xlabel("x")

pylab.ylabel("x ** 2")

pylab.show()

pylab.pause(10)

pylab.close()

Discussion

You need to hand in a discussion of your experimental results. The following questions should be addressed:

In graph N_versus_Energy, how close is the actual system energy to the total energy? How does it change as N changes? How do the plots differ for the two different initial system states?

Using histogram Final_Particle_Velocity, what kind of distribution do you judge the velocities to come from? How close is the molecule velocity to the initial velocity of sqr …… 此处隐藏：5452字，全部文档内容请下载后查看。喜欢就下载吧 ……