Final project template

Dear class,

I have posted on the course website the template for your final project report. Please use this template as it will ensure consistency when I compile the virtual simulation gallery.

Also, please do keep in mind that the report is intended to be very brief. I have listed some target numbers of sentences for each section. You do not need to prepare an extensive report for the final project. Essentially the report will serve to introduce the reader to your simulation approach and provide some background for the work and movie.

As you are working on or thinking about your final project, keep in mind that you want to keep it simple. I am not looking for extensive simulations here; rather, I simply want you to have some experience putting together your own model and simulation code. This should not be a terribly time-consuming project. If you are having trouble formulating a simple project, please see me or take a look at the suggestions in the final project handout.

Also, I have posted all but one of the remaining lecture notes, in case you are interested in reading ahead as you work on your project.

Cheers,
MSS

Visualization

Dear class,

Next Tuesday's lecture will cover visualization methods, but if you are starting to work on your final project and are interested in how to make a movie, I have posted a tutorial handout on visualization on the course website that I will distribute on Tuesday. The procedure is actually quite straightforward using the program UCSF Chimera, but you may want to run a quick test.

Cheers,
MSS

Advanced methods in final project

Here are some other ideas (perhaps more straightforward to implement) that would be acceptable as advanced methods in your final project. Keep in mind you only need to implement one if you do not do Ex 5:

• Andersen thermostat in MD (note that this is not what we have used before--you will need to resample velocities from the Gaussian Maxwell-Boltzmann distribution using np.random.normal)
• Berendsen thermostat in MD (you will need to rationalize a good value for the coupling constant tau)
• any MC move that is not a usual (unbiased) single-particle displacement
  
• block averaging analysis (to compute estimated errors in an observable)
• computation of any histogram (e.g., computing any distribution -- you might examine how this changes with some parameter)

MSS

Correction for reference in Ex 5

In exercise 5, there is a reference that is incorrect. The graph included corresponds to the following paper:

Phys. Rev. E 72, 021501 (2005)

This may be helpful in comparing your computed densities and pressures.

Cheers,
Scott

Some helpful models for the final project

There are two models that may be useful for developing simple models in your final project.

One is the screened Coulomb potential, which is a very simple, approximate pairwise potential for reproducing electrostatic interactions that does not require a special treatment of the long-range interactions (e.g., the Ewald summation).

The other is the Lennard-Jones wall or surface potential, which is used to approximate the net interaction of an atom with an infinitely wide and deep surface of uniform density.

Both of these have now been added to the lecture notes on classical force fields. You can find the equations for the energy functions there.

MSS

Please bring Ex2, 3 to class Tuesday

Dear class,

My excel file for the course grades has become corrupted and I cannot recover your grades for exercises 2 and 3. Please bring these graded assignments to class on Tuesday so that I can mark these down. Apologies for any inconvenience.

Cheers,
MSS

Final project

Dear class-

I have placed the final project assignment on the course website. This handout will be discussed further in class on Tuesday.

Keep in mind that you have the choice of completing Exercise 5 or you can implement an advanced technique in your final project (as described in the handout).

Cheers,
MSS

Extension on ex 4

Hi class-

If you prefer to turn in your assignment by Friday at 4pm (either to me, under my door, or in my mailbox), that is fine.

Cheers,
MSS

Typo in Ex4, part e

The expression for the virial pressure should be as follows:

= < (N kB T)/V - W/3V >

The original expression was missing the 3 and the averages should be performed over the entire expression (both V and W fluctuate).

MSS

Even more on Ex4

There is a slight typo in the lecture notes that I believe may cause confusion regarding your homework. When we perform a simulation in reduced units, such as the monatomic Lennard-Jones system, Boltzmann's constant kB is absorbed into the dimensionless temperature:

T* = kB T / epsilon

Thus, the acceptance criterion does not explicitly contain the quantity kB. Another way of thinking about this is that kB = 1 for reduced units:

Pacc = min{ 1, exp[ -(U2* - U1*) / T*] }

The point is, you should not need to specify kB in your simulation runs.

MSS

More on Ex4

Hi all-

In your Fortran loop to compute the interaction energies between a selected atom and all other atoms, you will have to modify the test between atoms i and j to see if they are bonded or not. The reason behind this is that your loop will no longer run over pairs (i,j) such that j > i always. The following Fortran code will test if any two i or j are bonded:

abs(i-j) == 1 .and. mod(max(i, j), M) > 0

Also, if you are using f2py, be sure to keep in mind that you should always place dimension variables (e.g., NAtom, Dim) at the end of your subroutine declaration statement. The reason for this is that f2py will automatically re-order subroutine arguments this way, and it might come as unexpected when you are calling these compiled routines from Python. In any case, you do not need to send these variables to the Fortran routine when you call them from Python as f2py will automatically take them from the dimensions of the other variables you send (e.g., Pos).

Cheers,
MSS

Exercise 4

For this assignment, let's only consider the cases M=1,2,4. The original problem statement included longer-length polymers, but I think we might run into problems with sampling at these lengths.

MSS