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What We Get Out, Part 2

© Adam Hughes

Last week, we talked a little about the kinds of properties that can be calculated from a classical dynamics simulation. We saw that quantities can usually be classified as either static or dynamic, as well as some brief examples of both types. In this article, we're going to talk which of each type of properties a scientist will generally be interested in, as well as discuss some of the details involved in actually calculating these values.

Static properties are generally calculated "on-the-fly". Let's look at temperature as an example. Temperature is a measure of kinetic energy, and so the old familiar equation comes into play : T=1/2m*v*v, where m is the mass of the particle and v is its velocity. Depending on which temperature scale we're interested in, there may be some conversion factor involved, but this is basically the expression. Now, every particle in real space has an x, y, and z component, so it also has these dimensions in its total velocity, represented as vectors. To get the kinetic energy of a particle then, one must sum up the resultant three terms. To get the kinetic energy of a system of particles, one must sum up the three terms for EVERY particle. So, practically, this means that the sum is performed, given the present velocities, whenever it is desirable to know the temperature of the system, usually every 100 or 1000 time steps. A similar thing could be done for quantities such as pressure, volume, density, and any other static properties.

The scheme outlined above makes static properties very attractive to compute because it is not required to save any data, other than the calculated property itself. We use the data when we need it, and then we can forget about. The case of dynamic properties is not so neat and clearcut, however.

When discussing dynamic properties, we of course are considering quantities which have a time dependence. One useful example of a dynamic properties is the calculation of the self-diffusion coefficient. The self-diffusion coefficient basically tells a scientist how fast one particle can move through the entire system, and it's kind of a measure of how "sticky" the system is. In fact, the self-diffusion coefficient is closely related to the viscosity, with which we're probably all familiar from our dealings with motor oil.

Anyway, in order to calculate the self-diffusion coefficient accurately, it is necessary to know how each particle interacts with the system over a long period of time. Thus, we have to know how it interacts at time 0, at time t, and at every point in between. What's more, we have to save this information, because it must be correlated, which generally

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