Rutgers-Camden Physics Department

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Physics and Science Vision

The Rutgers Camden Physics Department firmly believes that computers must be an important part of the curriculum for all physics majors. The application of numerical techniques to problem solving in physics is probably what first comes to mind in this connection. Numerical solution methods can allow the student to concentrate on the physical, rather than the mathematical, content of the material. Indeed, the value of programming, executing, and analyzing problems in analytical mechanics, statistical mechanics, and quantum mechanics has been recognized for some time. In addition, and at the heart of the Science Vision concept, the numerical approach often leads naturally to a graphical representation of the results, which can facilitate the students' appreciation of their structure. The department offers a sequence of courses in computational physics, which introduces the standard techniques of numerical differentiation and integration and applies them to a variety of topics in physics, and then builds on these ideas to develop the powerful molecular dynamics and Monte Carlo simulation methods. We also believe that the use of powerful applications software spreadsheet and mathematics packages should be emphasized throughout the curriculum, starting with the introductory calculus based course. For example, using a spreadsheet program in the introductory course allows one to solve real world mechanics problems while providing insights into calculus and differential equations. The following figures depict visually a number of problems in statistical physics solved with the above mentioned techniques, as well as the method of finite element analysis (which is fully supported in the new Science Vision Center).

The first three pictures are results from a molecular dynamics simulation of diffusion in a system of hard-sphere atoms. The positions of the atoms are calculated from Newton's laws of motion, for a large number of closely spaced time steps.

This shows an early stage in a diffusion process. A wall has been removed between the two halves of a box of hard sphere atoms and the atoms from each half are now beginning to diffuse into the other side.

There has now been considerable diffusion. One of the red atoms has penetrated completely through the region originally occupied by the blue atoms.

The two sets of atoms are now completely mixed. There are, on average, equal numbers of the two types of atom in each half of the box.

This again shows a simulation of hard sphere atoms, but there is now a gravitational field present. The top of the box has been removed and the sides extended upwards. The numbers of atoms at different heights can be sampled at intervals, and the average distribution calculated.

The next two pictures show Monte Carlo simulations of a two-dimensional magnet (the Ising model). The red regions are magnetized up and the blue regions are magnetized down. In both pictures, there are equal amounts of red and blue, showing that the net magnetization is zero.

This picture corresponds to a very high temperature. The up and down regions are randomly arranged on a very fine scale, giving a "pepper and salt" appearance.

This picture corresponds to a lower temperature, only slightly above the so-called critical point. Although the net magnetization is still zero (equal amounts of red and blue), there is a clumping of the regions on a microscopic scale i.e. the values of neighboring spins are highly correlated. This high degree of correlation strongly influences all the physical properties.