Physics 141/241 and Physics 142/242
Physics 141/241 and Physics 142/242 are
neither progamming courses nor courses
on numerical analysis.
The purpose of these project based laboratory courses is to introduce
the
students to modelling in physics, where the modern use of computers
becomes an integral part of the problem solving process.
In general,
the major applications of computational physics are rather naturally
divided into two categories.
Modern probabilistic methods and
simulations, the focus of Physics 141/241,
were developed
in the last twenty years in order to attack very complex problems in
physics.
The N-body problem is an outstanding example with broad applications
in molecular dynamics of solids and liquids, in computational
astrophysics,
in biophysics and chemical physics, and in plasma physics.
The goal of
Physics 142/242 is to
develop more experience
in the solutions of modern
physics/engineering problems blending in the somewhat more traditional
methods of applied numerical analysis. The most frequent example is
the solution of
partial differential equations with finite elements built on the
foundation of matrix/vector linear algebra.
The main purpose of the
proposed new course sequence is to
demonstrate to the students the main aspects of physical modelling,
and their combined use, with carefully selected physics projects.
For example, to understand the physics of the curveball thrown by a
pitcher, the numerical model of choice
is the Navier-Stokes equations for laminar flows at large Reynolds
numbers,
just below the turbulence limit. However,
the onset of turbulence, (or some other important aspects
of fluid dynamics) would require statistical physics and
stochastic modelling with large scale computer simulations.
Similarly, the physics of molecules, quantum dots, or nanodevices
requires a mix of computational approaches drawing from the areas
of matrix methods and partial differential equations (Hartree-Fock,
density functional, etc.) as well as
stochastic methods (quantum Monte Carlo, molecular
dynamics, path integral, etc.).
The projects will vary from instructor to instructor over the years.
The main requirement is that the selected physics projects in each
course
should illustrate the most important aspects of the major categories
in computational physics. It is important that
the students should learn not only the methods, but the attitude
required
to attack physics problems with the computer.
We expect and welcome students
from diverse backgrounds and
departments, and will spend time on needed background from computer
architecture, software, and numerical analysis.
We will require each student to have a working knowledge
of a modern computer language, either Fortran, or C/C++.
The lectures will not deal with the problems on the level of the
progamming language. They will, instead introduce the students
to the physics of the projects, the general capabilities of the
public domain general packages (like LAPACK in Physics 142/242)
which are readily available in Fortran and C, and the general
strategy of the computational method.
The students will form small teams to solve the assigned laboratory
projects
of the courses. Each member of the team will have to work out a special
assignment and write a report on the laboratory project.