Can anyone give me an idea of what computational physics is?

Question

I need to write a paper on the importance of computational physics in today's society. My general idea of computational physics is that it is a combination of math, computer science and physics. It is important for modeling experimental data. I was wondering if I am on the right track. Is there anybody who knows a lot about this subject? If so pleas just give me your general idea and I can research it further. Thanks.

Answer 1

Good question. You're on the right track with your general idea.

The basic premise is that when we want to understand what the basic laws of physics imply in complicated phenomena, it is impossible to apply the basic laws analytically (ie, with pencil and paper) because the math is just too difficult. What we do instead is program a computer to calculate approximate solutions to the equations of physics. These calculations can be quite quick or they can take months, depending on the problem. Some problems are so complicated that they would take years, centuries, or longer to compute - so we have to wait for faster computers.

The numerical methods used include approximate solutions to differential equations, numerical integrations, monte carlo simulations, neural net schemes, and others. A bible for computational folks is the book series "Numerical Recipes".

These methods are applied in all fields of physics, including condensed matter physics, general relativity, particle physics, and astrophysics. I'm most familiar with the astrophysics applications, so I'll give you a few examples:

The physics that govern stars are well understood, and in the simplist case can be boiled down to four differential equations (plus an equation of state and an equation of nuclear reaction rate). But this requires that we assume the star is in steady state, is spherically symmetric, has no magnetic field, is nonrotating, is non-convective, etc. None of these assumptions are actually true in stars, so if we want a more accurate model, then we have to take into account these effects. The equations quickly become too complicated, and so we must use computational methods.

Another example is in Cosmology. If we assume basic parameters for the Universe (curvature, matter content, dark energy content, etc) then we can compute the evolution of the Universe. What we do is give some random fluctuations in the mass density of the early Universe, then use kinematics and the Law of Gravitation to see how the large scale structure in the Universe evolves from these perturbations. These predictions are then compared to large scale structure in the obsevable Universe to constrain the aforementioned cosmological parameters. I've attached a link to a Canadian collaboration which does a lot of work in this area.

Hope this is helpful.