Simulating Physics with Computers
“You don’t understand something, until you can program it; that is, until you can communicate it to that ‘speedy idiot’.” — Professor Robert W. MacCormack, Stanford
Contents |
Introduction
Here’s some interesting (to me anyway) hobby/work demo software projects, that I’ve worked on over the years, regarding the various ways of “Simulating Physics with Computers.”
The term “Simulating Physics with Computers” more or less originated from an article by Nobel laureate Richard Feynman back in 1981, International Journal of Theoretical Physics, Vol 21, Nos. 6/7 1982, in which he talks about the “possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.” An exact solution at the quantum level.
My projects aren’t quite so ambitious! They pretty much stick to the “classical” domain. For example, simulating Classical Electromagnetics (Maxwell’s Equations) with the Finite-difference time-domain (FDTD) algorithm. Or at the molecular level with Molecular Dynamics. Likewise simulating Physiology using Physiologically Based Pharmacokinetic (PBPK) techniques.
All open source of course.
Finite-difference time-domain (FDTD) Modeling
Finite-difference time-domain (FDTD) is a computer modeling technique to simulate Maxwell’s Equations. Maxwell’s Equations describe the physical laws of Electromagnetics (at the classical level).
The FDTD method belongs in the general class of grid-based differential time-domain numerical modeling methods. The time-dependent Maxwell’s equations are discretized using central-difference approximations to the space and time partial derivatives.
Included, are FDTD demos using the Maxwell Curl Equations and also the second order “Wave Equations.”
Molecular Dynamics
Molecular Dynamics is a computer modeling technique which simulates the movements of atoms and molecules using classical approximations of the underlying quantum mechanical physics.
Here is an old demo program of a Molecular Dynamics simulation of water done way back in 1994/1995:
Physiologically Based Pharmacokinetic (PBPK) Modeling
Physiologically Based Pharmacokinetic (PBPK) modeling is a computer modeling method for predicting the absorption, distribution, metabolism and excretion (ADME) of a compound in humans and other animal species. PBPK modeling is used in pharmaceutical research and development, and in health risk assessment.
Related to PBPK is Physiologically based pharmacodynamic (PBPD) modeling in which the model trys to simulate how the body will react to a compound. Generally a much harder task than PBPK.
Here are a couple PBPK demo programs I did essentially duplicating the work of Igari etal with a couple additions. The style of the articles are in keeping with Igari
PBPK simulation of Diazepam, with open source software (2/17/2008)
Test of a PBPK simulator, using Igari1983 as reference (2/16/2008)
Immune System Physiology Simulation
Using the same general principles as PBPK, here is an old physiological based simulation of the Immune System done around 2000-2002 or so. The model is primarily based on a bronchial tissue model from a 1994 article by Bocharov and Romanyukha and an immunological model based on an article, the localization-dose-time model, written in 2000 by Nobel laureate Rolf M. Zinkernagel. (Includes open source software)
MRI Simulation
Who in their right mind would make a computer simulation of an MRI Machine? I don’t know, but here’s one…
- MRI Simulation… circa 2002
Physics References
Articles
- Feynman1982, “Simulating Physics with Computers”, Feynman, Int J Theoretical Physics, Vol. 21, Nos. 6/7, 1982, 467-488
Books
- Balanis – Advanced Engineering Electromagnetics, 1989
- Bloch – Classical and Quantum Harmonic Oscillators, 1997
- Bohm – Quantum Theory, 1951
- Eisberg – Eisberg, Resnick, Quantum Physics, 1985
- Feynman – The Feynman Lectures on Physics (volumes I,II,III), 1964
- Feynman1985 – QED The Strange Theory of Light and Matter, 1985
- FeynmanHibbs – Feynman, Hibbs, Quantum Mechanics and Integrals, 1965
- Georgi – The Physics of Waves, 1993
- Griffiths – Introduction to Elementary Particles, 1987
- GriffithsED – Introduction to ElectroDynamics, (3rd edition) 1999
- GriffithsQM – Introduction to Quantum Mechanics, 1995
- Mandel – Optical Coherence and Quantum Physics, 1995
- Mead – Collective ElectroDynamics, 2000