PHYS 410:

Computational Physics

Term 2 – 2008/09

What is "computational physics"?1. Process and analyse large amounts of data from measurements;

fit to theoretical models; display and animate graphicallyEx: search for "events" in particle physics, image analysis in astronomy.

2. Numerical solution of equations that cannot be accomplished by analytical techniques (coupled, nonlinear etc.)Ex: fluid dynamics (Navier Stokes), numerical relativity (Einstein's field equations), electronic ground state wavefunctions in solid state systems, nonlinear growth equations

3. Computer "experiments": simulate physical phenomena, observe and extract quantities as in experiments, explore simplified model systems for which no solution is known.Ex: molecular simulations of materials, protein folding, planetary dynamics (N-body dynamics).

Theory - Computation - Experiment

Theoretical Physics

Construction and mathematical (analytical) analysis of idealized models and hypotheses to describe nature

Experimental Physics

Quantitative measurement of physical phenomena

Computational Physics

Performs idealized "experiments" on the computer, solves physical models numerically

predicts

testspredicts

pred

icts

test

s

tests

Computation across all areas of physics

• High Energy Physics: lattice chromodynamics, theory of the strong interaction, data analysis from accelerator experiments

• Astronomy and Cosmology: formation and evolution of solar systems, star systems and galaxies

• Condensed Matter Physics: - electronic structure of solids and quantum effects- nonlinear and far from equilibrium processes - properties and dynamics of soft materials such as polymers, liquid crystals, colloids

• Biophysics: simulations of structure and function of biomolecules such as proteins and DNA

• Materials Physics: behavior of complex materials, metals, alloys, composites

Example 1: Biophysics

314,000 atom simulation at UIUC

Chymotrypsin Inhibitor 2

Example 2: Materials Physics• Glassy polymers (eg.

PMMA, plexiglass) consist of long chain molecules

• Under load, the polymer forms a dense network of fibrils and voids that is controlled by the molecular level chain structure

• This process makes them "tough" to break and therefore useful materials

Molecular dynamics simulation of fracture in glassy polymers

Example 3: Materials Physics

Dislocation dynamics with a billion copper atoms at LLNL

Example 3: Materials PhysicsCrack propagation in Silicon

http://cst-www.nrl.navy.mil/~bernstei/projects/nb.html

Modeling materials on different length scales:

• quantum mechanics (tight binding)

• classical forces (molecular dynamics)

• continuum mechanics (finite element)

Example 4: Materials PhysicsPhase field models of dendrite growth

http://mse.mcmaster.ca/faculty/provatas/solid.html

• critical nucleus growing into an undercooled melt

• adaptive mesh refinement

• Directional solidfication in a binary alloy• Numerical solution of a PDE

• Phase field (order parameter) describes liquid/solid

2 3 2 2( ) (1 )t W n U

Example 5: High Energy Physics

• Particle colliders such as the LHC at CERN in Geneva are unraveling the interactions between fundamental particles

• These experiments produce large amounts of data that is analyzed worldwide (including here at UBC) using GRID computing

High Energy Physics group @ UBC

LHC

How is it done?• "Small simulations" on workstations such as this laptop

Program with numerical packages such as Maple/Matlab/Mathematica or in high-level programming languages such as C/C++ or Fortran

• "Large simulations" on compute clusters or supercomputersmay require lots of memory or calculation timedistribute the problem over many (~10 to 100) processors either separately or "in parallel"

• Grid computing: networks of supercomputing centers dedicated to scientific problems, spatially separated

How does the computational physicist work?

• Devise and implement a computer model for the physical question of interest

• Needs numerical mathematics toolkit: discretization, error analysis, stability, efficiency

• Perform the computation

• Analyse and visualize the data

• Interpret and compare to experiment and theory

• Improve model predictions

Exciting research opportunities• In computer simulations we can study more realistic physical models, but

still have full control over the degree of complexity.• Enables quantitative predictions• In Condensed Matter/Materials Physics an important goal is to be able to

predict material behavior:

Can we design new materials, new substances, new drugs etc. on the computer?

To achieve this goal, we need techniques that span the length and time scales from the atomistic (femtometers/seconds) to the scales we use in everyday life (say seconds/centimeters).

This is not easy; this research effort is called "multiscale modeling"

Outline of the course• Introduction to UNIX/LINUX

• Introduction to programming and compiling in C

• Data visualization

• Ordinary differential equations in physics:kinematics, oscillatory motion and chaos, orbital motion

• Partial differential equations in physicselectrostatics, wave equation, diffusion

• Stochastic MethodsRandom walks, fractals and percolation, Monte Carlo

• Quantum systemsSchrödinger equation, ground state energy and wavefunctions,wavepackets

How to get started?• Get an account on the departmental UNIX system by self-registering in

HENN 205

• Familiarize yourself with the environment (if new to you)

• Get material from the course webpage www.phas.ubc.ca/~jrottler/teaching/410/onres.htmland practice basic operations such as file manipulation, text editors, remote logins as demonstrated in class

• Experiment with basic C programming constructs, learn how to compile and run code

• Learn how to plot numerical data and functions using your favorite software. One possibility: gnuplot

now we are ready to start doing real computational physics!

Introduction to UNIX/LINUX

• Files and directories• Basic commands• Manipulating files• Working with the "shell"• Basic shell programming

please see also the notes by Prof. M. Choptuik: laplace.physics.ubc.ca/410/Notes_unix.html