PHYS 410: Computational Physics Term 2 – 2008/09 What is “computational physics” Theory – Computation – Experiment Computation across all areas of physics Example 1: Biophysics

PHYS 410: Computational Physics Term 2 – 2008/09 What is

PHYS 410: Computational Physics Term 2 – 2008/09 What is “computational physics” Theory – Computation – Experiment Computation across all areas of physics Example 1: Biophysics

Tsutsumi, Lynn, Founder and Editor in Chief has reference to this Academic Journal, PHwiki organized this Journal PHYS 410: Computational Physics Term 2 – 2008/09 What is “computational physics” Process in addition to analyse large amounts of data from measurements; fit to theoretical models; display in addition to animate graphically Ex: search as long as “events” in particle physics, image analysis in astronomy. 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 Computer “experiments”: simulate physical phenomena, observe in addition to extract quantities as in experiments, explore simplified model systems as long as which no solution is known. Ex: molecular simulations of materials, protein folding, planetary dynamics (N-body dynamics). Theory – Computation – Experiment Theoretical Physics Construction in addition to mathematical (analytical) analysis of idealized models in addition to hypotheses to describe nature Experimental Physics Quantitative measurement of physical phenomena Computational Physics Per as long as ms idealized “experiments” on the computer, solves physical models numerically predicts tests predicts predicts tests tests

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Computation across all areas of physics High Energy Physics: lattice chromodynamics, theory of the strong interaction, data analysis from accelerator experiments Astronomy in addition to Cosmology: as long as mation in addition to evolution of solar systems, star systems in addition to galaxies Condensed Matter Physics: – electronic structure of solids in addition to quantum effects – nonlinear in addition to far from equilibrium processes – properties in addition to dynamics of soft materials such as polymers, liquid crystals, colloids Biophysics: simulations of structure in addition to function of biomolecules such as proteins in addition to 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 as long as ms a dense network of fibrils in addition to voids that is controlled by the molecular level chain structure This process makes them “tough” to break in addition to there as long as e 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 Physics Crack propagation in Silicon Modeling materials on different length scales: quantum mechanics (tight binding) classical as long as ces (molecular dynamics) continuum mechanics (finite element) Example 4: Materials Physics Phase field models of dendrite growth 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

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 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 supercomputers may require lots of memory or calculation time distribute 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 in addition to implement a computer model as long as the physical question of interest Needs numerical mathematics toolkit: discretization, error analysis, stability, efficiency Per as long as m the computation Analyse in addition to visualize the data Interpret in addition to compare to experiment in addition to 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 in addition to time scales from the atomistic (femtometers/seconds) to the scales we use in everyday life (say seconds/centimeters). This is not easy; this research ef as long as t is called “multiscale modeling” Outline of the course Introduction to UNIX/LINUX Introduction to programming in addition to compiling in C Data visualization Ordinary differential equations in physics: kinematics, oscillatory motion in addition to chaos, orbital motion Partial differential equations in physics electrostatics, wave equation, diffusion Stochastic Methods R in addition to om walks, fractals in addition to percolation, Monte Carlo Quantum systems Schrödinger equation, ground state energy in addition to 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 in addition to 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 in addition to run code Learn how to plot numerical data in addition to functions using your favorite software. One possibility: gnuplot now we are ready to start doing real computational physics!

Introduction to UNIX/LINUX Files in addition to directories Basic comm in addition to s Manipulating files Working with the “shell” Basic shell programming please see also the notes by Prof. M. Choptuik:

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