FISIKA KOMPUTASI (COMPUTATIONAL PHYSICS) Ishafit Program Studi Pendidikan Fisika Universitas Ahmad Dahlan

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1 FISIKA KOMPUTASI (COMPUTATIONAL PHYSICS) Ishafit Program Studi Pendidikan Fisika Universitas Ahmad Dahlan

2 What is Computational Science

3 What is Computational Physics Reference: Resource Letter CP-2: Computational Physics Rubin H. Landau, Am. J. Phys. 76 4&5, April/May 2008

4 What is Computational Physics? 1. Process and analyze large amounts of data from measurements; fit to theoretical models; display and animate graphically Ex: 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).

5 What is Computational Physics? Computational Physics combines physics, computer science and applied mathematics in order to provide scientific solutions to realistic and often complex problems. Areas of application include the nature of elementary particles, the study and design of materials, the study of complex structures (like proteins) in biological physics, environmental modeling, and medical imaging. A computational physicist understands not only the workings of computers and the relevant science and mathematics, but also how computer algorithms and simulations connect the two.

6 Computational Physics

7 Theory - Computation - Experiment Computational Physics Performs idealized "experiments" on the computer, solves physical models numerically Theoretical Physics Construction and mathematical (analytical) analysis of idealized models and hypotheses to describe nature predicts tests Experimental Physics Quantitative measurement of physical phenomena

8 3 Pillars Theory Computational Physics Experiment

9 4 Pillars? Theory Computational Physics Data Mining Experiment 2 Computational Pillars

10 Mathematical Modeling

11 Mathematical Modeling

12 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

13 Computing

14 Career Opportunities for Computational Physicists A graduate degree in physics in areas such as biophysics, condensed matter physics, particle physics, astrophysics to name a few. A career in High-performance and scientific computing, in the energy and aerospace sectors, with chemical and pharmaceutical companies, with environmental management agencies. Employment in firms that develop scientific software, as well as computer games. A research career in an academic, industrial, or national laboratory A teaching career in physics A job in Wall Street. Even Wall Street employers are interested in people with a background in computational physics.

15 Computational Physics is an active field

16 Journals and Magazines

17 APS, EPS, IPS

18 Scientific Papers On-line at arxiv.org

19 Syllabus Modelling and Error Analysis Mathematical Modeling A Simple Mathematical Model Approximations and Round-Off Errors Significant Figures Accuracy and Precision Error Definitions Round-Off Errors Truncation Errors and the Taylor Series The Taylor Series Error Propagation Total Numerical Error

20 Syllabus Taking derivatives General discussion of derivatives with computers Forward difference Central difference and higher order methods Higher order derivatives Solution of nonlinear equations Bisection method Newton s method Method of secants Brute force method

21 Syllabus Interpolation Lagrange interpolation Neville s algorithm Linear interpolation Polynomial interpolation Cubic spline Numerical integration Introduction to numerical integration The simplest integration methods More advanced integration

22 Syllabus Matrices Linear systems of equations Gaussian elimination Standard libraries Eigenvalue problem Differential equations Introduction A brush up on differential equations Introduction to the simple and modified Euler methods The simple Euler method The modified Euler method Runge Kutta method Adaptive step size Runge Kutta The damped oscillator

23 Fundamental Convictions In approaching problems in physics, physicists Solve algebraic equations Solve ordinary differential equations Solve partial differential equations Evaluate integrals Find roots, eigenvalues, and eigenvectors Acquire and analyze data Graph functions and data Fit curves to data Manipulate Images Prepare reports and papers

24 Reference

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