Basics of Computational Physics

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1 Basics of Computational Physics What is Computational Physics? Basic computer hardware Software 1: operating systems Software 2: Programming languages Software 3: Problem-solving environment What does Computational Physics do? Atomic Physics studies atoms Nuclear Physics studies nuclei Plasma Physics studies plasmas Solid State Physics studies solids Computational physics does not study computers 2 What is Computational Physics? Computational physics is a synthesis of theoretical analysis, numerical algorithms, and computer programming. P. L. DeVries Am. J. Phys., vol. 64, 364 (1996) What is Computational Physics? Computational physics is a tool for solving complex numerical problems in physics 3 4 Example: university physics courses + = + = few analytically solvable problems solutions to very many problems 5 Why do we need computational physics? In physics we answer how nature works. Quite often we need equations (unless you are a poet or a philosopher) Using equations we create models to describe nature Exact (analytic) solutions are very rare unless a model is a very simple one We need computational physics when we cannot solve problems analytically we have too much data to process Many, if not the most, problems in contemporary physics could never be solved without computers 6 1

2 Computational physics in contemporary physics Numerical calculations: solutions of well defined mathematical problems to produce numerical solutions Examples: systems of differential equations, integration, systems of linear equations, Visualization and animation: the human eye + the visual processing power of the brain = very sophisticated tool traditional presentation: 2D and 3D plots new presentations: animation, using colors and textures Computer simulation: testing models of nature Examples: weather forecast, Data collection and analysis in experimental research Example: LabView Symbolic manipulation: Classification of computational models Deterministic or Stochastic models Deterministic models: Results of deterministic models depend on initial conditions. Stochastic models: an element of chance exists. Dynamic or Static models A dynamic models changes in time. A static model does not consider time Examples: Maple, Mathematica, 7 8 Computer Simulation (few examples) Molecular Dynamic Simulation Weather forecast Design of complex systems (aircrafts, ) Financial markets Traffic War games 9 10 more Many natural phenomena are nonlinear, and a small change in a variable might produce a large effect. But just few nonlinear problems can be solved analytically. Interest in systems with many variables or many degrees of freedom Computational Physics is a multidisciplinary field Computational Physics Millennium Simulation - the largest N-body simulation carried out thus far (more than particles). A 3-dimensional visualization of the Millennium Simulation shows a journey through the simulated universe 11 mathematics physics project management computers 12 2

3 Computers Hardware Amazing progress: two times more powerful processors in 18 months (Moore s law: the number of transistors per square inch on integrated circuits doubles every 18 months) Do we have twice more results in physics each 18 months? Software Computers in computational physics Basic computer hardware Hardware (internal) 15 CPU - central processing unit (speed in GHz), cache memory: cache 1, cache 2 RAM -random-access memory (MB or GB) communication with CPU by bus (MHz) PCI Peripheral Component Interconnect USB Universal Serial Bus HDD Hard Disk Drive (GB) Graphic card Network Interface (Mb/sec) (modems 56 Kb/sec) 16 Hardware (peripheral) Keyboard (I/O) Mouse (I/O) Printer (I/O) Monitor (Graphic card) Ethernet (network) Scanner, external storage, Critical hardware for calculations Desktops CPU RAM Clusters CPU and RAM number of CPUs fast network communication between nodes

4 Software Software 1: Operating Systems Operating system a set of programs to manage communication between hardware (device drivers) communication between a user and a computer running applications (software) file system security Types of Operating Systems Some of Operating Systems multi-user: Allows two or more users to run programs at the same time. Some operating systems permit hundreds or even thousands of concurrent users. multiprocessing: Supports running a program on more than one CPU. multitasking: Allows more than one program to run concurrently. multithreading: Allows different parts of a single program to run concurrently. real time: Responds to input instantly. General-purpose operating systems, (Windows, Linux are not real-time). Alive Windows Linux Mac OS Unix Dead by now DOS IBM OS/2 VMS IBM OS/ What OS is better for computational physics? Software 2: Programming Languages The answer depends on a problem Desktops Windows, Linux, Mac OS Clusters Linux Supercomputers Unix, Linux Parameters to consider: Available hardware, software and computer codes Stability Analysis of results and presentation

5 Most common in physics Fortran C/C++ The basic ideas behind computational physics are language independent Java What language to use? choice depends on a problem numerical simulation system programming web programming available libraries and computer codes experience The relevance of C++ to scientific computing is somewhat controversial A First Course in Computational Physics and Object Oriented Programming with C++, by D. Yevick C++ is also one of the most complex programming languages, with many pitfalls for the unwary. C a reference manual (5 th edition) by S.P. Harbison and G. L. Steele Jr. Spend your intellectual energies on the current problem - not on fancy tools. When the volume and sophistication of your problems demand these weapons you will know it. That is the time to learn a new tool - and learn it by re-doing an alreadysolved problem, not a new one. F.S. Acton Real Computing made real Fortran, C/C++, and others Fortran 77, C, C++, Fortran 90 Fortran legacy! Very many computer codes and libraries Fortran easy-to-learn and easy-to-use Normally, scientific C++ programs cannot be effectively optimized as Fortran programs (C++ codes run slower - from 10% to 10 times) Java and C# poses formal advantages (however, C++ is rather for industry) Scientific software may solve problems 1 excellent 2 good 3 fair 4 poor faster

7 Software 4: Applications Graphics Spreadsheets Word processors Internet Project Management in computational physics The art or skill of directing and organizing the work

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