| Computational physics |
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Computational physics is the study and implementation ofnumerical analysis to solve problems inphysics.[1] Historically, computational physics was the first application of modern computers in science, and is now a subset ofcomputational science. It is sometimes regarded as a subdiscipline (or offshoot) oftheoretical physics, but others consider it an intermediate branch between theoretical andexperimental physics — an area of study which supplements both theory and experiment.[2]
In physics, differenttheories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have aclosed-form expression, or is too complicated. In such cases, numerical approximations are required. Computational physics is the subject that deals with these numerical approximations: the approximation of the solution is written as a finite (and typically large) number of simple mathematical operations (algorithm), and a computer is used to perform these operations and compute an approximated solution and respectiveerror.[1]
There is a debate about the status of computation within the scientific method.[4] Sometimes it is regarded as more akin to theoretical physics; some others regard computer simulation as "computer experiments",[4] yet still others consider it an intermediate or different branch between theoretical andexperimental physics, a third way that supplements theory and experiment. While computers can be used in experiments for the measurement and recording (and storage) of data, this clearly does not constitute a computational approach.
Computational physics problems are in general very difficult to solve exactly. This is due to several (mathematical) reasons: lack of algebraic and/or analytic solvability,complexity, and chaos. For example, even apparently simple problems, such as calculating thewavefunction of an electron orbiting an atom in a strongelectric field (Stark effect), may require great effort to formulate a practical algorithm (if one can be found); other cruder or brute-force techniques, such asgraphical methods orroot finding, may be required. On the more advanced side, mathematicalperturbation theory is also sometimes used (a working is shown for this particular examplehere). In addition, thecomputational cost andcomputational complexity formany-body problems (and theirclassical counterparts) tend to grow quickly. A macroscopic system typically has a size of the order of constituent particles, so it is somewhat of a problem. Solving quantum mechanical problems is generally ofexponential order in the size of the system[5] and for classical N-body it is of order N-squared. Finally, many physical systems are inherently nonlinear at best, and at worstchaotic: this means it can be difficult to ensure anynumerical errors do not grow to the point of rendering the 'solution' useless.[6]
Because computational physics uses a broad class of problems, it is generally divided amongst the different mathematical problems it numerically solves, or the methods it applies. Between them, one can consider:
All these methods (and several others) are used to calculate physical properties of the modeled systems.
Computational physics also borrows a number of ideas fromcomputational chemistry - for example, thedensity functional theory used by computational solid state physicists to calculate properties of solids is basically the same as that used by chemists to calculate the properties of molecules.
Furthermore, computational physics encompasses thetuning of thesoftware/hardware structure to solve the problems (as the problems usually can be very large, inprocessing power need or inmemory requests).
It is possible to find a corresponding computational branch for every major field in physics:
Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics, namely:accelerator physics,astrophysics,general theory of relativity (throughnumerical relativity),fluid mechanics (computational fluid dynamics),lattice field theory/lattice gauge theory (especiallylattice quantum chromodynamics),plasma physics (seeplasma modeling), simulating physical systems (using e.g.molecular dynamics),nuclear engineering computer codes,protein structure prediction,weather prediction,solid state physics,soft condensed matter physics, hypervelocity impact physics etc.
Computational solid state physics, for example, usesdensity functional theory to calculate properties of solids, a method similar to that used by chemists to study molecules. Other quantities of interest in solid state physics, such as the electronic band structure, magnetic properties and charge densities can be calculated by this and several methods, including theLuttinger-Kohn/k.p method andab-initio methods.
On top of advanced physics software, there are also a myriad of tools of analytics available for beginning students of physics such as the PASCO Capstone software.
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