Computational physics

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This article is about computational science applied in physics. For theories comparing the universe to a computer, see digital physics. For the study of the fundamental physical limits of computers, see physics of computation.
Computational physics
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Fluid dynamics
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Computational physics is the study and implementation of numerical analysis to solve problems in physics.[1] Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics — an area of study which supplements both theory and experiment.[2]

Overview

A representation of the multidisciplinary nature of computational physics both as an overlap of physics, applied mathematics, and computer science and as a bridge among them[3]

In physics, different theories 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 a closed-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 respective error.[1]

Status in physics

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 and experimental 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.

Challenges in computational physics

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,

computational cost and computational complexity for many-body problems (and their classical 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 of
exponential 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 worst chaotic: this means it can be difficult to ensure any numerical errors do not grow to the point of rendering the 'solution' useless.[6]

Methods and algorithms

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 from computational chemistry - for example, the density 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 the

processing power need or in memory requests
).

Divisions

It is possible to find a corresponding computational branch for every major field in physics:

  • electromagnetic fields with physical objects and the environment. One subfield at the confluence between CFD and electromagnetic modelling is computational magnetohydrodynamics
    .
  • quantum many-body problem
    .
  • Computational
    material science
    .

Applications

Due to the broad class of problems computational physics deals, it is an essential component of modern research in different areas of physics, namely:

soft condensed matter
physics, hypervelocity impact physics etc.

Computational solid state physics, for example, uses

ab-initio
methods.

See also

References

  1. ^ a b Thijssen, Jos (2007). Computational Physics.
    ISBN 978-0521833462
    .
  2. ^ Landau, Rubin H.; Páez, Manuel J.; Bordeianu, Cristian C. (2015). Computational Physics: Problem Solving with Python.
    John Wiley & Sons
    .
  3. ^ Landau, Rubin H.; Paez, Jose; Bordeianu, Cristian C. (2011). A survey of computational physics: introductory computational science.
    ISBN 9780691131375
    .
  4. ^ a b A molecular dynamics primer Archived 2015-01-11 at the Wayback Machine, Furio Ercolessi, University of Udine, Italy. Article PDF Archived 2015-09-24 at the Wayback Machine.
  5. S2CID 124545445. Article PDF
  6. ^ Sauer, Tim; Grebogi, Celso; Yorke, James A (1997). "How Long Do Numerical Chaotic Solutions Remain Valid?". Physical Review Letters. 79 (1): 59–62.
    S2CID 102493915
    .

Further reading

External links

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