Definition
Calculation Physics (English: ComputationalPhysics) is a discipline that studies how to use numerical methods to analyze physical problems that can be quantified. Historically, calculating physics is the first application of a computer; calculating physics is considered to calculate the scientific branch.
Computational Physics is sometimes considered a branch discipline or sub-problem that is theoretical physics, but it is also believed that calculating physical and theoretical physics and experimental physics are close, and relatively independent, is the third largest branch of physics.
Background
In physics, the theory of various mathematical models is required, and the behavior of the systems described in these theories can be given an accurate description. Unfortunately, many problems cannot be accurately solved (ie, analytical), or the process of seeking precision is too complicated. (For example, multi-body problems in classic mechanics. In quantum mechanics, most of the problems approximately approximation.) At this time, the numerical approximation will be used to solve such problems. Computational physics is such a numerical approximate discipline, which uses a limited calculation step (often large amount of calculation) and simple mathematical method (algorithm), using computer operation, calculating, to obtain corresponding approximate solutions and corresponding Approximation error.
Calculate the status of physics in physics. Sometimes it is considered an important tool for theoretical physics, sometimes as a "computer experiment", and some people think it is to be seen in a third physics branch between theoretical physics and experimental physics. Considering that the computer is also applied to recording experimental data and performs corresponding analysis, it may not be adequately classified as computational science.
Problem and Challenge
Even if the calculation physical method is used, physical problems often difficult to solve. This is usually caused by the following (mathematics) reasons: lack of corresponding algorithms, unable to perform corresponding analysis, complexity and chaotic phenomena for numerical solutions. For example, Solution of Electronic Wave Function in Stark Effect (Quantum Mechanics, when atoms are in strong electric fields, electronic behavior will change accordingly), will need a very complex algorithm to solve (can only solve it Part of the situation); Some problems, must use the algorithm for violent calculation or high complexity complexity, such as solving and graphical methods for complex equations. Sometimes it is also necessary to use the intramidism in math (such as the perturbation theory in quantum mechanics) to approximately solve, such as the Stark effect mentioned above.
In addition, the solution of many problems in quantum is in the form of an index, and its numerical solution also generates an index explosion accordingly; in addition, the macro system tends to have a number of molecular numbers of 1 magnitude and improves simulation calculation. Difficulty.
Finally, many physical systems are normally non-linear, even chaotic. This also makes it difficult for us to determine if the "solution" obtained by the computer is caused by the approximation error of the value approximation itself.
Method and Algorithm
Since computational physics can be studied is very extensive, people usually classified according to their solution or mathematical methods used, generally can be classified as follows:
| Mathematical Problem | Algorithm or Method Example | Physical Problem | |||
|---|---|---|---|---|---|
| Calculation of the integration | numerical integral or Monte Carlo points | Solving position, field superimposed | Solution of the normal differential equation | Longge - Kutta method (initial value problem), target method (boundary value problem) | Classical mechanism in the classic mechanics, multi-body problem |
| Defial Equation Solution | Differential Method, Finite Element Analysis and Pseudo - spectrum | Wave Problem, Transportation Problem, Static Ball Problem, Convection / TD> | |||
| Matrix Solution | Matrix Analysis related methods, such as accurate diameter, density matrix reorganization group | Quantum Mechanical System Solving Evasive Values and Solution of this Sproduction | |||
| Multi-Series Random Events | Monte Carlo Method | Molecular Dynamics, Plasma Dynamics Equation |
These methods are used to study the physical properties of the modeling system.
Calculation physics is often affected by computational chemistry, such as solid physicists use density functional theory to study the physical properties of solids, and the chemist study molecular behavior is basically consistent.
In addition, calculating physics research also requires corresponding software and hardware to support, and sometimes requires related technical support for supercomputers and high performance operations. For example, a super computer is used to simulate plasma behavior in the study of thermal nuclear fusion.
Branch and Cross
Almost all physics main branches can find a place in computational physics, such as calculation, calculating electric mechanics, calculating plasma, etc. Computational mechanics is also calculated by calculating fluid mechanics (CFD), computational solid mechanics, and calculate contact mechanics. And calculating fluid mechanics and calculating electrodynamics also contributes to calculating magnetore physics. In the quantum mechanics N-body problem, when N approxishes infinity, it becomes a calculated chemical problem. As a calculated solid physics of the physical important branch, it is directly applied to material science.
A branch associated with calculating the condensed material characteristics is called calculation statistics, and some problems that are difficult to solve in other methods (such as transmissive filtration, magnetic spin, etc.).
Calculate the genus physics and the techniques and methods for the problem of betex physics.
Application
is mainly used to solve the problem of computing physics, and the application of modern physics research is an important part of modern physics research. Such as: Accelerator Physics, Earth Physics, Fluid Mechanics (Included: Calculation Flower Mechanics), Crystal Field Theory / Grid Point Specification Theory (Especially Live Dot Quantum Motorics), Plasma (See: Plasma Simulation), Simulation Physical system (applied in molecular dynamics), protein structure prediction, solid physics, soft substances and many other physics areas.
Computational chemistry in solid physics, such as a density functional, calculating the solids characteristics, is a strategy of studying physical properties of solid molecules by means of calculation chemical concept research, and participating in other large amounts of solids Physics calculation. Another example is the structure and magnetic properties of electronic energy, and the charge density can be calculated by these methods, including Lujing Galchen-model / k · p scrart theory and from head calculation.
Application software
Calculation Physical Common Software is mainly numerical computing software such as MATLAB, and Mathematica and Maple, which provides a large number of tools that are commonly described frequently, for use directly. application. Common advanced languages can also achieve the same computing function, sometimes capable of completing tasks at a higher speed, but this also requires corresponding programming skills and calculating physical knowledge.