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Perturbation or perturb may refer to: Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly; Perturbation (geology), changes in the nature of alluvial deposits over time; Perturbation (astronomy), alterations to an object's orbit (e.g., caused by gravitational interactions with other ...
An approximate 'perturbation solution' is obtained by truncating the series, often keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields and reaches its most sophisticated and advanced forms in quantum field theory.
In practice, convergent perturbation expansions often converge slowly while divergent perturbation expansions sometimes give good results, c.f. the exact solution, at lower order. [ 1 ] In the theory of quantum electrodynamics (QED), in which the electron – photon interaction is treated perturbatively, the calculation of the electron's ...
Perturbation methods start with a simplified form of the original problem, which is carefully chosen to be exactly solvable. In celestial mechanics, this is usually a Keplerian ellipse , which is correct when there are only two gravitating bodies (say, the Earth and the Moon ), or a circular orbit, which is only correct in special cases of two ...
Ecosystems can shift from one state to another via a significant perturbation directly to state variables. State variables are quantities that change quickly (in ecologically-relevant time scales) in response to feedbacks from the system (i.e., they are dependent on system feedbacks), such as population densities. This perspective requires that ...
The method removes secular terms—terms growing without bound—arising in the straightforward application of perturbation theory to weakly nonlinear problems with finite oscillatory solutions. [1] [2] The method is named after Henri Poincaré, [3] and Anders Lindstedt. [4]
Note that the "perturbation" term ′ gets progressively smaller as k approaches zero. Therefore, k·p perturbation theory is most accurate for small values of k . However, if enough terms are included in the perturbative expansion , then the theory can in fact be reasonably accurate for any value of k in the entire Brillouin zone .
In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints. [1]