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In hydrogeology, the superposition principle is applied to the drawdown of two or more water wells pumping in an ideal aquifer. This principle is used in the analytic element method to develop analytical elements capable of being combined in a single model. In process control, the superposition principle is used in model predictive control.
This is a restatement of Charles Lyell's original principle of inclusions and components from his 1830 to 1833 multi-volume Principles of Geology, which states that, with sedimentary rocks, if inclusions (or clasts) are found in a formation, then the inclusions must be older than the formation that contains them.
The law of superposition is an axiom that forms one of the bases of the sciences of geology, archaeology, and other fields pertaining to geological stratigraphy.In its plainest form, it states that in undeformed stratigraphic sequences, the oldest strata will lie at the bottom of the sequence, while newer material stacks upon the surface to form new deposits over time.
To further illustrate, Schrödinger described how one could, in principle, create a superposition in a large-scale system by making it dependent on a quantum particle that was in a superposition. He proposed a scenario with a cat in a closed steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it ...
In linear problems, for example, a family of linearly independent solutions can be used to construct general solutions through the superposition principle. A good example of this is one-dimensional heat transport with Dirichlet boundary conditions, the solution of which can be written as a time-dependent linear combination of sinusoids of ...
The superposition principle means that a linear combination of inputs to the system produces a linear combination of the individual zero-state outputs (that is, outputs setting the initial conditions to zero) corresponding to the individual inputs. [5] [6]
The superposition principle applies to any linear system, including linear systems of PDEs. A common visualization of this concept is the interaction of two waves in phase being combined to result in a greater amplitude, for example sin x + sin x = 2 sin x. The same principle can be observed in PDEs where the solutions may be real or complex ...
Engraving from William Smith's monograph on identifying strata based on fossils. Catholic priest Nicholas Steno established the theoretical basis for stratigraphy when he introduced the law of superposition, the principle of original horizontality and the principle of lateral continuity in a 1669 work on the fossilization of organic remains in layers of sediment.